Electrical principles : for the electrical trades [7 ed.] 9781743767238, 1743767234

Citation preview

UEENEEE104A Solve problems in d.c. circuits

CIII–Core, CII–Elective

UEENEEG101A Solve problems in electromagnetic devices and related circuits

CIII–Core

UEENEEK142A Apply environmentally and sustainable procedures in the energy sector

CIII–Core, CII–Elective

UEENEEG102A Solve problems in low voltage a.c. circuits

CIII–Core

UEENEEG006A Solve problems in single and three phase low voltage machines

CIII–Core

UEENEEG109A Develop and connect electrical control circuits

CIII–Core

UEENEEG108A Trouble-shoot and repair faults in low voltage electrical apparatus and circuits

CIII–Core

UEENEEE141A Use of routine equipment/plant/technologies in an energy sector environment

CII—Elective

Written in a clear and concise manner, the text employs full-colour diagrams and photographs to illustrate key concepts and topics. The new design supports practical and effective learning. FEATURES INCLUDE: New chapter on sustainable practices in the electrical trades Examples with worked solutions Improved chapter structure and layout to enhance readability and ease of use Full-colour illustrative material End-of-chapter summaries

Connect is proven to deliver better results. Content integrates seamlessly with enhanced digital tools to create a personalised learning experience that provides precisely what you need, when you need it. Maximise your learning with SmartBook, the first and only adaptive reading experience designed to change the way you read and learn. It creates a personalised reading experience by highlighting the most impactful concepts you need to learn at that moment in time. To learn more about McGraw-Hill SmartBook® visit www.mheducation.com.au/student-smartbook

7TH EDITION

Electrical Principles

for the Electrical Trades

Jenneson • Harper • Moore • Lowe Hemmingsen • Buckridge • Dickie • Frew

• • • • •

Electrical Principles for the Electrical Trades

The new edition of Electrical Principles for the Electrical Trades carries forward the rich legacy of previous editions. It has been substantially revised and restructured to meet the needs of students and trade professionals in Electrotechnology. Each chapter is now comprehensively aligned to the knowledge and skills specified in units of competency in national training packages for an electrical trade qualification. These units include:

7e Jim Jenneson ● Bob Harper ● Bob Moore ● Paul Lowe Mark Hemmingsen ● Terry Buckridge ● John Dickie ● Paul Frew

www.mhhe.com/au/jenneson7e

spine: 17.81mm

Electrical Principles for the Electrical Trades 7TH EDITION

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7TH EDITION

Electrical Principles for the Electrical Trades

Jim Jenneson ● Bob Harper ● Bob Moore ● Paul Lowe Mark Hemmingsen ● Terry Buckridge ● John Dickie ● Paul Frew jen21014_prelims_i-xviii.indd iii

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Copyright © 2019 McGraw-Hill Education (Australia) Pty Ltd Additional owners of copyright are acknowledged in on-page credits. Every effort has been made to trace and acknowledge copyrighted material. The authors and publishers tender their apologies should any infringement have occurred. Reproduction and communication for educational purposes The Australian Copyright Act 1968 (the Act) allows a maximum of one chapter or 10% of the pages of this work, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that the institution (or the body that administers it) has sent a Statutory Educational notice to Copyright Agency (CA) and been granted a licence. For details of statutory educational and other copyright licences contact: Copyright Agency, 66 Goulburn Street, Sydney NSW 2000. Telephone: (02) 9394 7600. Website: www.copyright.com.au Reproduction and communication for other purposes Apart from any fair dealing for the purposes of study, research, criticism or review, as permitted under the Act, no part of this publication may be reproduced, distributed or transmitted in any form or by any means, or stored in a database or retrieval system, without the written permission of McGraw-Hill Education (Australia) Pty Ltd, including, but not limited to, any network or other electronic storage. Enquiries should be made to the publisher via www.mheducation.com.au or marked for the attention of the permissions editor at the address below. National Library of Australia Cataloguing-in-Publication Data Authors: Jim Jenneson, Bob Harper, Bob Moore, Paul Lowe, Mark Hemmingsen, Terry Buckridge, John Dickie, Paul Frew Title: Electrical Principles for the Electrical Trades Edition: 7 ISBN: 9781743767238

Published in Australia by McGraw-Hill Education (Australia) Pty Ltd Level 33, 680 George Street, Sydney NSW 2000 Portfolio lead: Norma Angeloni Tomaras Product developers: Isabella Mead and Asad Shabir Production editor: Genevieve MacDermott Permissions editor: Sarah Thomas Copyeditor: Paul Hines Proofreader: Julie Wicks Cover design: Simon Rattray Typeset in 10.5/14pt STIX MathJax Main-Regular by SPi Global, India. Printed in Singapore on 70 gsm matt art by Markono Print Media

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Contents in brief Chapter 1 Chapter 2

Solve problems in d.c. circuits (UEENEEE104A and UEENEEE141A) Solve problems in electromagnetic circuits (UEENEEG101A and UEENEEE141A)

1

113

Chapter 3

Apply environmentally and sustainable procedures in the energy sector (UEENEEK142A) 183

Chapter 4

Solve problems in a.c. circuits (UEENEEG102A and UEENEEE141A)

203

Solve problems in single- and three-phase low-voltage machines: Part 1 Single- and three-phase transformers (UEENEEG006A and UEENEEE141A)

303

Chapter 5

Chapter 6

Solve problems in single- and three-phase low-voltage machines: Part 2 Alternating current rotating machines (UEENEEG006A) 331

Chapter 7

Develop and connect electrical control circuits (UEENEEG109A) 403

Chapter 8

Reference section

449

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Contents in full Chapter 1

Solve problems in d.c. circuits

1



1.1 The electrotechnology industry

2

1.2 Static and current electricity

3

1.3 Production of electricity by renewable and non-renewable energy sources

7

1.4 Transportation of electricity from the source to the load

8

1.5 Utilisation of electricity by the various loads

9

1.6 Calculations for quantity of electricity, and velocity and speed in its generation and transportation

12

1.7 The basic electrical circuit

14

1.8 Symbols used to represent an electrical energy source, a load, a switch and a circuit protection device in a circuit diagram

15

1.9 Effects of an open circuit, a closed circuit and a short circuit 17 1.10 Multiple and sub-multiple units

19

1.11 Basic d.c. single-path circuit

20

1.12 Measuring electricity—devices and units

22

1.13 Voltage, current and resistance in a circuit

23

1.14 Relationship between force, power, energy and work

25

1.15 Power dissipated in a circuit from voltage, current and resistance values

25

1.16 Power ratings of devices

29

1.17 Measurement of electrical power in a d.c. circuit

29

1.18 Physiological effects of electrical current and the fundamental principles for protection

30

1.19 Basic principles by which electric current can result in the production of heat, the production of magnetic fields or a chemical reaction

31

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Contents

1.20 Typical uses of the effects of current

32

1.21 Mechanisms by which metals corrode

33

1.22 Principles for protection against the damaging effects of current

34

1.23 Basic principles of producing an electromotive force (EMF) 35 1.24 Principles of producing an electrical current

40

1.25 Input, output, efficiency or losses of electrical systems and machines

42

1.26 Effect of losses in electrical wiring and machines

42

1.27 Principle of conservation of energy

43

1.28 Resistors

43

1.29 Variable resistors

45

1.30 Power ratings of a resistor

47

1.31 Power loss (heat) occurring in a conductor

48

1.32 Reading resistors

48

1.33 Selecting a resistor

51

1.34 Series (connected) circuits

51

1.35 Characteristics of a series circuit

52

1.36 Parallel connected circuits

55

1.37 Series/parallel circuits

58

1.38 Factors affecting resistance

59

1.39 Effects of resistance on the current-carrying capacity and voltage drop in cables

66

1.40 Selecting an appropriate meter

67

1.41 Measuring resistance using direct, volt-ammeter and bridge methods

69

1.42 Instruments used to measure voltage, current, resistance and insulation resistance

73

1.43 Contact testing equipment

75

1.44 Neon testers

78

1.45 Hazards involved in using electrical instruments

79

1.46 Operating characteristics of analogue and digital meters

81

1.47 Techniques for reading the scale of an analogue meter

82

1.48 Types of voltmeters used in the electrotechnology industry 83 1.49 Non-contact testing instruments

88

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Contents

1.50 Using and selecting an appropriate meter

89

1.51 Resistance measurement

90

1.52 Continuity and resistance testing

92

1.53 Capacitors and capacitance

93

1.54 How a capacitor is charged in a direct current circuit

98

1.55 Calculation of quantities from given information

100

1.56 Hazards and safety control measures involved in  working with capacitance effects

101

1.57 Effects of capacitors connected in parallel

102

1.58 Effects on the total capacitance of capacitors connected in series

103

1.59 Application of capacitors in the electrotechnology industry 105 Summary 105 Questions 106

Chapter 2

Solve problems in electromagnetic circuits

113

2.0 Introduction

114

2.1 Magnetism

114

2.2 Electromagnetism

118

2.3 Magnetic circuits

121

2.4 Electromagnetic induction

130

2.5 Inductance

136

2.6 Measurement instruments

147

2.7 Magnetic devices

153

2.8 Machine principles

156

2.9 Rotating machine construction, testing and maintenance

158

2.10 Generators

163

2.11 Motors

169

2.12 Machine efficiency

177

Summary 179 Questions 180

Chapter 3

Apply environmentally and sustainable procedures in the energy sector

183

3.0 Introduction

183

3.1 Sustainable work practices

184

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Contents

3.2 Effects of neglecting sustainable work practices

185

3.3 The greenhouse effect—causes and consequences

186

3.4 International and national greenhouse imperatives

187

3.5 The role of regulators and similar bodies

190

3.6 Legislative requirements

191

3.7 Economic benefits of sustainable initiatives

191

3.8 Techniques for reducing carbon-produced energy and greenhouse gases

192

3.9 Domestic, commercial and industrial strategies

195

3.10 Trade-related technologies and methods

196

3.11 Trade-related retrofits

197

3.12 Renewable energy technologies

198

Summary 201 Questions 201

Chapter 4

Solve problems in a.c. circuits



4.1 Alternating current

203 204

4.2 Use of the oscilloscope to measure d.c. and a.c. voltage levels

208

4.3 Sinusoidal voltage generated by a single-turn coil rotated in uniform magnetic fields

217

4.4 Sinusoidal waveform

219

4.5 Phasor diagrams

225

4.6 Single-element a.c. circuits

232

4.7 Capacitors

236

4.8 RC and RL series a.c. circuits

238

4.9 R–L–C series a.c. circuits

241

4.10 Parallel a.c. circuits

246

4.11 Power in an a.c. circuit

250

4.12 Power factor improvement

255

4.13 Harmonics and resonance effect in a.c. systems

263

4.14 Three-phase systems

268

4.15 Three-phase star connections

273

4.16 Three-phase, four-wire systems

274

4.17 Three-phase delta connections and interconnected systems

278 ix

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Contents

4.18 Energy and power requirements of a.c. systems

282

4.19 Fault loop impedance

292

Summary 297 Questions 299

Chapter 5

Solve problems in single- and three-phase low-voltage machines: Part 1 Single- and three-phase transformers

303

5.1 Transformer construction

303

5.2 Transformer operation

309

5.3 Transformer losses, efficiency and cooling

316

5.4 Transformer voltage regulation and per cent impedance

320

5.5 Parallel operation of transformers and transformer auxillary equipment

321

5.6 Special transformers

323

Summary 326 Questions 327

Chapter 6

Solve problems in single- and three-phase low-voltage machines: Part 2 Alternating current rotating machines

331

6.1 Operating principles of three-phase induction motors

331

6.2 Three-phase induction motor construction

337

6.3 Three-phase induction motor characteristics

342

Summary 6.1–3

348

6.4 Single-phase motors—split phase

349

6.5 Single-phase motors—capacitor and shaded pole types

356

6.6 Single-phase motors—universal motor

360

Summary 6.4–6

363

6.7 Motor protection Summary 6.7

364 377

6.8 Three-phase synchronous machines—operating principles and construction

379

6.9 Alternators and generators

389

Summary 6.8–9

397

Questions 399 x

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Contents

Chapter 7

Develop and connect electrical control circuits

403

7.1 Basic relay circuit

403

7.2 Relay circuits and drawing conventions

404

7.3 Control circuit variations

415

7.4 Control devices

418

7.5 Programmable relays

419

7.6 Three-phase induction motor starters

424

7.7 Three-phase motor reversal

436

7.8 Speed control of a.c. induction motors

440

Summary 445 Questions 447

Chapter 8

Reference section

449

8.0 Introduction

450

8.1 Mathematics, numbers and units

450

8.2 SI units

450

8.3 SI derived units

451

8.4 Transposition

456

8.5 Energy, work and power

459

8.6 Scalar and vector quantities

462

8.7 Trigonometry

468

Summary 475

Index 477

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Text at a glance SETTING A CLEAR AGENDA

Solve problems in electromagnetic circuits

Each chapter begins with a list of objectives that the reader can aim to achieve.

Electrical Principles

2

CHAPTER OBJECTIVES • understand natural magnetism • use fields to predict reactions between magnets

At any angle between 0° and 90°, the voltage will be between 0 V machines and 1 V. The actual value is calculated using • apply magnetic principles to simple magnetic effects to electric current E = Emax × sin(θ). The value increases from 0°•• torelate 90°, then reduces again to 0 V at 180°. The voltage then becomes predict magnetic fields around conductors • apply right-hand to determine negative from 180° to 270°, when it is –1 V, and returns togrip 0 rule V at 360°. polarity • calculate electromagnetic values • understand the characteristics of magnetic materials • compare magnetisation and hysteresis curves for various materials • describe the effects of Lenz’s Law • explain inductance as an electrical effect • explain time constant • describe inductor types • describe a magnetic circuit, magnetic leakage and magnetic fringing • describe the construction and operation moving-coil and by) moving-iron meters conductor cuts across (or isofcut across a magnetic • explain how to extend the range of meters and calculate the component sizes

2.4.4 Calculation of induced EMF in a coil, given the number of turns in a coil and the rate of change of flux An EMF can be induced in a conductor if the field. That is to say, when there is a relative movement between a conductor and a magnetic field, a current will be induced in the conductor if there is a complete circuit. Michael Faraday found that the voltage generated in a coil due to a changing magnetic field is directly proportional to the change in flux and inversely proportional to the change in time. He also noted that increasing the number of conductors, or turns of a coil, is equivalent to increasing the current.

Electrical Principles

8.0

Introduction

To understand electrical principles, it is necessary to understand mechanical principles. This inLaw turn requires an appreciation of a system Faraday’s of units—in the case of Australia and New Zealand (and many other The value induced in acalled circuit countries), the units of of thethe SI EMF system, formally thedepends ‘Systèmeon the number of conductors in the circuit and the rate of change the magnetic flux linking international of (d’unités)’ but better known the as conductors. the ‘metric’ system. Electricians oftenInneed to manipulate mechanical, as well as electrical, mathematical terms: 113 values to come up with a method of wiring or repairing an electric circuit. An understanding of graphs, methods of graphical solution and ΔΦ ____ trigonometry is required, as is knowledge of the relevant mathematical V = N Δt processes. This chapter gives a working understanding of the units of measurement, mathematical processes and simple mechanics that are where: used by electricians. jen21014_ch02_113-182.indd

8.1

113

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V = induced voltage N = number of turns ΔΦ = flux change in webers Δt = time change in seconds

Mathematics, numbers and units

WORKED EXAMPLES

In school,chapter maths starts by concentratingthe simplytheoretical on numbers and then evolves to by manipulating values such as length, Each supports aspects providing In engineering science, thethegenerated voltage weight and time. These concepts are progressively built upon, and eventuallyand algebra’s use in applied maths in is often denoted by the symbol ε for ‘EMF’, so the following practical applications thea good theory covered. The theory is will be useful in electrotechnology comes into focus. of Having grasp of school-level mathematical concepts formula represents the same law: getting the most from the content in this chapter. illustrated by fully worked examples. These examples give ΔΦ ε = N ____

Δt

students a template to use when completing similar exercises. 8.2 SI units EXAMPLE 2.8

The international metric system consists of seven base units, two supplementary units and many derived units. Australia legislated to use the metric system in the early 1970s, and the Australian Standard is defined in AS ISO 1000-1998.

A coil of 600 turns has a flux of 80 μWb passing through it. If the flux is reduced to 30 μWb in 15 ms, find the average induced voltage.

8.2.1 Base units

ΔΦ Base units are not formed from other units, although the SI system defines ____ ε = N them as having specific dimensions which are derived from physical constants. Much of the maths used by electricians Δt works with these base units and the derived units. −6 −6 80 × 10 − 30 × 10 = 600 × _____________ 15 × 10−3

Length—the metre

−6

50 × 10 The original ‘metre’ was intended to be the distance from the equator to = the600 Pole×divided by 10 000 000. However, ______ −3 the orange–red line the metre is now defined as being equal in length to 1 650 763.73 wavelengths in a15 vacuum × 10of spectrum for the isotope krypton-86. To make it easier for non-scientists to understand, there is a prototype ‘metre’ =2V in France which is a length of platinum bar which (at standard temperature and pressure) is exactly one metre long.

(1) (2) (3) (4)

xii

Mass—the kilogram

132

The kilogram was first defined as the amount contained in 1 litre of pure water at 0°C. It is now defined as the mass of a particular piece of platinum (another prototype) stored under special conditions in France. Although ‘weight’ is usually measured in kilograms, weight and mass are not the same. Weight is the force caused by the mass of the body. 450 jen21014_prelims_i-xviii.indd xii

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Solve problems in electromagnetic circuits

Summary ∙ A magnetic field acts outwards at the north pole and inwards at the south pole.

Chapter 2

SUMMARY Each chapter ends with a comprehensive summary listing the core concepts covered, making it an excellent tool for revision and reference.

∙ A magnetic field tends to expand to fill the available space, to produce a field of flux that will extend to infinity in a Electrical Principles vacuum. ∙ Like poles repel. ∙ An inductor is a component that generates a magnetic field when current passes through it, and that magnetic field in ∙ Unlike poles attract. turn causes a current to be generated in the inductor while the magnetic field is changing. ∙ Lines of force existing outside the desired magnetic path are called leakage flux. ∙ The inductance of an inductor is determined by: ∙ –Induction is a process whereby magnets induce a magnetic field in other magnetic materials. the material in the core

number of turns of wire inmaterial the coilindicates the ease with which magnetic induction can occur. ∙ –Thethe permeability of a magnetic – the cross-sectional area of the coil ∙ Paramagnetic materials have low permeability and are termed non-magnetic materials. – the length of the coil. ∙ Ferromagnetic materials have high permeability and are termed magnetic materials. ∙ The core of an inductor is usually air, solid iron, laminated iron or iron-powder. ∙ Materials that are used for permanent magnets are called hard materials. ∙ The unit of inductance is the henry (H). A henry is the inductance of a closed circuit in which an EMF of 1 volt is ∙ produced Materials when that can easily becurrent induced to exhibit properties but at lose magnetic field when the the electric flowing in themagnetic circuit varies uniformly thethe rateinduced of 1 ampere per second. magnet is removed are called soft materials, and are useful in electromagnetism. ∙ When a conductor cuts through a magnetic flux, a voltage is induced that is proportional to the number of turns, the ∙ strength Magnetism apparent in athe material thetime magnetising force has been removed is called residual magnetism. of the flux and inverseafter of the taken to cut across the flux (i.e. the induced voltage is proportional to NΔΦ velocity of the voltage is therefore found by as theMu-metal. formula: E = _____. ∙ the Magnetic fields canconductor). be shieldedInduced by highly permeable materials such Δt ∙ The voltage induced rule into for an inductor cancan be be calculated e = Blv Sinθ. or for a solenoid. right-hand-grip magnetism used forusing: a straight conductor

EXERCISES Each chapter contains Questions to test a student’s understanding of the chapter content.

∙ Lenz’s Law states by theconductors induced current will appear a direction it opposes thethe change produced it. and The force created in a magnetic fieldinissuch proportional to that the flux density, lengththat of the conductor the current in the conductor, and can be found from the formula: F = BIl. ∙ Magnetomotive force (MMF) creates a magnetic field: Fm = IN (ampere-turns).

Questions

∙ Magnetising force: H = IN/l (ampere-turns/metre). ∙ Flux density is the flux per unit of area: B = Φ/A (webers/m2). Exercises

Solve problems in electromagnetic circuits Chapter 2

∙ Permeability of free space: μ  = 4 × 10−7π (or 4π × 10−7). 2.1 How would you determine 0whether a piece of iron was magnetised? 2.19 What is an electromagnetic relay? Why is it used? ∙ Permeability (actual): μ = μ  × μ0 (for air, μ = 1) = B/H. 2.2 What is meant by the termr ‘magnetic field’? Describe a magnetic field. 2.20 What is a contactor? How is it different from a relay? ∙ Relative permeability is the permeability of a material relative to free space: μr = μ /μ0. 2.3 Show how a sensitive instrument may be protected against an external magnetic field. 1 2.21 Name the unit of inductance and define the unit. ∙ Reluctance of a magnetic circuit: Rm = _____. 2.4 Draw the general arrangement of an electromagnetic relay switch, labelling all parts. μoμrA What isis related meant by the terms ‘primary coil’ and ‘secondary coil’? ∙ The reluctance in a magnetic circuit is related to the MMF and the flux in much the same way as 2.22 resistance 2.5 What effect do electromagnetic forces have on magnetic materials and non-magnetic materials? IN to voltage and current. Therefore, reluctance can be found by the formula: Rm = ___. 2.23 What is a time constant? What symbol is used to represent it? Φ 2.6 Draw a single wire bent into a coil with 20 turns. One end is attached to a battery positive terminal and the other to a ∙ The magnetisation curve for a non-magnetic material is a straight line. 2.24flow What value of current and voltage after one time constant? battery negative terminal. (Do not try this, as the current would be very high.) Draw the current in is thethe wire ∙ The curve for magnetic is awire. curve with a pronounced ‘knee’ at saturation.2.25 What happens when a highly inductive circuit is quickly opened? What adverse effect could result from this? andmagnetisation show the expected magnetic fieldmaterials around the 2.26 List typesfrom of inductors and their common uses. ∙ Magnetic hysteresisShow is thea direction differenceofbetween the increasing and decreasing magnetisation curves resulting 2.7 Draw a solenoid. current flow, and the magnetic polarity of the solenoid (N and S). magnetism coercive force required it. back again. Will the current cause 2.27 the Explain of the commutator in a d.c. machine. 2.8 residual In street lighting, and two the wires carry the current up to theremove street and wiresthe to function be

∙ The area within a hysteresis is proportional to the losses attracted or repelled? (Usecurve a diagram to help visualise this.) in a magnetic material. 2.28 List the physical differences in construction between series- and shunt-field windings. 2.9 How can the force of a solenoid bestraight calculated? What values beand known? ∙ Permeability can be found using the portion of the B/Hmust curve the formula: μ = B/H 2.29 Why is a shunt generator the only type of connection that can be run on a short-circuit? 2.10 What is leakage the important difference the permeability of a ferromagnetic material and that of air? ∙ Magnetic is a magnetic fluxbetween that passes outside the intended magnetic circuit. 2.11 Sketch afringing typical B/H curve for flux a magnetic core made silicon steel.intended Label thewhen axespassing with thethrough correctan units. Mark ∙ Magnetic is a magnetic that expands over afrom wider area than air gap in Calculations a magnetic circuit. the estimated saturation region on the curve. What is the significance of this saturation region? 2.30 Two conductors placed 10 mm apart carry a current of 35 A to and from a d.c. motor 50 m away. What force acts ∙ Electromagnetic relays have a fixed magnetic called a stator, a moving magnetic part called an armature, a coil 2.12 What is the value of the permeability of free part space? between the conductors per metre length? Are they attracting or repelling? a set of contacts that on.the terms ‘magnetic leakage’ and ‘magnetic fringing’. 2.13and Briefly explain what is switch meant by 2.31 What magnetomotive force (MMF) is generated by an electromagnet with 150 turns when a current of 12 A flows in the coil?179 2.14 State Lenz’s Law in your own words and explain what it describes. 2.15 What is electromagnetic force? Describe it in your own words.

2.32 Determine the MMF necessary to create a flux of 0.2 Wb in a magnetic core which has a reluctance of 2000 At/Wb.

2.16 When and where does magnetic leakage occur?

2.33 A magnetic circuit has a reluctance of 750 At/Wb. The coil, having 800 turns, carries 0.5 A. Find the total flux 08/21/18 02:38 PM produced.

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179

2.17 Where does magnetic fringing occur? 2.18 State typical applications of electromagnets.

2.34 The mean length of a magnetic path is 600 mm. The cross-sectional area is 800 mm2. The relative permeability is 600. Determine the reluctance of the magnetic path. 2.35 The magnetising force in an iron ring is 1500 At/m. It creates a flux density of 0.95 T. Find the relative permeability for these conditions.

180

2.36 A long solenoid of 0.8 m has a current of 2 A flowing through a coil of 2000 turns. What is the magnetising force?

CALCULATIONS

08/21/18 02:38 2.37 Calculate thePMvoltage that would appear across the terminals of a 10 H inductor if the current of 5 A is reduced to zero in 0.2 seconds.

Calculations are mathematical exercises designed to give the student experience at solving typical problems found in the electrical trades.

2.38 What is the inductance of an inductor that has a d.c. resistance of 35 Ω and takes 0.8 s to charge to 63.2% of full current?

jen21014_ch02_113-182.indd

180

2.39 A 0.8 H inductor has an internal resistance of 10 Ω. What is the maximum current it will take when supplied from a 12 V battery? 2.40 What is the current rating of a 25 kW 400 V d.c. generator at full load? What current will flow at half load?

xiii

2.41 The terminal voltage of a 15 kW shunt-connected generator is 600 V on full load. If the field resistance is 200 Ω and the armature resistance is 0.1 Ω, what is the actual value of generated voltage?

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2.42 A 25 kW shunt-connected generator operates with a terminal voltage of 250 V. The armature has an effective resistance of 0.18 Ω and the shunt field has a resistance of 110 Ω. Calculate: (a) the full load current (b) the field current 08/22/18 07:08 AM (c) the total armature current (d) the induced armature voltage

Preface Welcome to the 7th edition of Electrical Principles for the Electrical Trades. This well-established and much respected text has undergone a range of changes to make it more user-friendly and relevant to the modern electrical student and tradesperson. The chapters have been more closely aligned to the current National Training Package and allow easy-to-follow content that better supports the units of competence. We have taken into account the many suggestions and comments from teachers and students, producing a comprehensive publication to complement McGraw-Hill Education’s Electrical Wiring Practice publication. The content has been presented in an easier-to-read format and all revisions have been undertaken by teachers who are currently involved in the training and assessment of Electrical Trade students in Australia. It has been a pleasure to work with Mark Hemmingsen, Terry Buckridge, Paul Frew and John Dickie, who have provided practical hands-on backgrounds combined with a sound technical knowledge of the subject matter. Their insights and experiences in the classroom, along with their combined talents, have shaped both the sequence and content of this new edition. The content of this publication is designed to augment and assist in the classroom-based and blended delivery of electrical trade qualifications in Australia. The content is not exhaustive but represents comprehensive details of the fundamental principles and theories that will assist and inform an electrical trade student. I would also like to thank the staff members of McGraw-Hill Education, Australia, particularly Norma Tomaras (Portfolio Lead), Isabella Mead (Content Developer), Genevieve MacDermott (Production Editor) and Asad Shabir (Content Developer), who have contributed to this project. I also acknowledge the ongoing support of McGraw-Hill Education in the production of leading resources in electrical training. Paul Lowe

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About the authors Jim Jenneson, Bob Harper and Bob Moore  Jim Jenneson, Bob Harper and Bob Moore provided the original content upon which this text is based. This seventh edition would not exist without the work of these authors, whose distinguished careers spanned many years. Paul Lowe  Paul Lowe has worked in the electrotechnology field for over 35 years. During the past 13 years Paul has worked for TAFE NSW as a teacher, head teacher and more recently, Industry Liaison Manager responsible for Electrotechnology across NSW. Paul has been an active participant in the development of training package qualifications and units for the last five years as a member of technical advisory committees and has represented NSW on the National Technical Advisory Group. He currently sits on the Commonwealth Industry Skills Committee as a technical expert representing the electrotechnology training package. Mark Hemmingsen  Mark Hemmingsen is an electrician with nearly 30 years’ experience in the electrical industry across most areas of the sector, including domestic, commercial and industrial industries. He finished a 12-year full-time teaching position at the Canberra Institute of Technology to follow his passion and build up his electric vehicle company, Electric Vehicles Canberra. Although he considers himself a born and bred Canberran, Mark now lives with his two kids in Murrumbateman, just across the ACT/NSW border, on what he calls a ’small farm’. Terry Buckridge  Terry Buckridge has been teaching for over 10 years and has spent most of that time as head teacher of Electrotechnology at Mt Druitt TAFE. For five of those years his responsibilities also included Engineering Services at OTEN. Prior to his teaching career, Terry spent over 20 years working on the design and implementation of large electrical and telecommunications projects across Australia. John Dickie  John Dickie joined the TAFE sector in 2009 as a lecturer. John’s experience as an industrial electrician held him in good stead to teach all aspects of the Electrotechnology qualifications. He applied himself to all subject matter within the UEE qualification and with this additional experience is well respected in the Western Australian TAFE sector. John will continue to help students achieve their goals in Western Australian from an organisational and teaching perspective. Paul Frew  Paul Frew is an Electrical Trades teacher at TAFE Digital NSW, providing teaching, training and assessment to students via distance education. Paul has been with TAFE NSW for over 16 years, previously teaching at Mount Druitt, Meadowbank and Miller TAFEs and at OTEN since 2011. Paul’s goal as a teacher in the electrical trade industry is to assist students in gaining an understanding of what they are learning. He found learning the electrical trade difficult, hence his empathy and passion to assist students by trying to simplify difficult concepts so the information learned can be practiced in the field. Outside of teaching, Paul likes to create music and produce videos. He is now experimenting with this interest by creating training videos for TAFE Digital students to assist in their preparation for attending ­ face-to-face practicals. xv

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1

CHAPTER OBJECTIVES • • • • • • • • • • • • • • • • • • • • • • • •

explain the structure of matter as relevant to electrical phenomena explain the effects and cause of static electricity explain dynamic electricity as a source of power define potential difference and voltage define electric current and electron flow use instruments to measure potential difference and current state and apply Ohm’s Law calculate electric power and energy differentiate between passive electric components calculate heat generated by electric means state the six common effects of electricity explain the need for and means of circuit protection define the dangers of electricity and the means of personal protection understand fundamental principles (as listed in AS/NZS 3000) define the terms ‘electrolyte’, ‘electrode’, ‘anode’ and ‘cathode’ explain conduction in an electrolyte explain electrode potentials with reference to simple battery chemistry calculate battery terminal voltage from electrode potentials compare primary and secondary cells explain voltaic cells explain how electrolysis works discuss electrochemical processes used in manufacturing discuss the electrochemical effects that cause corrosion discuss methods of combating corrosion using electrical processes

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Electrical Principles

1.1   The electrotechnology industry 1.1.1 Introduction Electrical energy is intrinsic to our everyday experience, but as recently as the first part of the twentieth century there were still many houses without it. Those that did have it used it mainly for lighting. In some places, the electricity only came on at around 5.00 pm and went off before midnight so that the generator operator could go to bed. Today, things are very different. The electrotechnology industry employs hundreds of thousands of people across Australia in a wide range of industrial sectors1. These sectors can be divided into two main groups, the electrical industry and the electronics industry.

The electrical industry The electrical industry consists of four subsectors:

1. 2. 3. 4.

generation, supply and distribution industrial and mining commercial construction and maintenance domestic construction and maintenance.

The generation, supply and distribution subsector is responsible for electrical power generation, transmission and distribution from electrical power stations to end users. It employs a range of people, including electrical engineers and operators, electrical lines workers and electricians. These professionals design, construct and maintain the electrical network (or grid) that supplies electricity across the country. The companies that owned and managed the electrical assets and infrastructure used to be public, but the past few decades have seen them move into private ownership. In their original form they were typically limited to generation, transmission or distribution. In this century, the industry has become increasingly complex, with large companies acquiring many of its assets. The advent of renewable technology has brought many new entrants, ranging from companies that provide large-scale wind or solar generation to individuals who supply the grid with solar power fed in from their roof. The industrial and mining subsector employs many electricians to install and maintain machinery and electrical wiring and equipment to industrial installations, factories and mining sites. Larger companies employ full-time electricians while smaller ones use specialist electrical contractors. The industrial and mining subsector also includes instrumentation, which is the installation, maintenance and calibration of instruments used in processing and manufacturing to measure data such as voltage, current, flow rates, temperature and location. These in turn can be part of a process that involves control wiring and equipment to regulate motors, valves and other devices used in electrical equipment such as conveyor belts, smelters, lifts and escalators. Also working in this subsector are refrigeration mechanics, who are responsible for the installation and servicing of air-conditioning and refrigeration equipment for both large systems and smaller individual appliances. Smaller categories of industrial and mining are motor servicing and repair, and small appliance servicing. The commercial and domestic construction and maintenance subsectors both employ licensed electricians to install and maintain wiring, protection equipment and appliances for lighting, power points, heating and cooking. The commercial subsector consists of offices, large retail outlets, shops, restaurants, hotels and the like, whereas the domestic subsector consists of residential dwellings. The work of both subsectors can range from the construction of new buildings to refurbishment of existing premises, as well as servicing and maintenance.

1

http://www.australianindustrystandards.org.au/wp-content/uploads/2016/08/Electrotechnology-IRC-Skills-Forecast-V1.pdf

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Any low voltage (greater than 50 V a.c. and 120 V d.c.) work must be completed by a licensed electrician or suitably qualified person as these voltages are lethal.

The electronics industry The electronics industry is similar to the electrical industry in that both require people with a high level of electricity-related knowledge and skills. The electronics industry tends to focus on electronic components whereas the electrical industry focuses on wiring and larger electrical equipment and apparatus. But it is not unusual for either industry to cross over and perform tasks associated with the other. For example, those employed in the data and telecommunications industry are required to install associated wiring and cables to connect equipment as well as installing, testing, commissioning and maintaining the equipment itself. Electrical license holders often now obtain specialised electronic qualifications (and vice versa with electronic license holders). The electronics industry has many subsectors. These can be broadly categorised as:

1. 2. 3. 4. 5. 6. 7.

data and telecommunications radio communications computer systems security systems industrial electronics commercial electronics consumer electronics.

Data and telecommunications involves the installation of cable and optical fibre across the country, and more recently has seen many changes with the introduction of the NBN (National Broadband Network). It also includes the installation of associated equipment and apparatus such as telephone and data systems, networking equipment and satellite and microwave equipment (including towers). People in this industry require a Telecommunications Cabling Registration if their work involves connecting to the telecommunications network. Radio communications involves the installation, maintenance and servicing of equipment associated with radio systems for radio and televison stations, aviation and marine radio, emergency services and other public radio networks such as taxi systems and UHF/VHF CB repeaters. Computer systems involves the installation, servicing and maintenance of IT equipment, including computers, data hubs and uninterruptable power supplies (UPS). Security systems involves the installation, servicing and maintenance of commercial and domestic security and monitoring equipment such as CCTV, infrared and motion detectors and X-ray scanners. Industrial electronics involves the installation, servicing, maintenance and repair of electronic equipment associated with industrial processes such as electronic motor controls and industrial computer process integration for factories. Commercial electronics involves servicing, maintenance and repair of photocopiers, cash registers and similar equipment used in offices and retail outlets. Consumer electronics involves the servicing, maintenance and repair of consumer electronic equipment such as televisions and microwaves.

1.2   Static and current electricity 1.2.1  Electrical energy Electrical energy was not invented; it is a natural phenomenon that humans have learned to use. Throughout history, scientists have studied it and developed methods of harnessing its power. 3

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1.2.2  Natural electricity Electricity occurs when a form of energy that is common in nature moves from one place to another. Everything around us is either solid, liquid or gas; and there is a fourth state known as ‘plasma’ that is not widely understood. Lightning, a natural form of electricity, is plasma (or superheated gas) that has so much energy that it gives off light.

1.2.3  Static electricity Static electricity is electrical energy that has gathered in one location. Most people have experienced the effects of static electricity in one form or another, common examples being lightning or the ‘zapping’ phenomenon experienced when shuffling along carpet or removing nylon clothing.

Production of an electrical charge

Dry flannel

Ebonite rod

Figure 1.1  Electrostatic charge by friction

Repulsion

Ebonite

Ebonite

Both rods rubbed with flannel

(a) Attraction Ebonite Glass

Glass rod rubbed with silk

(b)

Figure 1.2  Attraction and repulsion between electrical charges

The ancient Greeks observed that the material we call amber, when rubbed with cloth, attracted light particles such as feathers. (The Greek word for amber, elektros, which is petrified tree sap, was used to name this phenomenon, and it is from this word that the term ‘electricity’ is derived.) The same effect can be created when glass is rubbed with silk, or when vulcanite (ebonite) is rubbed with flannel or fur. The cause of this effect is known as ‘static electricity’ (Figure 1.1) and the material it affects is said to be ‘charged’ with electricity. The following experiments show the effects of the charges of electricity on rods of glass and ebonite. 1. If an ebonite rod that has been rubbed with fur or flannel is suspended by a dry silk thread and a second, similarly rubbed, ebonite rod is brought near the first, the suspended rod will move away from the second rod; it is said to be ‘repelled’ (Figure 1.2 (a)). A glass rod rubbed with silk will attract the suspended ebonite rod (Figure 1.2 (b)). 2. If an electrically charged glass rod is suspended from a silk thread, a second glass rod that has been rubbed with silk will repel it when brought near, while an ebonite rod that has been rubbed with fur will attract it. 3. If the suspended ‘electrostatically charged’ rod is replaced with an uncharged rod, this will be attracted to either the electrified glass rod or the electrified ebonite rod when either is brought near it. The charge exhibited by glass or vitreous materials when rubbed with silk is called ‘positive’ (meaning the glass is positively charged), and the state of electrostatic charge of ebonite or resinous materials when rubbed with fur is ‘negative’ (meaning the ebonite is negatively charged). Electrical charges of the kind indicated by the movements of

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Solve problems in d.c. circuits  Chapter 1

the rods are termed ‘static’ electrical charges, because electrons are not moving but are stored on the surface of the materials. The friction of fur on an ebonite rod causes a transfer of electrons from the fur to the surface atoms of the rod; the rod is now negatively charged because it carries a larger number of electrons than it usually does. In the process, the fur becomes positively charged because it has lost electrons. The electrons involved in the transfer come from the outermost electron orbits of the atoms, and this leaves the atoms temporarily ionised. In an attempt to return to the electrically neutral, stable state, the ions exert an attracting force on the electrons in orbit around adjacent atoms. The charges on the rod remain there (as ‘static’ charges) because the rods used are very poor conductors of electrical charges.

CONCLUSIONS 1. Like charges repel. 2. Unlike charges attract. 3. A neutral mass (no charge) is attracted by both positively and negatively charged rods.

Electrical potential When two different materials are rubbed together, the electrons from the surface of one material are transferred to the surface of the other. Experiments have shown that the intensity of the electric charge is different for different combinations of materials. Displaced electrons and their ‘parent’ atom, now an ion, have an electrostatic charge that produces an electrostatic field. The strength of this electrostatic field increases as the number of displaced electrons increases. A material with an electrostatic charge is said to possess an ‘electrical potential’, and the difference in electrical potential between two bodies is referred to as the ‘potential difference’ (pd), which is measured in volts. A potential difference is the electrostatic pressure required to remove electrons from one insulated surface and store them on another insulated surface. The return of the electrons from the negatively charged body to the positively charged body results in the potential difference reducing to zero. Equilibrium is restored and the two materials are once again neutral.

Partial charge In a perfect (if theoretical) world, a charged body would always discharge to an exactly neutral state where the number of protons is exactly equal to the number of electrons. What happens in the real world is that bodies of materials that come close to one another share what they have until they have an equal charge, at which point it is said that they reach ‘local equilibrium’. In dry summer weather, a person may experience an electric spark by touching a car door. The car has picked up an electrostatic charge from driving against the hot, dry wind. Touch the car a second time and often a second spark will result. This is because the first spark made the charge on the driver equal to the charge on the car, but the driver, standing on the ground, has already lost much of that charge to the ground. So the second spark comes from a mass that is still charged (the vehicle) to the mass that is now less charged (the driver). Figure  1.3 illustrates three bodies with a small number of atoms each. In the first row they are charged +6, neutral and −5. This means that the first body has six electrons too few, the second is neutral and the third has five electrons too many.

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Electrical Principles

Charged +ve (+6)

Uncharged

Charged +ve (+3) Charged +ve (+3)

Charged +ve (+3)

Charged –ve (–5)

Charged –ve (–5)

Charged –ve (–1) Charged –ve (–1)

Charged +ve (+1) Charged +ve (+1)

In the second row, the centre body touches the body to the left and, to equalise the charge between the two bodies, gives up three electrons so that each of the two bodies is now positively charged to +3. In the third row, the centre body touches the body to the right and, to equalise, takes four electrons so the two bodies are each negatively charged to −1. In the fourth row, the centre body again touches the body on the left and equalises, with both bodies having one positive charge. In the last row, the centre body touches the right body and both become neutral. This is because each already has the correct number of electrons for the number of atoms present. What will be the final state of each body? Assume that nothing will happen if there is a difference of just one electron, so the three changed bodies will remain charged to their present states. What would have happened if the centre body in the second row had swung to the right instead of the left?

Charged –ve (–1)

Uncharged Uncharged Charged +ve (+1) Can you predict what happens next?

Figure 1.3  Transfer of electrons between bodies

SUMMARY

1. Matter is composed of molecules made up of atoms of different elements. 2. There are well over 100 known elements, each with its own characteristics. 3. The smallest part of an element is an atom. 4. Atoms consist of three main particles: protons (positive), neutrons (neutral) and electrons (negative). 5. All atoms can be ionised. 6. If an electron is removed from an atom, the atom becomes a positive ion. 7. If an atom gains an electron, the atom becomes a negative ion. 8. A material that has a large number of excess electrons is considered to have a negative electrostatic charge. 9. A material that has a large number of missing electrons is considered to have a positive electrostatic charge. 10. The difference in the charge levels of two materials is called the potential difference. 11. Materials with no potential difference are considered to have reached equilibrium.

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1.2.4  Current (dynamic) electricity Electrostatic discharge illustrates that electricity is the flow of electrons from a place with an excess of electrons to a place with fewer electrons. That is, from a more negatively charged point to a more positively charged point. However, large electrostatic charges can exist without necessarily causing electricity to flow. An electron flow can only occur if a conducting path exists between the bodies and if there is a sufficient difference in potential between those bodies to cause an electron flow. The force that causes the electrons to flow is ‘electromotive force’, or EMF. The strength of the EMF is measured by the potential difference in volts between two points. Between electrostatic charges, electrons can flow directly from one body to another when the bodies touch. If points of different potential are joined by an electrical conductor, the electrons will be forced away from the point where there is a surplus of electrons towards the point where there is a deficiency. Electrons will flow from a point of high electron potential to one of lower electron potential whenever a conducting path exists between those points. Therefore, electrostatic discharge is not much use as a power source because the electron flow ceases when it runs out of charge. To make electricity more useful as a power supply, this and three other matters must be addressed. 1. Potential difference (source). Once the potential difference between two points has been reduced to zero, the flow of electrons stops. This irregular flow of electrons is unsatisfactory for power-supply purposes. To ensure a continuous flow of electricity, a continuous source of electromotive force is required. 2. Electrical materials (path). Electrical energy needs to be guided from where it is generated to where it can be used effectively. One type of material (a conductor) conducts the electrical energy to where it can be used, while another type of material (an insulator) prevents any unwanted flow from an electric circuit to other materials. 3. Use (load). Electricity is energy, and that energy can serve many purposes. But a way must be found of changing the electrical energy into another form so it can do the work required of it. Devices that convert electrical energy are called either ‘appliances’ or the ‘load’ (the latter being the more common term).

1.3  Production of electricity by renewable and non-renewable energy sources Electricity has historically been mainly produced from non-renewable sources. A non-renewable energy source is one that will eventually be depleted on Earth. Coal, petrol and gas are examples. As climate change and environmental concerns put pressure on these technologies, renewable sources of electrical energy have increasingly been used. Renewable types of electricity include solar, wind, hydroelectric, bio-fuel and geothermal. These can all be replenished or come from a source that won’t run out. Developing technology and associated efficiencies has led to their increased viability. Another type of electricity that is non-renewable but is debatably ‘clean’ (meaning that it has little or no carbon dioxide, or CO2, emissions) is nuclear. But the (few) devastating accidents that have occurred with reactors have led to a decline in its popularity. Nuclear fission reactors are being decommissioned across the globe. Technological breakthroughs have led to the possibility of nuclear power being utilised again, but the wealth of other clean renewable resources mean that it is highly unlikely to be a favourable option in Australia.

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1.4   Transportation of electricity from the source to the load 1.4.1  Early power-distribution systems The first power-distribution systems supplied consumers with direct-current (d.c.) power. The simplest system consisted of two conductors, with the current flowing outwards from the generator in one conductor and returning via the other. As with any long conductors, the voltage gradually became lower and lower the further the conductors were located from the supply. To try to minimise the size and length of conductors in street lighting, the circuits in some towns initially had the lamps connected in series. The overall voltage of a circuit had to be quite high so that each lamp would receive enough power to light it. Only one conductor was required but it would have to go up one street and return via another, going around the block. If any one lamp failed, the whole block went out. If lamps had to be added, the voltage had to be increased to compensate for the added lamp voltage drops. As distribution systems grew in size and the number of customers increased, cable sizes became larger. In some systems, the ground was used as the return path. This practice had sometimes serious consequences such the early deterioration of metal pipes buried in the ground. Another consequence was unwanted voltages, for example between iron fences and metal pipes entering the ground. The two-wire d.c. series system needed to be replaced with something better.

1.4.2  Modern power-distribution systems Almost without exception, electrical energy is today distributed to consumers with a three-phase, four-wire system (see Chapter 4) that uses distribution transformers to change the voltages.

Transmission lines

Power station (steam)

Step-up transformers

Transmission lines

Hydroelectric station

Feeder line Transmission to distribution step-down transformers

Distribution line

Distribution substation

Distribution transformer Meter

Figure 1.4  Stylised distribution system

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Power stations generate at voltages ranging from 6.6 kV (kilovolts) to 33 kV, which are then transformed in a switching yard into higher voltages suitable for the transmission stage. Long-distance transmission of power usually means that the voltage is converted to very high levels. In Australia, voltages of 66 kV, 132 kV, 178 kV, 330 kV and 500 kV are used. In Europe and some parts of the USA, voltages are even higher. The reason for using high voltages is to reduce power-transmission losses, which are greatest at low voltage levels. At the consumer end of the transmission line, the conductors lead into a substation where the voltages are reduced to lower levels for distribution. A result of this is that few power stations are needed, but there is an increased need for substations to convert voltages to suitable levels. These are often cross-linked to other substations so that alternative routes for supplying them are available. Figure 1.4 shows a stylised layout for a transmission system. In this example the power station generates 26 kV and the voltage is increased to 178 kV, which is then transmitted to the distribution substations. The voltage is then reduced to 11 kV for the feeder lines for transmission to the suburban substations, where it is again transformed to 400/230 V for supply to households and small businesses.

1.5   Utilisation of electricity by the various loads 1.5.1  Electrical components Components used in electrical circuits are categorised into two main groups, ‘passive components’ and ‘active components’. Passive components are comprised of resistors, inductors and capacitors that don’t require any source of external signal or power other than the circuit that they are contained in. Active components are comprised of semiconductor devices such as diodes, transistors and integrated circuits, as well as thermionic valves that supply power and/or signals from other external sources to control voltage and/or current in the main circuit. Resistors, inductors and capacitors are designed and manufactured in a variety of styles and types, depending on their intended uses. The following is a brief introduction to their construction and use (each is dealt with more fully in other chapters).

1.5.2 Resistors Resistors are components that resist the flow of electric current. In doing so, they cause a drop in voltage and radiate heat. If enough heat is generated, a resistor glows with incandescent light. Resistors usually consist of a length of conductor which is sometimes wound into a coil or laid into a grid so that the heat can escape. In electronics, resistors can be as small as 1⁄8 watt and just 2 mm by 1.5 mm. Even smaller resistors exist in microelectronics, but they can be as large as necessary for their particular function. Resistors are used to:

∙ ∙ ∙ ∙

restrict current flow develop a voltage drop generate heat generate light.

Resistors are in fact the most common method of generating heat from electricity, and almost every electrical source of heat is a resistor. Electric toasters, ovens, cooktops, space heaters, hot-water systems and even bathroom heat lamps are based on resistors. Electric lighting is currently undergoing a revolution, with incandescent lamps being replaced by arc lamps and light-emitting diodes (LEDs). Lighting based on Thomas Edison’s incandescent lamp has the disadvantage that most of the energy is lost as heat and not light, which is too inefficient for today’s energy-conscious requirements. 9

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Electrical Principles

In electronics and some electrical applications, resistors are used to control current flow. For example, an operator can change settings, such as volume and tone in an amplifier, by adjusting resistance. In this instance a variable resistance device such as a rheostat or potentiometer is mounted on a front panel. Turning the device changes the resistance.

1.5.3 Inductors Figure 1.5  Surface Mounted Device SMD resistor compared to a match

Figure 1.6  The heating elements in an electric toaster

Figure 1.7  Conventional versus Compact Fluorescent Lamp CFL-type lamp

Figure 1.8  Various inductors

An inductor is a component with the property of ‘inductance’, meaning that it produces an induced voltage when the current varies. The mechanism of induction is magnetism, where the changing current creates a magnetic field, the flux of which cuts through a conductor and induces a voltage. The induced voltage opposes the original current flow so inductors are used for power supply filtering to reduce current ripples. In that context the inductor is called a ‘choke’. Technically, inductance is the ratio of the voltage to the rate of change of current. Conductors—whether short, long or coiled—all have the property of inductance. Coiled conductors serve to concentrate the magnetic flux, even more so when they are wound around a core. This concentrated effect is the basis for electromagnets. The most common electromagnetic effect is that seen in solenoids. An inductive coil by itself is called a ‘solenoid’, though generally the term ‘solenoid’ is only applied where a coil’s length is much longer than its diameter and is wound on a movable core. Energising the solenoid pulls the core into the centre of the magnetic field and this mechanical action can be used as the basis for operating a set of contacts. The contacts can then operate another circuit and thus control a larger current. A solenoid switch such as this can also operate a series of circuits, each with its own solenoid switch. This kind of circuit was at one time used for telegraphic communications to relay messages, so solenoid switches became known as ‘relays’ or ‘relay switches’ (see Figure 1.9). When current changes constantly it is referred to as alternating current (a.c.). When current alternates, the magnetic field it creates also alternates and this generates a voltage in any nearby coils. This is known as ‘the transformer effect’ or ‘mutual coupling’. A transformer can transform voltages from one magnitude to another, either high to low or low to high. It does this by converting electrical energy to

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Figure 1.9  Relay switches

Figure 1.10  Small transformer

magnetic energy, then converting the magnetic energy back into electrical energy in a coil with a different number of turns, generating a voltage appropriate to the particular requirement. For example, a battery charger can convert 230 V from the mains supply into approximately 12 V for a battery (a battery charger is more complex than this simple explanation suggests.) Passing a conductor through a magnetic field, or a magnetic field past a conductor, also generates a voltage in the conductor. This effect is used in generators and alternators. There are many types of inductor and they have many uses. See Chapter 2 for a thorough explanation of their application and the theory behind them.

1.5.4 Capacitors Capacitors are devices for storing an electrical charge. While inductors store a current as a magnetic field, capacitors store voltage as an electrostatic field. Capacitors come in a large range of sizes and shapes, depending on the particular manufacturer and their intended use. A capacitor is constructed of two conductive surfaces separated by an insulator so that an electrostatic field can be Figure 1.11 Capacitors stored between those surfaces. Capacitors can store electric energy when the voltage is high and return it when the voltage is low. They are commonly used in power supplies to remove high-voltage surges and then smooth out the voltage. Capacitors are also used in electric single-phase motors (see Chapter 6) to help them start and develop full torque. Inductors are very common in electric circuits while capacitors are more common in electronic circuits. 11

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1.6  Calculations for quantity of electricity, and velocity and speed in its generation and transportation 1.6.1  Terms and units Electric charge A unit of charge is known as a ‘coulomb’, which is the quantity of electricity conveyed in one second by a current of one ampere, with one ampere being 6.24 × 1018 electrons.

Electromotive force (EMF) Electromotive force is the force that moves electrons. It is the electrical pressure that causes a current to flow. Electric-circuit sources are measured by their EMF in units known as ‘volts’, after the physicist Alessandro Volta. Electromotive (ε) force is usually abbreviated to EMF, or simply E. As this E is easily confused with energy (also E), EMF will be used in this book for electromotive force, except where there is no doubt that that is what E represents.

Voltage and potential difference When electrons are stored, their quantity is measured in coulombs. The energy required to store them is measured in E joules (J). The ratio of work energy to the quantity stored is measured in volts and calculated from V = ​​ __  ​​(this is not a Q required formula). So, the more energy it takes to store a given amount of electricity, the greater the measured voltage. Stored electricity has the potential to do work, and is, therefore, a form of potential energy. If two bodies are charged with different potential energies, there is a potential difference (or a difference in potentials). In physics, energy is expected to flow from a body with high potential energy to a body with low potential energy. In electrical contexts, the term ‘potential difference’ is generally called ‘voltage’ as potential difference is measured in volts. One volt is the EMF causing one watt to be dissipated in a circuit when one ampere is flowing.

Electric current Current was described above as a flow of electrons from a place of excess electrons to a place of insufficient electrons. For convenience, these small charges are grouped into larger units called coulombs. The rate of flow of electricity is given as coulombs per second. In SI units (see Table 1.1), the ampere is given as the base electrical unit of flow and defined according to the magnetic force between parallel conductors that results from a flow of 1 amp. By definition, a current flow of 1 amp transfers a charge of 1 coulomb or 6.24 × 1018 electrons per second.

Electrical resistance Electrons passing between the atoms of a conductor is what we refer to as ‘current flow’. Some electrons collide with ionised atoms and give up their energy as photons of heat or light. The more collisions, or the greater the energy lost in each collision, the greater the heat generated by the conductor. The energy source supplies more energy to lift electrons out of their orbit and back into the current flow. The amount of energy required to release the electrons differs between materials, and so different materials are said to have different ‘resistance’ or ‘resistivity’. Resistance is the property that opposes current flow in a conductor. The resistance of a conductor depends on four factors: length, cross-sectional area, type of material and temperature of the conductor.

SI units The electrotechnology industry uses a standard set of measurements, quantities and associated calculations known as ‘SI units’. This is an agreed international standard. The building blocks of this system are the SI base units that form the basis of all physics calculations. These are listed in Table 1.1. 12

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Solve problems in d.c. circuits  Chapter 1 Table 1.1   Summary of SI base units Name

Unit symbol

Quantity name

Definition

Dimension symbol

metre

m

length

Originally corresponding to 1/10 000 000 of the distance between the equator and the north pole, but now the distance travelled by light in a vacuum in 1/299792458 second.

L

kilogram

kg

mass

Originally the weight (mass) of a cube of pure water measuring 0.1 m × 0.1 m × 0.1 m at its freezing point, but now the international prototype kilogram.

M

second

s

time

Originally based on 1/86 400 of a day (24 hours × 60 minutes × 60 seconds), but now based on the change in energy levels of the caesium −133 atom.

t

ampere

A

electric current

The constant current that produces a force equal to 2 × 10−7 Newtons per metre of length between two conductors placed 1 m apart.

I

kelvin

K

temperature

Originally, temperature SI units were based on the centigrade scale of 0°C being the freezing point of water and 100°C being the boiling point of water; but now the Kelvin is used (it is the theoretical point where molecular movement stops). 0° Kelvin equals −273°C

T

mole

mol

amount of substance

The amount of substance based on atoms in 0.012 kg of carbon-12[n 4].

N

candela

cd

luminous intensity

The intensity of light in any direction from a source of light equal to 5.4 × 1014 hertz at 1 m from the source.

J

From these base units a set of derived units has been formulated to measure other physical quantities and attributes. The quantities and attributes that are relevant to the electrotechnology industry are described below.

1.6.2  Distance and displacement Distance and displacement are similar, but different. Distance is a scalar measurement, meaning it refers to magnitude only. Displacement is a vector measurement, meaning that it refers to magnitude and direction. For example, a runner sprinting around a 400 m track will have travelled a distance of 400 m when completing one lap. But their displacement will be 0 m since they started and finished in the same position. The symbol used to represent distance and displacement in a formula is generally d or sometime s (from the latin spatium meaning ‘space’). Rotating objects use either d for degrees or r for radians.

1.6.3  Speed and velocity As with distance and displacement, the difference between speed and velocity is one of direction. Speed is a scalar quantity, while velocity is a vector quantity. Velocity could also be called ‘directional speed’. If the runner in the above example ran the 400 m track in 100 seconds, the speed would be 14.4 kmph. But the average velocity would be zero since the displacement is zero metres. However, if the runner were instead to run the 400 m in a straight line, the velocity would be 4 m/s. 13

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The symbol used to represent average velocity is v. d  ​v = __ ​   ​​   t

1.6.4 Acceleration

Acceleration is defined as the rate of change of an object’s velocity, that is, how quickly the velocity changes. When an object changes its velocity or direction, it is either accelerating or decelerating. This change is measured in velocity per second. But as velocity is expressed as metres per second, the formula used for acceleration is calculated by metres per second squared. The symbol used to represent acceleration is a. The symbol for change in value is Δ (delta). Δ velocity Δv a = _________ ​​   ​​    or a = ​​ ___ ​​  Δ time Δt

d ​ __ ​   ​  ​ ( t) d Δd as v = _​​  ​​ this can be substituted into the above equation as a = Δ _____ ​​   ​​   or a = ___ ​​  2  ​​. t t Δt d This can be further simplified to a = __ ​​  2  ​​. t

1.7   The basic electrical circuit 1.7.1  Circuit types One way to categorise circuits is by their complexity, meaning whether they have just one or many loads, one or many paths and one or more sources of energy. There are five types of circuits that can be categorised in this way:

1. 2. 3. 4. 5.

simple circuits series circuits parallel circuits compound circuits complex circuits.

Three-phase circuits, which are circuits with three power sources, are discussed in Chapter 4; they can be in any of the last three category types.

1.7.2  Parts of electric circuits A basic circuit has to contain three parts: a source, a load and a path, as shown in Figure 1.12. A circuit may also contain control devices and measuring instruments.

The source A circuit must contain a component that supplies the energy. In many cases, the source is a battery but in most it is the power-supply distribution network. The source may also be a generator or solar cell or one of many other means of generating electricity. The source is simply where the energy comes from.

The load The load is the ‘working’ part of the circuit. This is in the form of heat and/or light or electromagnetism to produce motion.

Path Load

Source Path Figure 1.12  Minimal circuit parts

The path The word ‘circuit’ is derived from the Latin words circus or circa, which have meanings relating ‘to go around’. Electricity will only flow if a circuit is complete. This can

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Solve problems in d.c. circuits  Chapter 1

also be referred to as the ‘current path’ or simply ‘the path’. A circuit needs a conductor to carry the current and the conductor is the path of the electricity.

Protective devices Protective devices are comprised of circuit breakers and fuses. There is a wide variety of each. They are not essential for the operation of the circuit but are there to prevent shocks to people and animals, and to ensure that all components (including the current path conductors) are not damaged or become a fire threat. When a circuit breaker is closed or a fuse is intact, the circuit can operate as usual, but when the circuit breaker ‘trips’ and opens, or a fuse ‘blows’, the circuit is opened and no current flows.

Control devices Paths often include ‘control devices’ such as switches and electronic devices that are neither a source nor a load. Switches and electronic devices control current flow within a circuit. A switch is simply a mechanical device that opens or closes a circuit. When a circuit is open, no current flows and the switch is said to be ‘off’. When the switch is closed, current flows, and both the switch and the circuit are said to be ‘on’.

Measuring instruments Voltmeters and ammeters are measuring instruments that are commonly shown in circuits to represent the value of voltage or current at a given point and to identify where the measurement has been taken. Ammeters must be placed in line with a conductor, as a replacement for a part of a conductor, for the meter to read current. This is because ammeters must pass the current through themselves to read the value. Voltmeters, on the other hand, must be placed across a component, or across two points in a circuit, to measure the voltage difference or ‘potential difference’ between those two points. Ammeters do not measure anything when the circuit is open. Voltmeters may, however, measure voltages when the circuit is open, depending on where they are placed.

1.8  Symbols used to represent an electrical energy source, a load, a switch and a circuit protection device in a circuit diagram 1.8.1  Electric circuits Understanding electric circuits is essentially what an electrical worker does. People in other occupations may also need to understand them: automotive mechanics find an ever-increasing electrical aspect to automobile technology, and electronics technicians cannot understand or repair electronic circuits without understanding electric circuits. Instrument technicians now rely principally on electrics and electronics in instrumentation to replace older technologies such as hydraulics and pneumatics. An electrician’s most valuable tool is the power to calculate the electrical values in a circuit before it is even turned on.

1.8.2  Direction of current flow When there is no voltage present, electrons wander around the metallic conductor in a random manner, with no particular direction. When a voltage is placed across two points of the conductor, the electrons will migrate away from the negative of the supplied voltage and towards the positive of the supplied voltage. This controlled, coordinated flow of electrons forms what we call a ‘current’. Before electrons were known of, the (arbitrary) convention was that current flowed from positive to negative. When electrons were discovered and found to flow from negative to positive, the term ‘conventional current’ was coined to refer to the old convention and ‘electron current’ to what we now know of as the flow of electrons. 15

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Electric current is the coordinated flow of electrons from a point of lower potential to a point of higher potential. Electron flow is from negative to positive, and (conventional) current flow is from positive to negative. The conventional current-flow term had been in use for so long that it was considered unwise to adopt ‘electron flow’ as the standard, but it is often used in the USA. To avoid the confusion caused by this practice, it is always a good idea to check which method is being used when using circuits from the USA, especially in textbooks.

Note: When no convention is stated, it is always assumed that conventional current flow is being referred to. If ‘electron flow’ is being used, this should be clearly stated. For the rest of this book, unless specifically stated otherwise, conventional current flow is to be assumed and the term ‘current flow’ refers to conventional current flow.

‘Polarity’ refers to the direction of potential difference found across two terminals, or ‘poles’. A battery, for example, has one ‘positive pole’ and one ‘negative pole’, and the current flows from positive to negative. Abbreviations are commonly used to nominate the poles as positive, (+) or (+ve), and negative, (−) or (−ve).

1.8.3  Drawing a circuit Circuit diagrams are a pictorial method of recording the connections of a circuit quickly, simply and in a way that is easy to understand. Standard symbols are used to represent the parts of a circuit, the components and connections, and a standard is also applied to labelling a circuit. A circuit drawn by one person must be able to be easily read by others who know the standards. The symbols generally represent a concept rather than a picture. The figures in this chapter present several common symbols, most of which may be to various degrees familiar.

1.8.4  Labelling a circuit Components are labelled from left to right and top to bottom. They have a capital letter and a subscript number or letter that is used in formulas and calculations. For example, resistor one can be labelled ‘R1’ while the power supply might be labelled simply ‘E’. A switch might be ‘S5’ and a fuse ‘F2’. The total current can be labelled ‘ITotal’. These symbols and their names (or ‘nomenclature’) quickly become familiar. Circuits for analysis should also be marked to show the polarity of the voltage source and the direction of current flow. Voltage sources should have an arrow beside the symbol, as shown in Figure 1.13.

F1

Sw1

P =— 3 = 0.5 amps Itotal = — V 6

(+) Etotal

6 volts

(+) L1

6 volts

3 watts

Figure 1.13  Labelling a simple circuit diagram

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COMMON ELECTRICAL ABBREVIATIONS Circuits are often labelled with abbreviations to simplify the circuit and make reading it quicker. Although the student will notice many abbreviations, some unique to their own place of work, the following are commonly used. +ve = positive. Labels the positive terminal of a component or supply. −ve = negative. Labels the negative terminal of a component or supply. V = voltage in volts (V). pd = potential difference, the difference in potential between two points. VD = voltage dropped, the voltage difference between two points, e.g. across a component. cct = circuit. Used mainly in example questions. I = current in amps (A). R = resistance in ohms (Ω). P = power in watts (W). E, EMF or emf = short for electromotive force. E is also used to represent energy, but the different uses are generally obvious from their context.

Current direction should also be noted on a circuit by placing an arrowhead (a filled triangle) as a pointer on the conductor in the direction of current flow. A label is usually drawn beside the symbol to name the current, e.g., ‘Itotal’ (see Figure 1.13).

1.9  Effects of an open circuit, a closed circuit and a short circuit 1.9.1  Electric circuits Electric circuits can usually be turned on or off, although they can at times have a fault which changes them entirely. In electrical circles, the term ‘circuit’ may often be abbreviated to ‘cct’.

1.9.2  Open circuit If the current path is not continuous between two points of potential difference, the circuit is referred to as an ‘open circuit’ (see Figure 1.14 (a)). The circuit has a break in it and the switch is said to be ‘open’. No current can flow and the lamp will not light. This condition occurs in a normal circuit when it is switched off, but may also occur when a wire is broken. 17

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1.9.3  Closed circuit (a) Open circuit

Closed circuit (b)

Short circuit

If the circuit is complete, as in Figure  1.14 (b), current can flow and the lamp lights up (assuming it is a lamp meant for 12 V and the battery is not flat). This condition occurs in a normal circuit when it is switched on and the switch is ‘closed’. A closed circuit is an essential condition for current flow. For a continuous current flow, a continuous source of electrical energy must be provided. In Figure 1.14, a car battery is shown as the source of energy, but other devices such as generators can be used when greater quantities of energy are needed. Static electric charges generated by friction are not usually able to carry out this function. The circuit in Figure 1.14 (b) is known as a ‘simple circuit’.

1.9.4  Short circuit

This type of circuit is one that has a ‘fault’, a condition that is to be avoided. In Figure 1.14 (c), the lamp is bypassed by a conductor connected directly from one terminal of the (c) battery to the other. The circuit is now shorter than it was before and the lamp is said to be ‘shorted’ out of the circuit, or the circuit is said to have a ‘dead short’ in it. Figure 1.14  Light circuits based on a car battery ‘Shorted’ means that the current has a shorter path than otherwise. Because of this, the current flow through a circuit’s component or components is limited or entirely prevented and so the circuit does not function as expected. ‘Dead short’ refers to a zero resistance short as compared to a partial short circuit where the resistance is low but not zero. A dead short is a dangerous situation where large amounts of current can flow. Usually a protection device will operate to open the circuit and prevent further current flow. In a short circuit, no current flows through the lamp, but an excessive current flows directly from one terminal of the energy source to the other. The current flow is not limited by the load, as in Figure 1.14 (b). In this particular case, unless the energy source (such as a battery) is protected against excessive current flow internally, the battery and the conductors can easily be damaged and may melt before the current stops. The battery may even explode. Short circuits are not always bad and are sometimes introduced deliberately to cause a particular effect. When a load is short circuited, the high current generated by the low-resistance current path is what activates the circuit breaker or fuse. For example, if a wire was to break off from the circuitry in an appliance and touch the outside metal frame there now exists a danger of someone touching the electricity. However, by connecting an earth wire to the frame, a low-resistance circuit path is created; once the dangerous wire touches the frame, a high current is produced, activating the circuit breaker and protecting the circuit.

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1.10   Multiple and sub-multiple units 1.10.1  Prefixes and multipliers While most of the calculations in this book equate to simple, easily describable values such as 5 ohms (5 Ω), 10 V and 0.5 A, the values of units in the real world can also be very large or very small. As a result, other systems of communicating these values simply have been devised. These include multiples and sub-multiples and scientific and engineering notation. In the multiple and sub-multiples system, large or small units are abbreviated using prefixes such as ‘kilo’, ‘mega’ and ‘giga’ for large values and ‘milli’, ‘micro’ and ‘nano’ for small values. These are then abbreviated further through the designation of a single letter for the particular unit. For example, 1000 Watts can be abbreviated to 1 kilo Watt, which can be further abbreviated to 1kW. Table 1.2 lists the commonly used multiples and sub-multiples and their equivalent amount. Table 1.2   Summary of common multiple and sub-multiple units Prefix

Symbol

Multiplier

nano

n

10−9

micro

μ

10−6

milli

m

10−3

kilo

k

103

mega

M

106

giga

G

109

tera

T

1012

pico

pF

10−12

Extremely large and small values can also be represented using scientific or engineering notation. Both use the same principles but, as discussed later, engineering uses values that are easily translated into multiples and sub-multiples. Scientific notation simplifies large and small numbers by substituting decimal places with a multiple of 10 to the power of the number of decimal places that have been substituted. Conventionally in scientific notation, the number of decimal places that are substituted leaves one decimal place at the beginning of the simplified number. For example, 200 metres can be expressed as 2  ×  102 metres (or better still 2  ×  102  m), as 102 equals 100 and 2 × 100 equals 200. Alternatively, a small number such as 0.02 metres can be expressed as 2 × 10−2 metres (2 × 10−2 m), as 10−2 equals 0.01 and 2 × 0.01 equals 0.02. With engineering notation, the choice of exponent (or indices) used with the factor of 10 is a multiple of 3. This is due to the fact that all of the common multiples and sub-multiples are based on three decimal places. For example, 2000 metres can be expressed as 2 × 103 metres (or better still 2 × 103 m), which can then be easily converted to 2 kilometres (2 km) since 2 × 103 m equals 2000 metres. Alternatively, a small number such as 0.002 metres can be expressed as 2 × 10−3 metres (2 × 10−3 m), which can then be easily converted to 2 millimetres (2 mm) since 2 × 10−3 equals 0.002 metres.

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The difference between scientific and engineering notation can be explained using 25 000 metres as an example. In scientific notation this value would be simplified to 2.5 × 104 metres, whereas it would be expressed as 25 × 103 metres in engineering notation.

1.10.2  Scientific calculators There are many different brands of scientific calculators available today, including those that are applications on mobile phones and tablet devices. However, each brand generally only uses one of several types of function buttons to enter scientific (and engineering) notation. The function button that is required to enter the exponents is generally labelled as ‘EXP’, ‘×10x’ or sometimes ‘EE’. For the sake of simplicity, this button will be called ‘EXP’. To enter a number (for example, 4.15 × 106) expressed in scientific or engineering notation, do the following:

1. Enter the digits required for the number (4.15). 2. Use the ‘EXP’ button to enter the exponent (6). Do not use the ‘X’ function button (this is already assumed by the use of the ‘EXP’ button). 3. Use the ‘+/− ’ function button to change the exponential from positive to negative, if required.

Most calculators also have a function button to allow the resultant numbers to be displayed in normal, scientific or engineering notation. This button is typically labelled ‘SCI’ or ‘ENG’ and generally multiple presses or the use of a ‘SHIFT’ button will change the values back and forth. For a more detailed explanation of how to use a scientific calculator, refer to the manual for the particular device.

1.11   Basic d.c. single-path circuit 1.11.1  Ohm’s Law In 1826, Georg Simon Ohm carried out a series of experiments in which he connected various pieces of material (some conductive, some resistive and some insulating) as the resistance in a simple circuit. He then measured the amount of current that passed through those materials and the voltage that was required to cause the current to flow. Plotting his results, he was able to deduce from the resulting straight-line graphs that the current was directly proportional to the voltage. He also saw that, in all of his experiments, as the voltage approached zero, the current also approached zero, and the plotted line of the voltage and current values was straight or linear. The angle of this line on a graph only changed when the material he was testing changed. He was then able to state with confidence that in any electric circuit the current is directly proportional to the voltage and inversely proportional to the circuit ‘resistance’. This is known as Ohm’s Law, which can be stated as: The current flowing between any two points in an electric circuit is directly proportional to the potential difference between these points and inversely proportional to the resistance of the circuit between these points. The term ‘directly proportional’ means that, as one quantity increases (in this case the voltage), the quantity that depends on it (the current) will also increase. When two quantities are said to be ‘inversely proportional’, it means that, as one quantity increases (in this case, the resistance), the dependent quantity (the current) decreases. Ohm’s Law can be expressed by an equation: V I = __ ​​   ​​  R 20

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Solve problems in d.c. circuits  Chapter 1 Table 1.3   Ohm’s Law Quantity

Symbol

Unit

Unit symbol

Effect in circuit

Electromotive force

EMF or E

volt

V

Forces current through circuit

Potential difference

pd

volt

V

Forces current through circuit

Voltage drop

VD

volt

V

Enables current to flow through circuit

Current

I

amp

A

Electron flow

Resistance

R

ohm

Ω

Opposition to current flow

A 3A

6 volt lamp

Figure 1.15  Six volt battery connected to a lamp

V

6V

The electrical student must learn Ohm’s Law and be able to explain it in clear, concise terms. Ohm’s Law is the most important rule for any electrical worker, forming as it does the basis of many circuit calculations. Its importance in later studies of electrical theory, right through to electronics and engineering, cannot be overemphasised.

EXAMPLE 1.1 Given that a lamp draws 3 A when powered by a 6 V battery, determine the resistance of the lamp. In this example, the voltage and the current are known so the equation used is: V R = __ ​  ​  (1)  I ​​ ​    ​  6 ​  ​  ​​​ ​ = __ ​  ​  (2) 3 ​ = 2Ω​ (3)

1.11.2  Simple circuits Simple circuits have only one source and one load. They therefore have only one path. An example of a typical simple circuit is a standard torch. It has a battery, a lamp and a path which includes a switch. A desk lamp is the same circuit, except that the source is now the power distribution network, via a plug. The plug is not the actual source but, as it connects to a known source, most people accept that a socket outlet is the source when connected and switched on. 21

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Battery

(a)

(b)

Lamp

1.5 volt cell, 1.5 volt lamp

Figure 1.16  Simple circuit

Circuits are not usually shown as images or drawings, but as circuit diagrams that replace the components with symbols. So the simple circuit pictured in Figure 1.16 (a) is drawn as the circuit diagram shown in Figure 1.16 (b). Each component has its own symbol.

1.12  Measuring electricity—devices and units 1.12.1 Instruments Galvanometers One of the earliest electrical instruments, dating back to 1820, was the galvanometer (named after scientist Luigi Galvani). The original galvanometer was simply a compass within a coil of copper wire. Any deflection of the compass needle indicated that an electric current flowed in the coil, and the position of the galvanometer in the circuit determined whether the experimenter was measuring a voltage or a current. Before electronics, highly accurate instruments were generally based on the galvanometer, with a very light mirror used in place of the needle and a reflected light beam used to indicate deflection, perhaps on a far wall in a darkened room. Galvanometers may still be used in some laboratories, but have generally been replaced by ammeters and voltmeters with electronic amplification to allow very small currents and voltages to be measured. Although the principles of both are based on the moving coil galvanometer, their movements are optimised for the task they are intended to perform.

Ammeters

Figure 1.17 Galvanometer

Ammeters are intended to measure current. Current flows through a circuit so an ammeter must always be connected in series with a circuit. The positive (+) or red terminal must always be connected to the positive side of the circuit, otherwise the meter needle will attempt to move backwards against the meter stops and the instrument may be damaged. Ammeters have very low resistance so that they will not restrict the flow of current in a circuit any more than necessary. This means that an ammeter should never be connected in parallel with any points in

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a circuit that have a potential difference between them. The meter may be seriously damaged if it is connected in this way.

Voltmeters Voltmeters are intended to measure voltage, which can be measured across any two points in a circuit. They must therefore be connected in parallel with those two points. To avoid excessive current flow, the resistance of a voltmeter must be very high. Common digital voltmeters are at least 10 Megohms (10 MΩ), and many have an internal resistance of 200 MΩ. Older analogue voltmeters often have a much lower resistance, which may be given as ohms per volt. That is, a voltmeter with a 1000 Ω per volt rating Figure 1.18 Ammeter that will read up to 50 V on one range has an internal resistance of 50 × 1000 = 50 000 Ω (50 kΩ). The current flowing through the windings of this example analogue meter, when connected across a pd of 50 V, will be very small (1 milliampere), so no damage will be caused by excessive current flow. A digital voltmeter with 200 MΩ internal 50 resistance will only pass ​​ ___ ​​  × 106 = 250 × 10−9 A 200 (0.25 microamps). However, if the same analogue meter were connected across a 250 V supply, the current would be five times as great (5 milliamperes) and, although this is a small current, it is beyond the value for which the meter winding was designed, so the meter could be damaged. Meters can only be used to measure values within their capacity. The maximum capacity of a meter Figure 1.19 Voltmeter is termed its ‘full-scale deflection’ (FSD) value. If any meter pointer moves rapidly across the scale and beyond its FSD (the A highest division marked on the scale), the Switch Ammeter Resistor power should be switched off immediately, Power (Load) Source before damage occurs to the meter. Figure  1.20 shows the correct symbols and connections for an ammeter and a voltmeter when connected to read current and voltage in a simple circuit. Figure 1.20  Instrument connections

V Voltmeter

1.13   Voltage, current and resistance in a circuit 1.13.1  Determining voltage, current and resistance in a circuit The values of voltage, current and resistance can be determined in any circuit if two of the three values are present by using Ohm’s Law in either its given form or through transposition. 23

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Voltage

Relationship between voltage and current for a constant resistance

For example, to find the resistance required in a circuit that has 12 V applied and an allowable current of 2 A: V R = __ ​   ​  I ​​ ​  ​  __ 12​ ​ ​​ ​ = ​   ​  2

Current

​ = 6 Ω

Figure 1.21  Relationship between voltage and current for a constant resistance

Resistance

Relationship between resistance and current for a constant voltage Current

Figure 1.22  Relationship between resistance and current for a constant voltage

If the allowable current is known and the value of resistance is already determined, a transposed version of Ohm’s Law would apply. For example, if the allowable current is 3 A and the resistance is 20  Ω, the required applied voltage can be determined with: V = I × R ​​ ​ ​ =​  3 × 20  ​​​  ​  ​ = 60 V Similarly, the current that will flow through a known resistance with a known value of voltage can also found by using the third version of Ohm’s Law (by transposition). For example, if a resistor of 10  Ω has a voltage of 24 V applied to it, the current that flows through the resistor is determined with:

Voltage

Relationship between voltage and resistance to maintain a constant current Resistance

V I = __ ​   ​  R ​​ ​  ​  ___ 24​ ​  ​​ ​ = ​   ​  10 ​ = 2.4 A

By using the principles of direct inverse proportionality (as shown in Figure  1.22), these values can also be quickly determined by understanding their relationships. As resistance is equal to the voltage divided by the current, it can also be expressed as: resistance is directly proportional to voltage and inversely proportional to current. This is illustrated in Figure 1.21. Figure 1.23  Relationship between voltage and resistance to maintain a constant current

V l As R = __ ​   ​ then R α V and R α _​    ​ I I         ​​ ​  V​  =​  IR then V α I and V α R  ​​​​ As V 1 As I = __ ​   ​ then I α V and I α __ ​    ​ R R Increasing current in a fixed resistance, such as drawing more current through a conductor, has the direct consequence of lowering the voltage at the end of the conductor since V = IR. So, if the current is increased, the voltage drop through the conductor is increased. 24

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1.14   Relationship between force, power, energy and work 1.14.1 Force To move an object from one position to another requires an amount of ‘force’. Force is defined by the mass of the object multiplied by the change in velocity, or acceleration, of the object. This can be either from standstill to moving or while the object is moving. For example, to get a vehicle to move from standstill to a velocity of 10 m/s takes a certain amount of force. Similarly, to reduce the vehicle’s velocity from 10 m/s to 5 m/s takes a certain amount of force in the other direction. The symbol used to represent force is F and the unit for force is the Newton. The unit symbol for the Newton is N. ​F = m × a​ When an object is being raised or lowered, it is subjected to gravity, which has a constant acceleration of 9.81 m/s2. As this value is constant for earth, it has its own symbol in calculations (g). ​F = m × g​

1.14.2  Energy and work Energy and work are the same quantity regardless of whether it is mechanical, chemical or electrical. Energy can either be used to do work or can be stored. For example, pumping water up to higher dams in a hydroelectric power system requires work to be done and energy to be expended. Once the dam is full, it provides a store of energy which can be directed through generators later to produce energy. The symbol used to represent energy and work is W and the unit is the joule. The unit symbol for the joule is J. ​W = F × d​

Power ‘Power’ is defined as the rate of doing work or expending energy. Therefore, power is also the same, regardless of the system. In physics, power is calculated from the amount of work done divided by the time it takes to do the work. The symbol used to represent power is P and the unit is Watts. The unit symbol for the Watt is W. The Watt is defined as 1 J of energy expended in one second. W  ​P = __ ​  ​​   t

1.15  Power dissipated in a circuit from voltage, current and resistance values 1.15.1  Electrical power Electrical power is calculated from electromotive force and the current that flows due to that force. As current is already a rate (coulombs per second), power can be calculated from the force involved, the EMF and the displacement, or current flow. Therefore, power equals the voltage multiplied by the current. Power = V × I  (1) ​​     ​  ​  ​  ​  ​​​ i.e.  P = VI  (2) 25

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Sometimes, the information given contains the voltage and resistance, or current and resistance. The power can be found from those values as well. Using Ohm’s Law and the rules of transposition: P = VI  (3) ​​     ​  ​  V​  ​  ​​​ and I = __ ​   ​   (4) R Therefore:

also:

V P = V × ​ __ ​   (5) R ​​ ​    ​  2​  ​  ​​​ ​V​​  ​ ___ ​ = ​   ​   (6) R

P = VI  (7)     ​​  ​  ​  ​  ​​​ and V = IR  (8) Therefore: P = IR × I  (9) ​​ ​    ​  2 ​  ​  ​ ​​ ​ = ​I​​  ​R  (10) Electrical students should practise transposition by finding these two formulas from Ohm’s Law and the power formula. The formulas above show why power is said to be ‘proportional’ to voltage squared, or current squared. In a circuit with a fixed resistance, any increase in voltage will cause a proportional increase in current, and therefore the change in power will equal the change in voltage squared. Likewise, in a circuit with a fixed resistance, any increase in current will cause a proportional increase in voltage drop, and therefore the change in power will equal the change in current squared. This agrees with the formulas above. Finally, in a circuit where the resistance can be changed, any increase in resistance will cause a decrease in current flow, and, therefore, a decrease in power; and a decrease in resistance will allow more current to flow, and, therefore, an increase in power. So, power is said to be ‘inversely proportional’ to resistance. As an example, given the load resistance in 2 V2 12 144 a 12 V circuit is 4  Ω, the power consumed is ___ ​​  ​​    = ​​___ ​​     = ​​___  ​​   =  36  W. If the load resistance is doubled to R 4 4 8 Ω, the current flow drops to half and the power consumption becomes 18 W. (Try proving this yourself using Ohm’s Law.) Electrical calculations rarely correspond exactly to the basic formulas. As learning a formula for every situation would require learning thousands of them, students must be prepared to learn a basic set of formulas and then convert them via algebra and transposition into what they require for the problem at hand.

EXAMPLE 1.2 A car with a 12 V battery has two headlamps rated at 50 W each. When both lamps are alight, what current will be drawn from the supply? P = VI

 (1)

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Therefore, by transposition : ​ ​ P I = __ ​    ​ V

     (2)

    ​  ​     ​  ​  ​  2 × 50 ​  ​  ​  ​  ​​​ ​ = _____ ​   ​      (3) 12 100 ​ = ___ ​   ​  12

 (4)

​ = 8.33 A​ 

 (5)

EXAMPLE 1.3 A 12 V portable car cabin heater has 4 × 45 W elements. Calculate the resistance of the circuit (a) and the value of current drawn from the supply (b). ​P​  Total​​ = 4 × 45 W ​ = 180W

 (1)  (2)

​V​​  2​  P = ___ ​   ​  R

 (3)

​12​​  2​  ∴ R = ____ ​     ​  (4) 180 ​​             ​ ​    ​  ​  ​  ​  ​  ​  =​  0.8 Ω​   (5)​​​ P = VI  (6) P ∴ I = __ ​    ​  (7) V 180 ​ = ____ ​   ​   (8)  12 ​ = 15A  (9) check: P = ​I​​  2​  × R

 (10)

2

​​ ​ ​    ​  ​  ​  =​  ​15​​  ​  × 0.8  (11)​​​ ​ = 180W​

 (12)

1.15.2  Electrical energy Electrical energy, like mechanical energy, is a product of power and time. Energy is usually measured in joules; but as power is the common unit for the rating of appliances, electrical energy is instead measured by the power of the appliances multiplied by the time that they are in operation. Electricity is usually sold to customers and, therefore, needs to be measured in a quantity that a customer expects to pay for, one that does not sound too large. That is not megawatts or megajoules, but a more appropriate unit, the kilowatt hour. The measurement kilowatt hour (kWh) refers to the power in thousands of watts multiplied by the length of time the power was used in hours. One kWh is equal to 3.6 × ​ ​106 J or 3.6 MJ. 27

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EXAMPLE 1.4 How much power does a 100 W light bulb use in a month, assuming it is used for six hours a day and there are 30 days in a month. First as measured in joules: Step 1. Time in seconds: 60 minutes 60 seconds __________ The lamp would operate for 30 days × 6 hours × ​​_________  ​​ × ​​      ​​.    hour minute ∴ t = 30 × 6 × 60 × 60  (1) ​​ ​     ​  ​  ​  ​​​ ​ = 648 000 seconds  (2) Step 2. Energy is power multiplied by time: ∴ W = 100 × 648 000     (3) =​  64 800 000 J     (4)​​​ ​​ ​ ​    ​  ​  ​  ​ = 64.8 MJ​     (5) Now as measured in kilowatt hours (kWh): ​t​  (s)​​ P ​W​  (kWh)​​ = _____ ​     ​   × ​ _____    ​  1000 3600

      (6)

​​

P × t ​ = _____ ​   6   ​       (7) 3.6 × 10 ​     ​     ​  ​  ​  ​  ​  ​  ​​​​ 100 × 648 000 ​ = ____________ ​        ​ 3.6 × 106

      (8)

​ = 18 kWh​

      (9)

EXAMPLE 1.5 An electric heater rated at 2400 W is switched on for an average of six hours per day for the whole of winter, from 1 June to 31 August. How much electricity is used in that period by the heater? Step 1. Calculate the time in hours: Days = 30 + 31 + 31

 (1)

​ = 92 Days

 (2)

=​  Days × Hours  (3)​​​ ​​ Hours       ​      ​  ​  ​  ​  per day​  ​ = 92 × 6  (4) ​ = ​552  hours   ​ ¯¯¯¯

 (5)

Step 2. Calculate the power in kilowatts: P Power in kW = _____ ​     ​  1000 ​​

    (6)

​     ​  2400​  ​  ​​​ ​ = _____ ​   ​      (7) 1000 ​ = 2.4 kW​

    (8)

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Step 3. Calculate kWh: W = Power (kW) × Time (hrs)

  (9)

=​  2.4 × 552​  ​   (10)​​​ ​​ ​ ​      ​  ​ = 1324.8 kWh

 (11)

1.16   Power ratings of devices All electrical devices are rated in terms of their output power, or the power that they can dissipate without being destroyed. The output power rating is the power that a device performs its rate of work at or the amount of energy the device can convert. For example, a motor with a rating of 1 kW lifting a weight of 1000 kg up to 1 m: F = m × g ​ = 1000 × 9.81 ​ = 9810 N W = F × d ​​  ​    ​   ​​ ​  ​  ​  ​  ​ ​ ​ = 9810 × 1 ​ = 9810 J W  P = __ ​  ​  t Therefore:

As W = F × d d then P = F × _​  ​  t d Therefore t = F × ​ __ ​ P ​​       ​  ​  W​  ​  ​  ​​   = ​ __ ​  P 9810  ​ = _____ ​   ​  1000 ​ = 9.81 s

So the 1 kW motor can lift the 1000 kg up 1 m in 9.81 s. Similarly, a 1 kW heater can produce 9810 J of heat every second. The power rating of a device is the amount of work that it can do. It is also an indication of the amount of heat that the device can dissipate per second without suffering damage. If this value is exceeded for a period of time, the device will burn out. This time frame gets exponentially shorter as the amount of exceeded power increases.

1.17   Measurement of electrical power in a d.c. circuit The simplest method of measuring power in a d.c. circuit is by using a voltmeter and ammeter and multiplying the two values together. Power can also be measured directly with an instrument known as a ‘wattmeter’ or ‘power meter’. The method for connecting a wattmeter is shown in Figure  1.24. The meter has two measuring circuits: one to measure the current flow (I + to I−), the other to measure the supply voltage (V + to V).

I+

V+ I– V–

Figure 1.24  Connections for measuring (d.c.) power with a wattmeter

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The two measuring circuits control the instrument needle in such a way that its position indicates power instead of current or voltage.

1.18  Physiological effects of electrical current and the fundamental principles for protection 1.18.1  Electric shock Living tissue relies on electrochemical signals to enable physiological processes such as sensation and muscle contraction to occur. An external source of electrical energy causes a disruption to the normal functions occurring in living tissue. At very low levels, the normal chemical transfer between parts of a cell can be disrupted. Cellular heating can also occur and cells can be damaged in a way that is not immediately obvious. Higher levels of energy cause muscles to contract and internal body signals such as those that control heart and lung timing to be disrupted. A human being who sustains an electric shock may stop breathing, and their heart may either stop beating or enter a condition known as ‘ventricular fibrillation’. This is a state of rapid, uncoordinated muscle spasms. Blood stops flowing around the body and in around four minutes the brain starts dying.

Electrocution causes death, whereas a person who contacts electricity and lives has had an electric shock. Advances in electrical protection and safe working practices have dramatically reduced the incidence of electrocution.

The general effect of electric shock on the human body is unpleasant. Levels of current less than 10 mA cause muscle pain and shaking, while levels up to about 30 mA can cause severe muscle contractions, pain and internal organ stress. Over 30 mA, skin, body tissue, muscles and organs may be burned, torn or strained to an extent where hospitalisation is required. Unconsciousness and even death can occur, especially if help is not immediately available. Electricians and the general public should be aware that delayed-onset symptoms can occur long after the electric shock, and internal damage may not be obvious for many hours. In cases of electric shock, particularly across the chest or stomach, a medical check-up is mandatory (based on WorkCover rules). In severe or prolonged cases of electric shock, the heart may cease its rhythmic beating and enter a stage of fibrillation. Trained medical attendants use a defibrillator to attempt to restart the heart’s normal pumping action. A defibrillator is an electrical device in which a capacitor is charged to a pre-determined value. Electrodes connected to the machine are placed at appropriate places on the body and a capacitor is discharged in an attempt to shock the heart into resuming its normal rhythm. All training in the electrotechnology industry incorporates basic first aid training in CPR, and full first aid training is highly desirable.

1.18.2  The fundamental principles of AS/NZS 3000:2018—wiring rules AS/NZS 3000:2018 is the standard that is required by law under electrical safety acts in Australia and New Zealand. Clause 1.5 of AS/NZS 3000:2018 outlines the fundamental principles of the standard that ensures the safety of persons, livestock and property from the dangers and damage that can result from reasonable use of electricity. These dangers are identified as three major types. 30

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1. Electric shock: in the AS/NZS 3000:2018 context, this is defined as the shock current that can arise from contact with parts that are live during normal service and those that are live when a fault exists. Contact with parts that are live under normal service, such as touching live wires inside an appliance, is avoided by the use of basic protection (protection from direct contact). Contact with parts that are live under fault conditions, such as touching a live frame on a faulty appliance, is avoided by the use of fault protection (protection from indirect contact). 2. Excessive temperatures: electricity flowing through conductors produces a heat which, when it becomes excessive, can result in a hazard by either burning the insulation and other parts of the wiring or appliance or burning other materials in close proximity to the wiring or appliance. This results in a fire and smoke hazard, physical burns for people or livestock and/or impairment of the safe operation of equipment. 3. Explosive atmospheres: electricity and its resulting heat can cause the explosion of gases and dust. Special consideration must be taken when installing electrical equipment in areas where such hazardous atmospheres are present. Examples of hazardous areas are mines, petrol stations and grain silos.

1.19  Basic principles by which electric current can result in the production of heat, the production of magnetic fields or a chemical reaction 1.19.1  Electrostatic effects Although the electrostatic effects of electricity are less common than others, their uses are increasing. Chimney stacks in power stations, for example, have an electrostatic generator that energises the smoke particles so they become attached to an electrostatic grid. The collected particles cluster and then fall into a collection chute to be taken away as pozzolanic ash for use in making cement. This reduces pollution and acid rain. Electrostatic processes are also used in painting and even in making sandpaper.

1.19.2  Electrochemical effects Electrochemical processes occur in electric storage cells (accumulators) and batteries, electroplating and anodising. In fact, many chemical processes use electricity to separate, combine or refine chemicals and to separate gases. Manufacturing methods also commonly use electrical processes to etch and electroform, or for electroerosion (processes where electrical current removes material from—or shapes—the product being manufactured).

1.19.3  Heating effects When the opposition of a conductor (its resistance) is overcome by an applied voltage and a current flows, work is done and energy is expended. When heat is produced, this raises the temperature of the conductor and increases its resistance. If a conductor of high resistance is concentrated in a small area with suitable safeguards and insulation, a source of heat is available, as in the domestic radiator. This is a desirable outcome, but consider the end result if great quantities of heat are produced in the conductors supplying the electrical energy to the radiator. The conductors could be inside the hollow walls of a building and, if the temperature around the enclosed conductors were raised sufficiently, there would be a possibility of fire. Steps must be taken to prevent such an undesirable event. The current flow must be reduced or the conductor’s cross-sectional area increased. Both steps lead to reduced power loss and heating effect in the supply conductors. 31

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1.19.4  Magnetic effects Magnetism is created around any conductor with a current flowing through it. If this magnetism is unwanted, consideration must be given to rerouting the conductors to diminish it. Magnetic compasses are subject to stray magnetic fields and care must be taken to ensure that they are not affected in any way. With large currents, considerable magnetic forces can be set up between conductors, in which case precautions also have to be taken. When the magnetic effect is a desirable one, steps are taken to concentrate the magnetism in specific locations. The magnetic effect is increased by creating coils of conductors called solenoids. Many turns may be added to the coils to enhance the effects. For more details on magnetism, see Chapter 2.

1.20   Typical uses of the effects of current 1.20.1 Heating Heat is a fundamental effect of electric current and one of the most used. Electrical heating is highly efficient since any loss in efficiency is given off as heat. Heating devices range from radiant panel and oil heaters to fan heaters and large electric furnaces used in industrial processes. A comparatively more energy- and cost-efficient method of heating and cooling is the use of refrigeration and air-conditioning. Their efficiency is due to their operating principle of transferring heat from one space to another through the use of a refrigerant gas, an electric compressor pump and electric fans.

1.20.2 Lighting As the most noticeable effect of electric current after heat, light has been used for over a hundred years (although it was actually the introduction of electric refrigerators that accelerated domestic electricity in the middle of the previous century). More recently, lighting has progressed from old-fashioned incandescent lighting to gas discharge lighting such as fluorescent, sodium and neon to the highly efficient LED technology.

1.20.3  Producing motion Just as electricity can be produced by moving or rotating a conductor through a magnetic field, motion can be produced by reversing the process. That is, when a conductor with a current flowing in it is placed in a magnetic field, it will move as a result of both the field around it and the external magnetic field. This process can be used to move everything from small servos in robotics and compact disc drives to large machines such as those used in mining and rail. It can also be used to open and close switches in relays and contactors. Similarly, solenoids can be used in valves and locks to open and close mechanical devices.

1.20.4  Information storage, control and processing In its basic form, electricity can be used to energise and de-energise a switch. This is the basis of data storage, computing functions and information communication technology (ICT). By switching electronic circuitry in an ‘on’ or an ‘off’ state (or binary code), machines can make the sophisticated computations that are typical of most of today’s technology. Their ability to do this is becoming increasingly greater as the devices that enable this binary code become increasingly smaller.

1.20.5  Sound and radio frequencies Similar to the way that electromagnetism can create motion, it can also create sound through the use of a small solenoid attached to a diagram or cone. When an alternating or oscillating signal is applied to the solenoid, the 32

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cone vibrates and the result is sound. This principle can also be reversed to create a microphone. A variation of this circuit is used for transmitters and receivers for radios, televisions and mobile phones. The piezo electric effect is also used to produce sound as a microphone, as well as in ultrasonic cleaning and similar devices.

1.21   Mechanisms by which metals corrode 1.21.1  Electrolytic corrosion Dissimilar metals The best-known effect of destructive corrosion occurs when two different metals are in contact in the presence of an electrolyte. An increasing problem in Australia is the connection of copper conductors to aluminium conductors. The copper and aluminium act as electrodes when an electrolyte is present due to condensation or rain that contains dissolved sulphur products. A simple cell is created and is effectively short-circuited on itself, as illustrated in Figure 1.25. The metal with the higher potential becomes the anode that will tend to go into solution in the electrolyte (i.e. will corrode away). The result is a progressively deteriorating electrical connection, the generation of heat and the eventual failure of the connection. In some circumstances, the heat produced can set fire to an installation, and the problem then is more significant than just the failure of an electric circuit. One way to combat this type of corrosion is to minimise the number of connections where dissimilar metals are joined. Another method is to prevent the entry of moisture to the joint by applying paint or another covering such as a paste that is applied to both metals prior to termination. Alternatively, all the materials that are being joined can be electroplated with a common metal, e.g. cadmium.

Stray electric currents Underground pipes and cables can become corroded by the electrolytic action of stray underground currents. Dissimilar metals in damp ground that are adjacent to each other may produce these stray currents, or they may result from a nearby faulty electrical installation. The electrical bonding of tracks in electric traction systems helps to reduce underground stray currents. Covering underground pipes and conductors with plastic sheaths minimises the corrosive effects. The corrosion tends to be concentrated at sharp bends in underground pipework, and appropriate measures to avoid this should be taken where practicable.

Electrolytic protection: sacrificial anodes Electrolytic corrosion can be minimised by implementing sacrificial anodes. Anodes made of zinc blocks are bolted inside boilers or to the metal hulls of ships, adjacent to bronze propellers. The intention is to sacrifice a metal block, which can be replaced comparatively easily, rather than risking the corrosion of the boiler or ship’s hull.

Electrolytic protection: cathodic protection With this method, an external d.c. voltage is applied between the equipment to be protected

Moisture accumulates in crevices and joints

Zinc-plated fastener

Copper busbar Aluminium busbar

Electrolysis eats at one metal often leaving pit holes

Zinc-plated nut

Figure 1.25  Corrosion of dissimilar metals

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and earth, such that the equipment is at a lower potential than the surrounding soil. In practice, it has been found that most forms of corrosion can be prevented when the pipes or other metallic structures are approximately 0.5 V negative in relation to the surrounding soil. AS/NZS 3000:2018 clause 1.5.14 states that all parts of an electrical installation shall be protected from external influences that can occur under normal operation. This includes corrosion and galvanic action.

1.22  Principles for protection against the damaging effects of current As noted previously, AS/NZS 3000:2018 is founded on the fundamental principle that electrical installations must be safe. The two general methods of protection are called ‘basic protection’ and ‘fault protection’.

1.22.1  Basic protection Basic protection is the means of protecting persons and livestock from shock hazards that would arise from direct contact with parts of the installation that are live under normal operation. The four basic protection methods described in clause 1.5.4.2 of AS/NZS 3000:2018 are: 1. Insulation: the most common method, this involves covering the live conductors with a non-conductive material such as the thermoplastic insulation used for electrical cables. 2. Barriers or enclosures, such as equipment housing and switchboards which can only be opened by a key or tool. 3. Obstacles, such as the safety fences surrounding high-power transformers. 4. Placing out of reach, as with, for example, overhead power lines. The clause also notes that residual current devices (RCDs or, as they are more commonly known, safety switches) are only to be used as an additional means of protection (as is mandatory for power points and lights); the other means of protection listed above must be used.

1.22.2  Fault protection Fault protection is the means of protecting persons and livestock from shock hazards that would arise from indirect contact with parts of the installation that are not live under normal operation. These parts are only live when there is a fault, but they present just as big a risk of shock or injury as parts that are usually live. The four fault protection methods described in clause 1.5.5.2 of AS/NZS 3000:2018 are:

1. Automatic disconnection of supply, which is provided by circuit breakers, fuses or a combination of both. Rewireable fuses were used in the past and, although they are still in use in old installations, they are now prohibited. 2. Preventing the fault current passing through a body by the use of class II or double-insulated equipment, as defined in clause 1.4.32. This type of equipment is identified by the double square symbol and generally does not have an earth pin on the plug as it is not required. 3. Preventing the fault current passing through a body by the use of electrical separation where a transformer or other source of electrical supply (such as a battery) is used and connection to earth does not complete the circuit. 4. Limiting the value of shock current to being lower than a dangerous level of current. This is generally done through electrical circuitry that senses the output current and lowers the output energy if it becomes excessive. The clause also notes that, of these four methods, automatic disconnection of supply is the most commonly used. 34

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1.23  Basic principles of producing an electromotive force (EMF) 1.23.1  Sources of electromotive force (EMF) There are six common sources of electromotive force: 1. Electromagnetic—electricity generated from electric conductors moving through a magnetic field. 2. Electrochemical—electricity generated from the reactions between chemicals, as used in the cells of batteries. 3. Electrostatic—electricity resulting from friction between appropriate materials, which is used to generate very high voltages at low power levels. 4. Photoelectric—electricity resulting from the conversion of light into electricity, e.g. solar panels. 5. Thermoelectric—electricity generated by dissimilar metals being exposed to heat, e.g. thermocouples used to measure high-temperature ovens. 6. Piezoelectric—the electric potential generated by placing a crystal under stress or releasing it from stress, e.g. gas lighters. There are other sources of EMF mostly quite rare, such as direct nuclear generation of electricity, e.g. thermonuclear pulses. Thermonuclear electromotive force is not currently an efficient method and is considered dangerous.

1.23.2  Electromagnetic sources The bulk of electrical energy is still generated in the same way as it was a hundred years ago, through electromagnetic generation. Fossil fuel is burned to generate the heat required to turn water into steam to drive mechanical turbines which then drive electrical generators. However, renewable energy is beginning to replace conventional fuel in certain areas and renewable energy markets are projected to grow significantly in the near future. The burning of fossil fuel results in pollution and causes global warming, so a clean, green replacement for fossil fuels is needed and inevitable. For more information about sustainable sources of energy, see Chapter 3. The electric generator employs the principle of electromagnetism by forcing conductors through a magnetic field to generate a current and a voltage in them.

Figure 1.26  Snowy Mountains hydroelectric power station

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The only real variations in the process are in the type of prime mover used. The driving unit may be a steam, water or gas turbine or a diesel engine. Each has its advantages and disadvantages. The electromechanical method is used wherever large quantities of electrical power are supplied from a common source. The operating efficiency of these various processes has gradually been improved but is still a subject of great concern to engineers and environmentalists. Physicist Michael Faraday’s experiments with induction led to the development of rotating machinery to produce dynamic electricity. Rotating machinery was initially of open construction and was primitive by today’s standards. Figure 1.27  Early high-current dynamo Figure 1.27 shows an early dynamo (as generators were once called). It can be seen that there has been little change in the basic parts of direct current (d.c.) generators during the last hundred years. A generator still consists of an armature rotating within a magnetic field. There has, however, been extensive refinement of the construction and materials used.

1.23.3  Power generation Inventor and electrical engineer Nikola Tesla realised that alternating current (a.c.) offered many advantages over direct current (d.c.) in both the generation and transmission of electrical power. The changeover from direct current to alternating current took many years to implement, and both systems were in use for a considerable time. Early methods of producing the mechanical energy to generate electrical power remained the same, as the old steam-driven reciprocal engines originally used to drive low-speed d.c. generators came to be used to drive a.c. generators instead. Generators that produce an alternating current are usually called ‘alternators’.

1.23.4  Thermal steam turbines Steam engines were slow and had low efficiency. They gave way to steam turbines, which offered higher speed and efficiency. A steam turbine is similar to a jet engine in that escaping hot gases cause a number of fans to rotate, producing the power for the alternator. The most common method of generating power in the mainland states of Australia is with steam turbines. In the majority of cases, steam is produced by burning coal, oil or gas, as governed by local conditions. Coal-fired steam-powered generating stations are often sited adjacent to large quantities of coal and water for cooling and condensation purposes.

1.23.5  Geothermal steam Italy and New Zealand have been generating electrical energy for many years by harnessing steam that emerges naturally from the earth. The steam is cleaned and fed to low-pressure turbines that drive alternators. Precautions have to be taken to ensure that fine solids and ‘wet’ steam are prevented from reaching the turbine blades, otherwise they would erode away. Large volumes of steam are required, owing to the relatively lower temperature and pressure.

1.23.6  Nuclear power Nuclear energy has many advantages, including higher efficiency, lower pollution levels and greater reliability. It does not generate the levels of greenhouse gases that coal-fired power stations release. Nuclear reactors produce steam, which is then fed to turbines to drive alternators, just as in thermoelectric power stations. 36

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Nuclear reactors already drive power stations, ships and submarines in many countries but the safety of nuclear power generation and the storage of nuclear waste fuel are a concern to the general public. As we have seen, many nuclear power plants have been (or are due to be) decommissioned.

1.23.7  Hydroelectric power In many parts of the world, hydroelectric power is generated by releasing large volumes of water through low-speed turbines. The water is collected in high-level reservoirs (as high as possible) and a power station is then built at as low a level as possible to maximise the energy provided by gravity. The energy in the water is used to drive water turbines. These are like medieval waterwheels, but with much improved efficiency. The release can be controlled, as can the amount of electricity generated.

1.23.8  Tidal movements France and the United Kingdom have done innovative work in collecting seawater by tidal movement for generating power with hydroelectric turbines. In some coastal areas, these two countries have tidal movements of between 6 and 9 m. On the north-west coastal regions of Australia, there are similar variations in sea level but, because of low population densities, this kind of power generation is currently not an economic proposition here. The principle is to harness the energy of tidal flows by using directly driven propellers to generate electricity as the tidal water flows in and out of a channel. This provides maximum power at peak tidal flow, but no power at the top and bottom of the tides.

1.23.9  Engine-driven alternators In remote areas, gas or diesel engine-driven alternators are common. The power is generated in a somewhat similar fashion to that of a portable generator, although on a larger scale. A more expensive method of generating electrical power, it is used when other fuel supplies such as water and coal or furnace oil are not available to generate steam at an economical rate. Many small communities use diesel alternators for peak periods and battery back-up at other times.

1.23.10  Gas turbine engines Gas turbines, which are a form of jet engine driving a shaft, are noted for good efficiency and their ability to produce small quantities of electricity quickly. They can run up alternators and get them online quickly at peak times, and make excellent standby plants for emergencies. Gas turbines are high speed, which means that they can drive high-speed alternators efficiently, with good speed regulation.

1.23.11  Electrochemical sources Most electrochemical sources are ‘batteries’ of electric ‘cells’. These are discussed in detail in section 1.24, but, in general terms, secondary cells are used to store energy from other generating sources when it is plentiful, returning it when they fail. For example, a wind generator charges the batteries when it is windy so the user can have electricity when the wind drops. A less common method is the combination of chemical elements such as hydrogen, carbon and oxygen to form compounds such as methane, water or carbon dioxide. Chemical bonding involves ions and the transfer of electrons from one atom to another, energy being either generated or absorbed in the process. Adaptations of this method lead to several types of fuel cells. One type consists of two chambers with two porous electrodes separated by an electrolyte. Hydrogen and oxygen are supplied to the two chambers and, in the presence of a catalyst, react to provide ions and free electrons. (A by-product of this is water.) 37

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Fuel cells were used for the spacecraft that went to the moon, as well as on most of the spacecraft that came afterwards. They provide high efficiencies, and under ideal conditions can last for many years. The fuel cell has no moving parts, produces no noxious fumes and, in some cases, can produce drinkable water. This is an important reason for their use in space travel. Some fuel-cell systems require extensive (and expensive) auxiliary equipment, and their use is accordingly restricted.

1.23.12  Photoelectric sources The solar cell is basically a large semiconductor diode. When light falls on the junction, light energy is converted directly into electrical energy. Theoretically of unlimited life, they are in fact subject to some material deterioration and a consequent falling-off in efficiency if they are not cleaned regularly and coated with suitable protective chemicals. At 12 noon, when the sun is directly overhead or at its zenith, the energy that it shines on the earth is around 1000 W/m2. As most commercially available solar panels range from 15% to 25% efficiency, they will generate 150 W/m2 to 200 W/m2 at this time. Efficiencies greater than 40% or 400 W/m2 are available but are generally cost prohibitive and complex. As efficiency increases and costs decrease, houses can be built with solar arrays mounted on their roofs that not only supply the household energy requirement but also feed into the grid to help meet industrial needs. Photoelectric sources are also known as ‘solarelectric’ sources.

1.23.13  Electrostatic sources Figure 1.28  A bank of solar cells

Figure 1.29  Wimshurst machine

Electrostatic generators generate very high voltages at very low current capabilities. Usually they store an electrostatic charge either on their surface or in ‘Leydon jars’. The charge is released quickly and dramatically. Two common ways of producing substantial electrical charges are by the Wimshurst machine and the Van de Graaff generator. The Wimshurst machine consists of two parallel insulating plates rotating in opposite directions, the charge being conducted away by two contacts. The Van de Graaff generator has a motor-driven rubber belt which rubs lightly against a flexible conducting comb. At the other end of the belt, another comb conducts the charge to a hollow ball. This type of generator is mainly used in the study of high-voltage effects and testing insulators. The use of static electricity in industry is growing. Typical applications are dust precipitation and spray

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painting. The dust particles are charged negatively by passing them first through a charged grid and then through a positively charged collector. Rather than being discharged into the atmosphere, the charged particles are attracted to the collector, where they collect into a mass which is periodically shaken into a hopper for disposal. For spray painting, the object to be painted is made negative with respect to earth and the paint particles are attracted to it. The result is an evenly distributed coat of paint. The paint is even attracted around the sides of the object and into areas that are difficult to reach. It is important to remember that very high voltages are used (typically 50 kV) and precautions have to be taken when working on electrostatic units.

1.23.14  Thermoelectric sources The thermoelectric method of voltage generation is mostly used as a means of temperature measurement. A thermocouple consists of two dissimilar metals joined at a point where the heat is applied (a ‘hot junction’). A potential difference is created and appears at the other two ends of the conductors, where it is measured with a meter usually calibrated as a thermometer (see Figure 1.30). The electromotive force produced is very small, requiring sensitive meters to read it. A typical thermocouple made of copper and constantan (an alloy) would produce an EMF of the order of 9 millivolts for a temperature rise of 200°C. For greater voltages, thermocouples are sometimes connected as a group, so their voltages add up to a higher value. The unit is then called a ‘thermopile’. Other combinations of metals allow temperatures to be measured from levels that are very low to very high (−273°C to >2000°C).

1.23.15  Piezoelectric sources Some materials, when subjected to mechanical stress, generate a voltage between their faces. This is called the ‘piezoelectric effect’. One common use is the striking of an arc, or spark, to ignite the gas in a gas lighter, gas barbecue or gas stove. The voltage is also directly proportional to the pressure, so piezo microphones, which are very small, are often used in devices such as mobile phones. Audiophiles might notice that very high frequency speakers are also piezo devices, and the speaker in any mobile phone is also likely to be a piezo. In these cases, however, the piezo crystal is working the other way, converting a voltage into a mechanical deflection of the very thin piezo wafer. Piezo speakers can also be found as the initiating element in echo sounders and ultrasound diagnostic machines in hospitals. They are used for the generation of very high frequency sound waves in ultrasound cleaning machines and distance-measuring devices such as electronic (ultrasonic) rulers. The materials most commonly used are naturally occurring crystals such as quartz and Rochelle salts. These are cut into chips (also called crystals) with their two faces parallel to one of the three axes in the main crystal, and then mounted in holders before being connected into circuits.

Figure 1.30 Thermocouple

Figure 1.31  Piezoelectric striker ignition system

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When a voltage is applied to the opposite faces of the chip, the chip distorts and the movement can be measured. When the chip is distorted, a voltage appears at the opposite faces. At certain frequencies, the applied voltage causes a mechanical distortion, which causes a voltage to be generated in the crystal, which causes a distortion, and so on. This results in a natural rate of resonance, depending mainly on the angle of the cut and the physical dimensions of the crystals. This has led to one of the most common uses of crystals being to determine the operating frequencies in radio transmitter and receiver circuits.

1.24   Principles of producing an electrical current 1.24.1 Introduction The term ‘electrochemistry’ refers to the effects that electricity has on chemicals or the electrical effect of chemicals. The common process of corrosion is an electrochemical effect, and electrochemical processes are widely used to prevent rusting. The battery in a car or handheld torch or mobile phone is an electrochemical component. The human brain is also an electrochemical device. Many manufacturing processes use electrochemical effects as a means of protection, or even of electromachining metal parts. Electroplating is used to protect items from corrosion or make them more appealing, such as its use in silver-plating brass tableware to create the appearance of a more expensive item. More recently, electroplating technology has been improved to an atomic level through nanolaminating, where coats of dense and ultra-fine materials can be used to add strength and other physical properties to weaker metals.

1.24.2 Electrochemistry Electrochemistry in general refers to two opposite processes, one using electrical energy to create a chemical effect, the other using a chemical effect to create electrical energy. The first process is often used in electroplating, where an external voltage is applied across a pair of electrodes, causing a current to flow through the electrolyte. The electrode connected to the positive polarity of the supply is called the ‘anode’ and the electrode connected to the negative is called the ‘cathode’. The process of metal ions being removed from the anode and deposited onto the cathode has been adapted for electroplating and the refining of metals, as well as machining by electroerosion. The second process converts chemical to electrical energy, which is produced within a cell by the disassociation of chemical molecules. This energy will flow through an external circuit.

1.24.3  Electrochemical energy sources Primary cells  Primary cells are electrochemical devices that convert chemical energy into electric energy but stop when the chemicals are depleted. Until generators were invented, primary cells were the only source of electricity other than static electricity. Primary cells are fully charged when they are assembled and cannot be recharged. Many types of primary cells have been invented, but the one that has held the field for the longest time is the Leclanché cell. Its modern form still has many uses, although other types of cell have been developed with greater efficiency, longer lifespan and greater energy density.

Secondary cells  Another type of cell is the secondary or rechargeable cell. Secondary cell chemistries allow the cell to be recharged by reversing the current flow using another energy source. Secondary cells have a zero or low potential difference (voltage) when assembled and need to be charged. They can then also be recharged. 40

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Many types of secondary cell have been invented, and most are still in use. As with primary cells, modern examples have many improvements and new types are still being created.

Fuel cells Fuel cells are electrochemical devices that are similar to primary and secondary cells in that they have an anode, cathode and an electrolyte. However, there is a significant difference in that they use a ‘fuel’. This is typically hydrogen or hydrocarbons such as methane and LPG that combine with oxygen in the air to produce electricity with a waste product of water (for hydrogen) or water and carbon dioxide (for hydrocarbons). As long as this fuel is supplied, the fuel cell will deliver electricity. An essential part of this process is that the electrolyte is made of a specific material that only allows the passage of positive ions, forcing the electrons to seek an alternate route, thus creating electricity. There are several types of fuel cell, the most common at present being the proton exchange membrane fuel cell (PEMFC). The applications of fuel cells include energy storage and management for peak electrical supply periods (peak levelling), cogeneration (generation of both electricity and heat in the form of hot water from cooling the cell) and fuel cell electric vehicles (FCEV). Flow batteries are similar to fuel cells in their operation but have two sets of electrolytes stored outside them.

Voltaic cells Figure 1.32 shows a simple voltaic cell consisting of two electrodes, one of copper and the other of zinc, immersed in a solution of dilute hydrochloric acid. The electrolyte need not be hydrochloric acid; other acids such as chromic, acetic or sulphuric acid can be substituted; indeed, salt solutions such as common salt or copper sulphate can be used. To obtain a difference of potential between the two electrodes, only two conditions are necessary: the electrodes must be of different metals, and they must be immersed in an electrolytic solution comprising an acid, alkali or salt. These cells have come to be known as ‘galvanic’ or, more popularly, ‘voltaic’ cells after Luigi Galvani and Alessandro Volta, who were pioneers in this area. The container is made from a non-metallic material (e.g. glass) that will not be affected by the acid. It must not be made of a conducting material, and care should be taken that the electrodes do not touch each other. Dissolving an electrolyte of hydrochloric acid (HCl) in pure water allows the acid to separate out into positive hydrogen ions (H+) and negative chlorine ions (Cl−). The chlorine ions combine with the zinc atoms, creating positive zinc ions (Zn++). This leaves free electrons on the zinc electrode, giving it a negative charge. The positive zinc ions combine with free chlorine ions, forming zinc chloride (ZnCl), a solid which sinks to the bottom of the cell. Positive hydrogen ions move across to the copper electrode, where they combine with surface electrons from the copper electrode and become I neutralised hydrogen atoms. 1.1 volts The hydrogen collects as bubbles that rise to Cu Zn – the surface of the electrolyte and escape as free + H 2 hydrogen gas. The removal of electrons from the Negative copper electrode causes it to have a positive charge, Positive electrode + – electrode and the cell has a potential equal to the difference H Cl (cathode) (anode) between the negative charge on the zinc electrode ++ Zn and the positive charge on the copper electrode. H+Cl– This potential difference is usually about 1.1 V. Electrolyte This simple cell is not very practical. The copper electrode becomes covered with hydrogen Electrolyte is gas, preventing hydrogen ions from taking further hydrochloric acid ZnCl electrons from the surface. This effect is known in water as ‘polarisation’, and it increases the internal Figure 1.32  Voltaic cell resistance of the cell, reducing the output voltage.

V

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1.25  Input, output, efficiency or losses of electrical systems and machines All systems of energy conversion—mechanical, chemical, magnetic or light/heat—that produce work exhibit some form of energy loss. This loss is generally in the form of friction, resulting in the production of heat. Examples include heating due to resistance (from the friction of electrons in a conductor), mechanical friction in the motor bearings and air drag and noise loss, which in turn creates friction heat from the movement of air. In any work-related system there are three main forms of energy or power. These are Input Energy or Power, Output Energy or Power and Losses (which are the difference between the two). For example, in an old-fashioned electric lamp there is the electrical Input Power, the Losses as a result of the heat produced by the resistance of the lamp and the Output Power in the form of Light. Mathematically, this can be expressed by the equation Output = Input − Losses or Pout = Pin − Ploss Efficiency is the ratio of the Output to Input and is generally expressed as a percentage. To determine the percentage efficiency of a system, the Output is divided by the Input and multiplied by 100. Output Pout Mathematically, this can be expressed by the equation Efficiency % = ​​______ ​​ × 100 or η     % = ​​___  ​​  × 100 Input Pin The Output will never be more than the Input and the Efficiency will never be more than 100%.

1.26   Effect of losses in electrical wiring and machines All losses result in the dissipation of heat. A reduction in the amount of this loss results in an increase in the efficiency of the system. In the electrical industry, a low level of loss or high efficiency is generally considered desirable because of the economic and environmental advantages. Losses in an electrical system result in higher costs of energy production/supply on the Input side and the increased emissions from electrical energy produced from non-renewable sources. There are many other negative effects of low efficiency in an electrical system. Primarily, low efficiency means increased power, and increased power at the same voltage equates to higher current drawn. When higher current is flowing in circuit wiring, the heat resulting from the resistance of the wiring leads to breakdown of the wiring insulation and eventually short circuits between conductors. Alternatively, overheated conductors can also become open circuits when they melt. This issue with overheating and its effect on conductors can also apply to machines. Transformers or motors that have increased losses (perhaps from damaged bearings or cooling systems) will eventually fail if the internal insulation breaks down or conductors open circuit.

EXAMPLE 1.6 An electric motor rated at 5 kW output drives a machine for four hours. If the efficiency is 89%, calculate the energy consumed if it is running at full load. Step 1. Calculate the output energy: W = 5 kW  × 4 hours (1) ​​ ​     ​  ​  ​  ​  ​​​ ​ = 20 kWh (2) 42

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Step 2. Calculate the input energy: Eff

​P​  ​​ = ____ ​  Out ​  × 100% ​P​  in​​

100% ∴P ​ ​  in​​ = ​P​  Out​​  × ​ _____ ​  89%

(3) (4)

​P​  ​​ ​  ​ ​​    ​  ​  ​  ____ ​  ​​​ ​ = ​  out  ​  (5) 0.89 ​

20 = ____ ​    ​  0.89

(6)

​

=    ​22.472  kWh ​ ¯¯¯¯

(7)

1.27   Principle of conservation of energy Energy and matter can be neither created nor destroyed. Energy can be converted from one form to another, and energy can be converted to mass and mass can be converted to energy; but the net amount in a closed system remains the same. For instance, mechanical energy can be converted to electrical energy by a generator and electrical energy can be converted to mechanical energy by a motor. The same can be said for energy and mass (but the conversion of energy to mass had, until recently, only been proven by Einstein’s theory of relativity). Mass is, however, very easy to convert to energy. For example, a large amount of energy is produced when burning fossil fuels. This principle, the law of conservation of energy, states that energy in an isolated system cannot be created or destroyed but only transformed from one form to another. This statement is also the basis of the first law of thermodynamics. Looking at power and the work done by electrical equipment and machines by applying the law of conservation, we can see that the efficiency of an electrical system (for example, an electric motor) is always the power in equals the power out plus the power losses. As the Output power can never exceed the Input and there are always losses in the form of heat, the idea of a perpetual motion machine, such as a motor turning a generator which in turn supplies electricity to the motor, is impossible. Any conductor connecting a load to a supply has resistance, but is not called a resistor unless the resistance is drawn in a circuit for circuit analysis. In conductors, resistance is considered a disadvantage as unwanted voltage drop and heat are generated. Conductors must therefore be made of low-resistance materials such as copper or aluminium, and be made thick enough that the resistance is not noticed. Insulators have a very high resistance, but this is low enough that most insulators have a small leakage, perhaps just a few nano-amps. Resistance can also result from current passing through a liquid or gas or a semiconductor. For most electrical work, resistors are constructed from alloys of metals or from conductive chemical compounds. A few materials have non-ohmic properties, and they are used to make non-linear resistors that change their resistance when exposed to heat or light.

1.28   Resistors 1.28.1 Resistance Resistance is the opposition to current flow or the restriction caused by the atomic attraction between protons V and electrons. Resistance was first quantified by Georg Ohm, who established the relationship R = __ ​​  ​​ . As current I 43

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flowing through a resistance results in a voltage drop and heat generation, these two effects are the most common uses of resistors, often in cooking and lighting. The resistance value of a conductor is controlled by four factors: length, cross-sectional area, the resistivity of the material used to make the resistor and the temperature coefficient of the resistance material. Resistors can be labelled with their resistance, tolerance and power dissipation or encoded with coloured bands.

1.28.2  Resistor types Resistors are chosen according to a number of parameters, including their resistance, current-carrying capacity, voltage rating and power dissipation. Generally, the size of a resistor is determined by all of these.

EXAMPLE 1.7 A resistance of 100 Ω is required to carry 100 mA of current. What value of power dissipation is required? P = ​I​​  2​R (1) ​ ​​​    ​  =​  ​0.1​​ ​  2​  ​  × 100​  (2)​​​ ​ =1 ​   W   ​ ¯¯ (a)

(3)

Cast grid resistors 

Carbon-compound resistor Connecting leads

Insulation End cap

Carbon-compound rod

End cap

Carbon-film resisto (b)

Large high-power resistors were once commonly cast from iron or an iron alloy. They may be cooled by having forced air blown over them, or by a liquid such as water flowing through a hollow core. Cast resistors are generally used only where a very high current needs to be controlled, such as for speed control of winding motors for large lifts and cranes, and traction motors.

Co-axial sheathed elements  Spiral-trimmed carbon-film on ceramic rod Metal-film resisto (c)

Spiral-trimmed-metal film on ceramic rod (d)

The heating elements used in electric stoves, electric fry pans and strip heaters are commonly made from a resistive conductor inside an insulating ceramic powder, which is in turn within an earthed metal sheath. As used in stoves, the element heats the sheath to a temperature of around 660°C (hot enough to melt aluminium if an empty saucepan were to be left on the element unattended).

Wire-wound resistor in ceramic block

Wire-wound resistors 

300R 5W

Ceramic ‘box’ filled with insulating cement

Figure 1.33  Resistor types

Resistance wire wound on ceramic rod

Smaller resistors from 5 W to several hundred watts are commonly made by winding a resistance wire around a ceramic former. An insulating layer is generally used to cover the wire, not only as insulation but also to protect it from damage and corrosion. Large resistors, designed to dissipate a lot of heat, generally have a large surface area or some other means of conveying the heat away from

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them. Some resistors come in their own finned heatsink (which looks and acts like a radiator). Wire-wound resistors are usually large enough to have their resistance and power rating printed on their body. Some are made to be tapped or adjusted via a panel-mounted shaft and knob. Resistors that can be adjusted by a moving tap may simply be called ‘adjustable resistors’, while those that can be controlled from a control panel are often called ‘variable resistors’. In between is a class of resistors that are adjusted by using a tool such as a screwdriver, and they are known as ‘trimmer’ or ‘preset’ resistors.

(a)

Resistor (carbon)

(b) Resistor (wire-wound)

(c) Tapped resistor

Carbon-compound resistors  Carbon-compound resistors are physically (d) smaller and have lower power ratings than other types of resistor. Common ratings are Trimmed resistor ¼ W, ½ W, 1 W and 2  W. The construction or of a carbon-compound resistor is shown in Figure 1.33. The resistive material is placed on Variable potentiometer the ceramic tube and laser cut into the spiral to or attain the exact resistance required (within the Variable rheostat tolerance required). During manufacture, the thickness and composition of the compound Figure 1.34  Basic electrical symbols can be varied to make resistors of different values between 0.01 Ω and 10 MΩ. Carbon-compound resistors are small, so their resistor size and rating cannot easily be printed on them. This has led to the development of a standard colour-coding identification scheme. The coloured bands on fixed-value resistors are placed closer to one end of the body during manufacture. Carbon-compound resistors can age and their resistance can change as they do so, so a better type of small resistor has had to be used instead. The metal-film resistor is similar to the carbon type in size and appearance, and only its base colour identifies it as not being a carbon resistor. (Carbon resistors have a brown or cream base colour, while metal-film resistors are usually blue or green.) Carbon-film variable resistors are manufactured by applying a conductive paint to a non-conductive base material. A wiper contact slides over the conductive paint to allow the terminal resistance to be controlled.

1.29   Variable resistors Variable resistors with three terminals are often called ‘potentiometers’ as their main function is to control a voltage. The volume control on a conventional radio is an example of a variable resistor. Two-terminal variable resistors that are usually used to control a current are known as ‘rheostats’. Often a three-terminal potentiometer will have the middle terminal connected to one end to make it into a rheostat, even though it may still be called a potentiometer or ‘pot’ for short. 45

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1.29.1  Non-linear resistors Resistance varies according to temperature and the type of material used to make the resistor. Non-ohmic resistors exist that change resistance according to other physical parameters such as voltage, current flow and magnetism. These resistors are useful as sensors in instrumentation. Variable resistors are otherwise known as ‘transducers’.

1.29.2  Positive temperature coefficient (PTC) resistors Metals generally have a positive temperature coefficient of resistance, but a positive temperature coefficient (PTC) resistor is one in which the change in resistance is greatly increased over that of a normal conductor. Two main materials are used: one is a metallic oxide such as barium oxide, which has a large PTC over a limited range; the other is silicon-based and has a smaller PTC over a larger range. The typical characteristic is shown in Figure 1.35 (red). Usually the resistance values are shown on a logarithmic scale, but in order to illustrate the sharp knee of the curve as the PTC heats up, a representative curve has been drawn from test results on an actual resistor. It can be seen that the resistance is only 4 Ω at room temperature, but rises rapidly once the temperature rises above about 50°C. 10kΩ

4Ω

2kΩ

4Ω

10°C 20°C 30°C 40°C 50°C 60°C 70°C 80°C

Figure 1.35  Temperature-dependent resistors

1.29.3  Negative temperature coefficient (NTC) resistors Negative temperature coefficient (NTC) resistors are made from oxides of chromium or nickel that have been modified by the addition of small amounts of semiconductor material. Similar tests to those above were conducted on an NTC resistor and the results are shown in Figure  1.35 (blue). The usual logarithmic scales have been avoided. The test resistor had a resistance of 2000 Ω at room temperature of 10°C and, when raised to 80°C, the resistance fell to 4 Ω.

1.29.4  Low temperature coefficient resistors In some circumstances, a resistor is required to retain its value over a range of temperatures. One such material is manganin, which has a temperature coefficient of resistance given as 0.00001 (10–5). Its resistance change is so small compared with other metallic elements generally that it is often listed as zero. Manganin is used where resistors of hightemperature stability are required, for instance in measuring instruments.

1.29.5 Voltage-dependent resistors (VDRs) Figure 1.36  Voltage-dependent resistors (VDRs)

A voltage-dependent resistor (VDR) is manufactured from a mixture of materials to have a very high resistance at lower voltages but a very low resistance

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above a certain critical value. A VDR is usually presented in disc form with two leads for connection into a circuit. The VDR is connected in parallel with the voltage supply, close to the circuit it has to protect. Usually it does not conduct but, when the supply voltage exceeds a designed limit, it breaks down and conducts the excess energy away from the circuit it is protecting. The primary purpose of a VDR is to protect equipment against voltage surges Figure 1.37  Light-dependent resistors (LDRs) such as lightning strikes. The response time is extremely quick, an obviously necessary characteristic. In some circuits, VDRs are intended to blow a fuse or trip a circuit breaker to isolate the electric circuit being protected. Sometimes a VDR is built into a package called a ‘surge protector’, which can be installed in the main switchboard or on the consumer’s terminals. Depending on the individual device and on the severity of the surge, a VDR might have to be replaced after it has operated.

1.29.6  Light-dependent (LDR) resistors Light-dependent resistors (LDRs) are used to detect light levels such as in PE (photo-electric) cells on power poles to turn street lights on and off, or to control other night lighting. When light falls on the resistor, the resistance changes and an electronic circuit senses that change to turn a relay or solid-state switch on or off. Light-dependent resistors are usually made from cadmium-sulphide film mounted on a ceramic or phenolic plate and covered with a conductive grid. To ensure there is no build-up of contamination and to protect the active material, the resistor is mounted in an evacuated glass envelope or covered with a clear plastic encapsulation. See examples in Figure 1.37. The resistance of the device varies considerably with the amount of light received on the surface. Typically, the resistance in complete darkness can be as high as 10 MΩ, reducing to possibly 100 Ω in sunlight.

1.29.7  Non-inductive resistors At times, resistors need to be as purely resistive as possible (meaning as little inductance as possible). To avoid inductance, the wire-wound resistor (which is simply a coil of wire) is wound back on itself.

1.29.8  Liquid resistors Resistances for motor starters uses a liquid which is stored in a tank as the resistance. Two electrodes conduct the power to it. The resistance is free to cool through convection and conduction through the tank surface, so the tank size can be designed to suit the required dissipation. One advantage of liquid resistance is that the resistance value decreases as the temperature rises (NTC), which is useful for motor starters.

1.30   Power ratings of a resistor All components in an electric circuit have a limit to the amount of heat they can dissipate. This level of heat is expressed as power in watts. This power limit is considered to be the power rating of the component, and if this rating is exceeded the component will fail. 47

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In the case of resistors that are specifically used to either limit current flow or produce a voltage drop, this rating is the power level that the component will fail at. Care must be taken in circuit design not to exceed this level. In the case of resistors that are used to produce light and heat, this rating is the amount of energy that the device will output when it has the rated voltage and (as a result) current applied to it.

1.31   Power loss (heat) occurring in a conductor 1.31.1  Effects of conductor resistance The size of the conductors used to supply electrical equipment is governed by the current-carrying capacity of the conductor for that installation and the voltage drop of the conductors.

Power loss in a conductor  In a conductor supplying a load, there is an inherent resistance and a current flowing through that resistance. Accordingly, the power consumed in the conductor is ‘lost’ as far as the load is concerned. This loss shows up as heat by raising the temperature of the conductor and its surrounding insulation. Heat lost in the conductors is waste, which reduces the efficiency of the circuit.

1.32   Reading resistors 1.32.1  Resistor colour-coding Power resistors with a rating of 1 W or higher often have the decimal point in their resistance value replaced by a letter representing the multiplier value. So, with R equalling ohms, k equalling kilohms and M equalling Megaohms, for example, 47R = 47 Ω, 6k8 = 6800 Ω, 1M2 = 1.2 Megaohms. Resistors and other components may be so small that, in the past, writing their value on them was impossible. Ironically, as component sizes have decreased to the requirements of ‘surface-mount devices’ found in modern electronic circuits, writing their value on them has become customary. Reading very thin coloured lines is more difficult than reading the values when the device is as small as 0.8 mm × 1.2 mm.

1.32.2  Reading resistors To read a resistor, look at it and identify which end the main group of colours is nearest to. On four-band resistors, the colours are all together at one end. Make that end the left end by turning the resistor into that position. This is best explained with a particular resistor in mind, so let us assume a resistor has four colour bands: red, violet, yellow and gold. Reading from the band nearest to the end, the first band indicates the first significant figure and the second band the second significant figure. That is the value of the resistance. In our example, these are red and violet, which are 2 and 7 respectively. That makes the value 27. The next band is the multiplier, so the colour here simply specifies the number of zeros to write after the value. In our example, the fourth band is yellow, which means four zeros. So the resistance is 270 000 Ω or 270 kΩ. The final band on our resistor is the tolerance. Gold represents a tolerance of 5%, which indicates that the resistor has been made to be 270 kΩ +/−5%, or +/−13.5 kΩ. So the value will be between 256.5 kΩ and 283.5 kΩ. With one per cent or better resistors, there are three significant figures in the value. 48

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The gold and silver colours are mainly used in the fourth band (tolerance), but on small values of resistance (less than 10 Ω) gold and silver are multipliers of 0.1 and 0.01 respectively.

EXAMPLE 1.8 Determine the resistance values for the the resistance following resistors: Determine values for the following

resistors: (a)

= 10Ω = 10R

(b)

= 120Ω = 120R

(c)

= 1500Ω = 1k5

(d)

= 18000Ω = 18k

(e)

= 220kΩ = 220k

(f)

= 2700kΩ = 2M7

(g)

= 33E6Ω = 33M

(h)

= 390Ω = 390R

(i)

= 4700Ω = 4k7

(j)

= 56000Ω = 56k

(k)

= 68Ω = 68R

(l)

=1000Ω = 1k0

Figure 1.38

1.32.3  Preferred resistor values Manufacturers cannot be expected to produce resistors in every possible value, so initially only the most common values were produced. Later, a plan was adopted to make specific values, which would have overlapping (or very nearly overlapping) tolerances. For example, on the 10% tolerance scale, 10% of 10 Ω is 1 Ω. Approximately twice 10% (1 Ω) distant, there should be another standard value resistor, and that means 12 Ω. The tolerance of the 12 Ω resistor is 1.2 Ω, and 12 Ω plus twice that, 2.4 Ω, is almost 15 Ω. The tolerance of the 15 Ω resistor is actually 1.5 Ω, so 1.5 Ω plus 1.2 Ω is actually 2.7 Ω, so the tolerances very nearly overlap. Therefore, the E12 scale very nearly covers the whole range from 10 to 100 Ω, and then starts over again in another decade. The next decade has values from 100 to 1000 Ω and so on. Table 1.4 shows the preferred values for three E series of tolerances. There is also an E48 range which, naturally enough, has 48 values. 49

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Electrical Principles Table 1.4   Preferred range of resistor values E6 20% tolerance

E12 10% tolerance

E24 5% tolerance

10

10

10 11

12

12 13

15

15

15 16

18

18 20

22

22

22 24

27

27 30

33

33

33 36

39

39 43

47

47

47 51

56

56

10Ω 68

68

12Ω

8215Ω

18Ω

62 68 75 82 91

22Ω 27Ω 10Ω

33Ω

12Ω

39Ω

15Ω

47Ω

18Ω

56Ω

22Ω

68Ω

27Ω

82Ω

All E12 10%

33Ω1.39  E12 series from 10 Ω to 100 Ω 10% Figure 50 39Ω

47Ω jen21014_ch01_001-112.indd 50

56Ω

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Solve problems in d.c. circuits  Chapter 1

1.33   Selecting a resistor The primary factor in the selection of a resistor is its purpose in the circuit. As stated earlier, several types of resistor can be used for specific tasks such as measuring light, heat, voltage across their terminals or, in the case of manual variable resistors, varying voltage and/or current flow in a circuit for a desired output (volume control on a speaker). But the most common application of an electronic component resistor is to control voltage and/or current to a required level. This is generally to suit other components in the circuit. Resistors of this type are generally limited by calculated value; for example, if a current of 100 mA was to be maintained to a device with next-to-nothing resistance that requires a 12 V supply, a 120 Ω resistor would also have to be placed in the circuit to limit the current. The precise value required for this resistor would be determined by the resistance and tolerance of the device and the required tolerance to match the required value. Any shortfall could be made up for with a small variable resistor called a ‘trimpot’. Once this value is determined, the next factor to consider is the power rating of the resistor, which in turn determines its physical size. Smaller resistors have a lower power rating (up to 1 W) and larger resistors have higher power ratings. If the power applied to a resistor exceeds this value, the resistor will burn out.

1.34   Series (connected) circuits 1.34.1  What is a series circuit? There is only one path in a series-connected circuit. The components are connected one after the other like carriages in a train, and the current from the source flows through each component. Therefore, the current in each component is the same as in every other component and is also the same as that in the path and in the source. See also Figure 1.16.

1.34.2  Where are series circuits used? Series circuits are used where the effects of each component in a circuit is dependent on the other components in that circuit. The simplest example is a basic circuit with a source, resistive load (for example, a heater), a protective device (such as a fuse), a switch (for control) and the conductors connecting them together. If any of these items fails (or, in the case of the switch, is operated in the off position), the circuit will not be complete (closed circuit) and the heater will not operate. Also, if the heater load were to become short circuited, there would be a high current generated in the circuit and the fuse would blow. More complicated variations of this concept include multiple control arrangements where two or more switches are used for safety; for example, in power tools. In these, not only is the on/off button used but there is a separate

Lamp 1 Fuse

Switch

Battery

Lamp 2

Lamp 3 Battery = 9 volts, Lamps = 3 volts each (a)

(b)

Figure 1.40  Series circuit

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‘kill switch’ as a safety back-up. Some cars also use this principle to ensure that all brakes are engaged and the car is in a neutral gear before it can be started. Circuit protection is also arranged in series so that the protective device closest to the fault is operated and the effects on other parts of the electrical installation are minimised.

1.35   Characteristics of a series circuit Voltage in series circuits  As current flows through every component, according to Ohm’s Law every component must have a voltage drop— but the circuit cannot drop more voltage than it has to start with. Therefore, it makes sense that the voltage drop must add up to the total applied voltage. This simple but important fact was documented by Gustav Kirchhoff in 1845 and became known as Kirchhoff’s Voltage Law (KVL). Kirchhoff’s Voltage Law states: In any given circuit, the algebraic sum of the applied EMFs is equal to the algebraic sum of the voltage drops. This is written mathematically as: ​ΣE = ΣV​ Or put simply: ​​E​  total​​ = ​V​  1​​  + ​V​  2​​  + ​V​  3​​  +  … ​V​  n​​​

Current in series circuits  A series circuit is defined as having only one current path or loop. That means that all of the current coming from the source must pass through every component before getting back to the source. Therefore, every component will have the same current. This is written mathematically as: ​​I​  total​​ = ​I​  1​​  = ​I​  2​​  = ​I​  3​​  =  … ​I​  n​​​ So a current of 5 A flowing into a series circuit will flow through every component, and the current measured passing through every component will be 5 A.

Resistance in series circuits  Kirchhoff’s Voltage Law, Ohm’s Law and simple algebra dictate that the resistors in a series circuit, like the one shown in Figure 1.41, must also be added to find the total resistance (RTotal) or equivalent series resistance (RE). Series resistance formula derivation: Vtotal = V1 + V2 + V3 + . . . Vn and V = I × R therefore ITotal RTotal = I1 R1 + I2 R2 + I3 R3 + . . . In Rn but noting that the current in a series circuit is always the same . . . ITotal RTotal = ITotal (R1 + R2 + R3 + . . . Rn) therefore RTotal = R1 + R2 + R3 + . . . Rn which can be proven by experimentation. RTotal = R1 + R2 + R3 + . . . Rn 52

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Power in series circuits 

Series Circuit Formula Summary

Electrical power is calculated from:

∙ voltage and current ∙ or voltage and resistance ∙ or current and resistance.

Power is the energy being used at a given rate to perform work. Therefore, it makes sense to assume that any work done requires energy, which adds up as it is used. This is written mathematically as:

ITotal

R1

R2

ET

=

V1

+

V2

+

V3

+ ...

Vn

IT

=

I1

=

I2

=

I3

= ...

In

RT

=

R1

+

R2

+

R3

+ ...

Rn

PT

=

P1

+

P2

+

P3

+ ...

Pn

R3

...

Rn

ETotal

(Where ‘n’ refers to any number.) Figure 1.41  Resistors in series

​​P​  total​​ = ​P​  1​​  + ​P​  2​​  + ​P​  3​​  +  … ​P​  n​​​

EXAMPLE 1.9 Calculate the equivalent resistance to replace four resistors in a series circuit, given: ​​R​  1​​ = 5 Ω, R ​ ​  2​​ = 10 Ω, R ​ ​  3​​ = 20 Ω, R ​ ​  4​​ = 5 Ω.​ ​R​  Total​​ = ​R​  1​​  + ​R​  2​​  + ​R​  3​​  + ​R​  4​​

(1)

(2)​​​ ​ ​     ​​ ​  =​  5 + 10 + 20 + 5 ​  ​  ​  ​

=4 ​ 0  Ω   ​ ¯

(3)

The equivalent resistance of a number of series resistors is always greater than any individual resistance.

Faults in series circuits  When a number of components are in series, the current must pass through each component to return to the source. Therefore, should any one component, conductor or joint become open circuit, the current cannot flow and the whole circuit will fail. If a component becomes shorted, the voltage on all of the remaining components must increase, with a resulting increase in current flow. Therefore, the components must be carefully chosen in series circuits to be suitable for both normal and fault conditions. Series circuits are never used for distribution systems, as adding or removing loads would change the voltage requirements of every component in the circuit

Relationship between voltage drops and resistance in a simple voltage divider network A simple voltage divider network is a series circuit containing two resistors connected to a supply. As Kirchhoff’s Law explains that the voltage drops in a circuit equal the supply voltage, this circuit presents one way to produce multiple voltages in one circuit that add up to the supply. For example, if a d.c. series circuit has a supply voltage of 12 V applied to a circuit with an 8 Ω and 4 Ω resistor, the total resistance of the circuit is: ​ ​  total​​ = ​R​  1​​  + ​R​  2​​ R    ​ ​​​   ​  =​  8 + 4 ​​ ​ ​ ​

= 12 Ω 53

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And the current in the circuit is: V I = ____ ​     ​  ​R​  total​​ ​ ​​ ​  ​  __ 12​  ​​​  ​ = ​    ​ 12 ​ = 1 A Therefore, the voltage drop across R1 is: ​V​  1​​ = I  × ​R​  1​​ ​ ​​​ ​  =​  1 × 8  ​​​  ​  ​

= 8 V

And the voltage drop across R2 is: ​V​  2​​ = I  × ​R​  2​​ ​ ​​​ ​  =​  1 × 4  ​​​  ​  ​ = 4 V This is supported by Kirchhoff’s Law as: ​V​  supply​​ = ​V​  1​​  + ​V​  2​​ ​ ​​​      ​  =​  8 + 4 ​​ ​ ​ ​

= 12 V

A quicker method is to use the ratios of the resistances to determine the voltage drops in the circuit. For a circuit with two identical resistors, this is a simple matter of dividing the supply voltage by two. In fact, if there are more than two resistors in the circuit and they are all the same value of resistance, the supply voltage can be simply divided by the number of resistors. If the resistors are different values, the ratio of the resistance values can be used instead. For example, if a d.c. series circuit has 100 V applied to it and it has a 20 Ω and a 30 Ω resistor connected, the voltage drops across each resistor can be determined by adding up the total resistance: ​R​  total​​ = ​R​  1​​  + ​R​  2​​ ​ ​​​      ​  =​  20 + 30  ​​​​ ​

= 50 Ω

And then, using the ratio of the individual resistor and the total resistance to calculate the voltage drop across the individual resistor and multiplying it by the supply voltage: ​R​  ​​ ​V​  1​​ = ____ ​  1  ​  × ​V​  total​​ ​R​  total​​ ​​   ​    ​  ​  20  ​​ ​ ​ ​ = ___ ​   ​  × 100 50 ​

= 40 V

And: ​R​  ​​ ​V​  2​​ = ____ ​  2  ​  × ​V​  total​​ ​R​  total​​ ​​   ​    ​  ​  30  ​​ ​ ​ ​ = ___ ​   ​  × 100 50 ​

= 60 V

54

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Which again is supported using Kirchhoff’s Law: ​ ​  total​​ = ​V​  1​​  + ​V​  2​​ V ​       ​  =​  40 + 60  ​​​​ ​​​ ​

= 100 V

1.36   Parallel connected circuits In a parallel connected circuit (more usually known as a ‘parallel circuit’), the separate current paths each have a load. The current flowing from the source in Figure 1.42 is divided into three parts, with a part of the total current flowing through each lamp. After the current passes through the lamps, the current recombines to become the total current that returns to the source.

1.36.1  Applications of parallel circuits Parallel circuits are used where the voltages across the components are required to be the same and where the effect of one component connected in parallel is independent of the other components. A typical example is a lighting circuit in an office where each light is required to have the same voltage applied to it, irrespective of its power output or resistance. For safety and convenience’s sake, it is also important that each light functions independently of the other lights so that if one fails and becomes open circuit, the remaining lights stay on. Another use for parallel circuits is to divert or ‘shunt’ current around circuitry to avoid damage or allow control over sensitive parts of the circuit. Surge suppression devices that protect against lightning strikes and shunt circuits in analogue meters use this principle.

1.36.2  Voltage in parallel circuits Voltage is measured across the terminals of a component by placing the voltmeter in parallel with it. This is because we know that connecting in parallel is the only way to measure the voltage accurately. Therefore, the voltage across any number of components connected in parallel will always be the same, regardless of where it is measured. Another way to look at it is to recognise that a parallel circuit requires only two nodes and, as the voltage at a node is the same as everywhere on that node, the voltage between the two nodes must be the same anywhere between those two nodes, across any component. This is written mathematically as: ​​V​  total​​ = ​V​  1​​ = ​V​  2​​ = ​V​  3​​ = … ​V​  n​​​

Fuse

Switch

Battery

Lamp 1 (a)

(b)

Lamp 2

Lamp 3

Battery = 1.5 volts, Lamps = 1.5 volts each

Figure 1.42  Parallel circuit

55

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1.36.3  Current in parallel circuits Simple and series circuits have only one current path, but parallel circuits can have any number of current paths, sometimes referred to as ‘branches’. The voltage across each branch causes a current to flow, according to Ohm’s Law and the value of resistance of each branch. Kirchhoff also noticed this and stated it in what we now call Kirchhoff’s Current Law (KCL). Kirchhoff’s Current Law states: The sum of the currents entering a junction equals the sum of the currents leaving that junction. This is written mathematically as: ​Σ​I​  in​​ = Σ​I​  out​​​ or put simply: ​​I​  total​​ = ​I​  1​​  + ​I​  2​​  + ​I​  3​​  +  … ​I​  n​​​ In other words, current cannot accumulate in a junction and, as there are no losses, what goes in must come out.

1.36.4  Resistance in parallel circuits The resistors in a parallel circuit allow current to flow, and more resistors connected in parallel allow more current to flow. As the current is inversely proportional to resistance, less total resistance means more current. The formula for total resistance can be derived in what is known as the parallel resistance formula derivation: ​​I​  Total​​ = ​I​  1​​  + ​I​  2​​  + ​I​  3​​  +  … ​I​  n​​​ V and I = ​​__ ​​  R ​V​  Total​​  ​V ​  ​​  ​V​  ​​  ​V​  ​​  ​V​  ​​  ​∴ _____ ​  ​ = ​___1 ​  + ​___2 ​  + ​___3 ​  + … ​___n ​​   ​R​  Total​​  ​R​  1​​  ​R​  2​​  ​R​  3​​  ​R​  n​​ and noting that the voltage in a parallel circuit is always the same . . . ​V ​  ​​  1  1  1  1  _____ ___ ​ Total ​ = ​V​  Total​​​(___ ​   ​  + ​ ___ ​  + ​ ___ ​ + … ​     ​  ​  ​R​  Total​​  ​R​  1​​  ​R​  2​​  ​R​  3​​  ​R​  n) ​​ ​​      ​​​ 1  1  1  1  1  ∴ _____ ​      ​ = ___ ​    ​  + ​ ___  ​  + ​ ___  ​ + … ​ ___ ​   ​R​  Total​​  ​R​  1​​  ​R​  2​​  ​R​  3​​  ​R​  n​​ . . . which can be proven by experimentation.

1.36.5  Power in parallel circuits As in series circuits, power is used in individual resistors according to the voltage and current in the individual resistor. The total of that power is the sum of the power used in each resistor (so, the power formula is the same as for series circuits). ​​P​  total​​ = ​P​  1​​  + ​P​  2​​  + ​P​  3​​  +  … ​P​  n​​​ 56

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EXAMPLE 1.10 Calculate the equivalent resistance to replace four resistors in a parallel circuit, given: ​​R​  1​​ = 5 Ω, R ​ ​  2​​ = 10 Ω, R ​ ​  3​​ = 20 Ω, R ​ ​  4​​ = 5 Ω.​ 1 1 1 1 1 _____ ​     ​   = __ ​    ​  + ​ __  ​  + ​ __  ​  + ​ __  ​  ​R​  Total​​

​R​  1​​

​R​  2​​

​R​  3​​

​R​  4​​

(1)

1​  ​      ​​ ​  ​  ​  ​  ​  ​​​ ∴R ​ ​  Total​​ = ________ ​ _      ​ (2) 1 1 1 __ _ ​  51 ​  + ​ __    ​    + ​     ​    + ​     ​ 5 10 20 ​

=1 ​ .82  Ω   ​ ¯¯

(3)

The equivalent resistance of a number of parallel resistors is always smaller than any individual resistance.

1.36.6  Faults in parallel circuits Parallel circuits are preferred to series circuits in distribution systems. This is because one branch can become open circuit without affecting the others. More importantly, new loads can be added to a circuit without apparent effect on the voltage to other loads, providing the maximum capacity of the source is not exceeded. All devices and appliances can be manufactured to the same rated voltage as the voltage is the same in parallel circuits. In Australia, 230 V a.c. is the standard voltage. As we have seen, if one branch becomes open circuit, the other branches are not affected as they each have the same voltage applied. The total current is reduced by the amount that no longer flows in the open circuit branch. If one branch becomes short circuit, the voltage on the other branches would also initially drop. However, assuming branches have their own protection devices fitted, these others will be back to normal as soon as the offending branch is disconnected by its circuit protection (i.e. when its fuse blows or its circuit breaker opens).

1.36.7  Cells and batteries in a parallel circuit As a single cell only produces a relatively small voltage and current, different configurations for connecting multiple cells together are required to achieve higher levels of each. These cells have to be identical in their output voltage, ampere hour and output characteristics to avoid differences in voltage potential and one or more cells becoming discharged before the rest. Parallel Circuit Formula Summary ITotal To achieve a higher level of current, ... multiple cells must be connected in parallel. For example, if a current of 1 A is required E Rn R1 R2 R3 Total and each cell can only deliver 0.5  A without suffering damage, then two of these cells can be = = V2 = = ... ET V1 V3 Vn connected in parallel to meet the demand. The voltage remains the same as that of one cell. = + I2 + + ... I1 I3 In IT Paralleling cells and batteries also allows 1 1 1 1 1 —– —– —– = + —– + + ... —– R2 R3 RT R1 Rn for an increase in the total ampere hour = + P2 + + ... PT P1 P3 Pn capacity for a system. For example, two 50 ampere hour batteries connected in parallel (Where ‘n’ refers to any number.) can deliver 50 A for two hours or 100 A for Figure 1.43  Resistors in parallel approximately one hour. 57

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1.37   Series/parallel circuits Series/parallel circuits are the most common style of configuration in the electrotechnology industry. This is because the characteristics of both are generally required. Using the office lighting example mentioned in applications for parallel circuits, each light not only needs to be connected in parallel but also requires circuit protection and control. If these lights are all on one circuit and are controlled from one switch, the protection (the circuit breaker, for example) and switch are connected in series with (and prior to) the parallel connections. Series/parallel connections are also used where voltage control (series) and ‘shunt’ current control (parallel) are required, such as in motor connection and control circuits.

1.37.1  Series/parallel or compound circuits Compound circuits (see Figure 1.44) are made up of both series and parallel parts, but the components are always clearly in series—or else clearly in parallel—with another component. The series or parallel components can always be replaced by a single component to simplify the circuit. Compound circuits are the most common type of circuit.

1.37.2  Complex circuits Complex circuits are those that cannot easily be simplified down to series and parallel connections. The analysis of complex circuits like the one shown in Figure 1.45 may require more complex mathematical methods. Complex circuits may use more than one source of energy, sources of perhaps different voltages and even different frequencies or phase angles. (As an electrical apprenticeship only covers the first four circuit types, electrical apprentices are not expected to deal with complex circuits.)

1.37.3  Equivalent resistance Before delving into circuits of multiple components, students should understand what is meant by the term ‘equivalent resistance’. When resistors are connected together, they can be replaced by a single resistor that has the same overall resistance. That is how compound circuits are analysed (on paper at least), by replacing groups of resistors with a single resistor. A resistor that has the same value as a group of combined resistors is called an ‘equivalent resistance’ (RE).

(a)

Fuse

Switch

Battery of 2 × 1.5 volt cells

Lamp 2

Switch

Lamp 1 Lamp 3

(b)

Battery of any number of cells

Lamp 1 = 3 volt, Lamps 2 & 3 = 1.5 volts

Figure 1.44  Compound circuit Note: This circuit is illustrated for educational purposes only

Figure 1.45  Complex circuit

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1.37.4  Nodes and loops

Paths have nodes that connect components. Node 1 Node 2 Node 3 Node 4 R2 SW

It is extremely helpful to think in terms of the ‘voltage across two points of a component’ and the ‘current flowing through a point or ETotal component’. Thinking that way makes circuit R1 R3 analysis much easier. Voltage can be measured across a component, but current must flow through a component. Node 5 Electrical engineers and technicians work SW with ‘networks’ in terms of ‘nodes’ and ‘loops’. Voltage is measured across nodes, and current R2 is measured passing into and out of nodes. ETotal R1 R3 In any circuit, a conductor that joins two or more components is called a node. Nodes join components. Assuming that the conductor has zero resistance (conceptually a perfect Paths may also be referred to as loops. A loop is any current conductor), the order in which the components carrying path that completes a full circle. How many loops can be are connected to a node does not matter. The counted in the circuit above? (Including those marked.) shape of a node also does not matter. Figure 1.46  Nodes and loops A node could just as easily be a sheet of copper or the earth itself. What we call ‘earth’, or ‘ground’, is one node. The chassis of an automobile is one node. Nodes can be labelled by numbers or letters, usually at a point where conductors are joined. Nodes are often identified by a black dot at the junction (see Figure 1.46). As circuits become more complex, the likelihood that two electricians will draw different circuit diagrams of the same circuit increases. Yet if both have drawn accurate representations of the connections, the nodes will be the same. ‘Loops’ are an engineering term for what electricians would usually call ‘current paths’. When current flows around any complete circuit, it follows a current path, or has gone around a loop. (Kirchhoff’s Voltage Law refers to voltages around a complete loop.) Loops are often marked as a circle or arrow next to the conductor path they represent. Simple and series circuits have only one loop. Two points to remember are:

1. The order of connection of series or parallel loads does not change the operation of a circuit. (However, order may be an important consideration in compound or complex connected circuits.) 2. The manner in which nodes connect to loads does not change the operation of a circuit.

1.37.5  Simple circuit analysis The analysis of simple circuits requires nothing but Ohm’s Law and perhaps the power rule to calculate the values. However, as circuits become more complicated, so does the process of analysing them.

1.38   Factors affecting resistance 1.38.1  Electrical resistance Electrical resistance is defined as ‘the opposition to current flow’. When considering the factors that affect resistance, two categories of materials must be recognised. Ohmic materials are those that have a fixed resistance regardless of the applied voltage. The voltage-versuscurrent graph will be a straight line showing a constant resistance value. (As most common resistors are ohmic resistors, the word ‘ohmic’ is generally not mentioned.) 59

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In electronics, non-ohmic resistors change their resistance according to some other parameter such as applied voltage, pressure or temperature. (Again, the particular type of resistor is named but the term ‘non-ohmic’ is not usually used.) Examples of non-ohmic resistors are tungsten lamp elements, photo-resistors, voltage-dependent resistors and temperature-sensitive resistors. All parts of an electric circuit (the supply source, the conductors and the load) offer resistance to current flow. Even the chemicals inside a battery have resistance that changes with temperature, state of charge and the gases dissolved in the electrolyte. To understand resistance, and therefore electric circuits, it is necessary to understand that resistance is most commonly determined by four factors:

1. length 2. cross-sectional area 3. type of material 4. temperature.

1.38.2 Length Electrical resistance is associated with the collisions between moving electrons (the electric current) and the atoms of the conducting material. As with driving down a road, the risk of having a collision increases the further one travels. In fact, travelling twice the distance doubles the risk of a collision. So, the resistance of a conductor is proportional to its length. This can be stated as R α l. This can be proved quite simply by measuring the resistance of the active conductor in a 100 m roll of 1 mm2 cable (it should be about 1.7 Ω). Then measure the resistance of the neutral conductor (again, about 1.7 Ω). Finally, measure the resistance of both the active and neutral conductors joined together at one end of the roll (i.e. now 200 m of wire). The resistance should be twice the resistance of either wire, as the total length is twice as long (approximately 3.4 Ω, or twice what was measured for one wire).

1.38.3  Cross-sectional area (CSA) The roll of cable used above should be labelled ‘CSA = 1 mm2’. That is the area of the end of the wire if it is cut across at 90°, which is known as the ‘cross-section’ of the wire. The area of the cross-section is called the ‘crosssectional area’ or ‘CSA’ (not to be confused with the diameter). If the CSA is doubled, it is easy to imagine that more electrons can pass easily down the wire, and therefore it will have less resistance. The resistance is said to be proportional to the inverse of the CSA. In other words, as the 1 CSA increases, the resistance decreases, so R α __ ​​    ​​. A Using the roll of cable again and knowing the resistance of the conductors, connect both ends (which is the same as increasing the CSA to 2 mm2, or double what it was). The resistance of 100 m of 2 mm2 wire should be half the resistance of one wire (approximately 0.85 Ω).

1.38.4  Type of material (resistivity) The effects of the length and CSA of the conductors are easy to prove, as shown above, assuming that the figures measured were reasonably close to those predicted. So how can the resistance values be predicted? The copper used to make the wire has a known value of resistance. A cube of copper 1 m on each side has a resistance approximately 1.7 × 108 Ω. That is a very small resistance for a large lump of copper (around 9 tonnes), so a more manageable size is used. This would be a size such as 100 m of wire with a constant CSA of 1 mm2, which will have a resistance of 1.7241 Ω. The standard of one square metre of material one metre long is based on the SI system, but no lab would attempt to measure the resistance of such a large lump of material. Instead, a sample such as our 100 m of 1 mm2 is used and

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the resistivity is calculated mathematically. (Resistivity is given the Greek letter ‘rho’ (ρ, pronounced ‘roe’), which looks like a rounded ‘p’.) So R α ρ Resistivity of a material is defined as the resistance between the opposite faces of a 1 m cube at a specified temperature (e.g. 25°C) RA So ρ = ​​___  ​​   l or transposing to define R: ρl R = ​​__ ​​  A where ρ = resistivity. Knowing the resistivity of any material, the resistance of any conductor can be calculated, due allowances being made for temperature differences where necessary. In Table 1.5, some electrical materials are listed together with their resistivity values. A(m2) The values in the table are given in ohm-metres because the formula R(Ω) × ​​______ ​​,   when simplified, becomes:​​ l(m) 2 2 Ω​ m ​​  ​ Ω​ m ​​  ​ ____  ​​  = ____ ​​  ​​  = Ω ​ m​. m m The resistivity also changes, depending on whether the material is mechanically hard or soft. Annealed copper (copper which has been heated to make it more flexible) has a higher resistivity than hard copper. The resistivity of a conductor also depends on the purity of the material and the nature of any gaseous inclusions in the material. Hi-fi speaker installers pay higher prices for ‘oxygen-free’ speaker leads. Table 1.5 shows that silver has the least resistance, closely followed by copper, but copper is less expensive than silver so it is used extensively as an electrical conductor. The four materials listed at the end of the table are alloys that are generally used for making resistors; that is, they restrict the flow of electricity far more than those above them.

When calculating the resistance of a solid material, there are 1000 × 1000 square millimetres in a square metre, 1 m 2 = 1 × 106 mm2.

Table 1.5   Resistivity of selected materials Conductor

Resistivity (ρ) @ 20°C

Use

Aluminium

2.83 × 10−8 Ωm

Pure metals used for conductors

Copper

1.72 × 10−8 Ωm

Gold

2.44 × 10−8 Ωm

Lead

2.04 × 10−8 Ωm

Platinum

10.09 × 10−8 Ωm

Silver

1.63 × 10−8 Ωm

German silver

33 × 10−8 Ωm

Advance

49 × 10−8 Ωm

Manganin

48 × 10−8 Ωm

Nichrome

112 × 10−8 Ωm

Alloys used as resistance wire

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EXAMPLE 1.11 Find the resistance of a copper cable 500 m in length if it has a cross-sectional area of 2.5 mm2. Take the resistivity of copper to be 1.72 × 10−8 Ω/m. Note that 2.5 mm2 is 2.5 × 10−6 m2. ρl R = __ ​   ​  A

(1)

​​ ​      ​  1.72 × 10 ​  ​  −8 × 500​  ​​​ ​ = ____________ ​        ​ (2) −6 2.5 × 10 ​ = 3.44 Ω​

(3)

EXAMPLE 1.12 To manufacture a 15 Ω resistor from 0.2 mm2 diameter manganin wire, what length of wire is required? πd2 A = ____ ​​ 4 ​​   π × (0.2 × 10−3)2 = _____________ ​​    ​​  4 = 0.0314 mm2 ρl R = __ ​​  ​​  A RA ∴ ​l​ = ___ ​​  ​​   ρ 15 × 0.0314 × 10−6 = ________________ ​​       ​​ 48 × 10−8 = 0.981 m = 981 mm

1.38.5 Temperature In all these calculations, the resistance value is accurate only at 20°C. As the temperature increases or decreases, allowances may have to be made for a change in resistance. For some materials, an increase in temperature causes an increase in resistance. These materials are said to have a ‘positive temperature coefficient’ (PTC). When a material has a lower resistance at higher temperatures, it is said to have a ‘negative temperature coefficient’ (NTC). Some resistors are made from specific materials to take advantage of these characteristics. The temperature coefficient of resistance is defined as the change in resistance per ohm per degree Celsius (or Kelvin). Resistivity values are specified at a particular temperature because resistance can change with temperature. The resistance of most metallic conductors increases with temperature (PTC) and over a limited range. The increase is a linear function of temperature, or very close to it within that range. This leads to what is called the ‘inferred zero’ method of calculating the resistance of conductors at another temperature. The inferred zero value varies for different materials, but the method is illustrated in Figure 1.47. 62

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Resistance

Solve problems in d.c. circuits  Chapter 1

Inferred zero (–234.5°)

0°C

R2 R1

t2 t1 Temperature

Figure 1.47  Effect of temperature on resistance

Copper has an inferred zero resistance at −234.5° C, and the increase of resistance plotted against temperature is basically linear. The resistance of a length of copper wire can be given as a resistance of R0 at 0°C, and the increase in resistance per degree C will continue to be linear through R1 and R2. Therefore, at any temperature significantly above −234.5° C, the resistance can be calculated from any other known resistance at a known temperature. The calculation is a simple ratio: ​R ​  ​​  ​t​  ​​  ___ ​​ 2 ​ proportional ​__2 ​. ​  ​R​  1​​  ​t​  1​​ Temperatures are usually taken as relative to 0°C, so the formula needs to recognise the inferred zero resistance at −234.5°C plus the resistor temperature. 234.5  + ​t​  2​​ ​​R​  2​​ = ​R​  1________ ​​​   ​​  234.5  + ​t​  1​​ where: ​R​  1​​ = resistance at temperature ​t​  1​​     ​​ ​​​ ​R​  2​​ = resistance at temperature ​t​  2​​

EXAMPLE 1.13 The resistance of a coil of copper wire is 34 Ω at 15°C. What would be its resistance at 70°C? 234.5 + ​t​  2​​  ​  ​R​  2​​ = ​R​  1________ ​​​  234.5 + ​t​  1​​

(1)

234.5 + 70 ​ = 34 × ​ ________ ​  (2) 234.5 + 15 ​ ​​     ​  ​  ​  ​  ​  ​  ​​​ ​

304.5 = 34 × ​ _____ ​  249.5

(3)

​

= 41.49 Ω​

(4)

An electric motor may be tested to see how hot the windings become in full load use. To measure the temperature directly would require the motor to be disassembled for a temperature probe to be inserted into the windings, but another method is often used. 63

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The motor winding resistance is measured when the motor is cold and then measured immediately after it is shut down. The temperature can be calculated from the cold temperature and the resistance change of the windings using the formula above.

EXAMPLE 1.14 A motor at 20°C has a winding resistance of 16 Ω. After running up to temperature at full load, the resistance is measured as 24.8 Ω. What is the temperature of the windings? 234.5 + ​t​  2​​ ​R​  2​​ = ​R​  1​​​​ _ ​​​   ​​  ​​​ [234.5 + ​t​  1​​] by transposition : ​ ​

(1) (2)

​R​  ​​ t​ ​  2​​ = __ ​  2 ​  × (234.5 + ​t​  1​​)  − 234.5 (3) R ​ ​​              ​      ​  ​    ​  1​​ ​  ​  ​  ​  ​  ​​​ 24.8 ​ = ____ ​   ​    × (234.5 + 20) − 234.5 16

(4)

​ = 1.55 × 254.5 − 234.5

(5)

​ = 160° C​

(6)

Resistance values can also be calculated from the temperature coefficient of resistance, which is defined as the change in resistance per ohm per degree change in temperature (symbol α, pronounced ‘alfa’). Change in resistance ​per ​​  ∘​C     ​      ​ ​​α = _______________________ ​​ Resistance at ​t​  1​​ Table 1.6 lists a selection of conductors and the temperature coefficients of resistance for those conductors at 0°C and 20°C. For most metals, the change in resistance per ohm per °C is relatively constant, but the coefficient changes as temperature changes. The temperature at which the value of the coefficient is effective is usually given by a subscript to the symbol (e.g. α0 and α20, indicating the temperature coefficients at 0°C and 20°C respectively). Mathematically, the new resistance can be calculated by adding the change in resistance to the original resistance, which in turn is the change in temperature multiplied by the temperature coefficient. ​​R​  2​​ = ​R​  1​​[1  +  α(​t​  2​​  − ​t​  1​​)]​ where: ​R​  1​​ = resistance at temperature ​t​  1​​ ​R ​​    ​  ​  2​​​  =​ ​  resistance at temperature ​t​  2​​​

∘

​​

α = temperature coefficient of resistance  (Ω  /  Ω​/​​  ​C) Table 1.6   Temperature coefficients of resistance Temperature coefficient of resistance (Ω/Ω/°C) Conductor

α0

α20

Aluminium

0.00423

0.0039

Copper

0.00427

0.00393

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Temperature coefficient of resistance (/°C) Gold

0.00368

0.00343

Lead

0.00411

0.0039

Platinum

0.00367

0.0039

Silver

0.004

0.004

Zinc

0.00402

0.004

German silver

0.0004

0.0004

Advance

0.00002

0.00002

Manganin

0.00001

0.00001

Nichrome

0.0002

0.0002

EXAMPLE 1.15 A 2.5 mm2 copper conductor has a resistance of 0.241 Ω at an ambient temperature of 20°C. Find its resistance at 75°C. ​R​  2​​ = ​R​  1​​[1  + α (​t​  2​​  − ​t​  1​​)] ​

(1)

= 0.241 × [1 + 0.00393 × (75 − 20)]

(2)

​ = 0.241 × [1 + 0.00393 ×  55 ] (3) ​ ​​      ​  ​  ​  ​ ​  ​  ​  ​  ​ ​ = 0.241 × [1 +  0.23485 ] (4) ​ ​​​

= 0.241 × 1.21615

(5)

= 0.293 Ω​

(6)

Do the sums in the brackets first.

EXAMPLE 1.16 Copper conductors of 2.5 mm2 cross-sectional area are supplying a current of 15 A to an air-conditioner. If the conductors have a total resistance of 0.43 Ω, calculate the power lost in the conductors. P = I​​​  2​R

(1)

2

(2) ​ = ​15​​  ​  × 0.43 ​ ​​    ​  ​  ​  ​  ​  ​  ​​​ ​ = 225 × 0.43 (3) ​ = 96.75 W​

(4)

1.38.6 Superconductors Many materials produce an effect known as ‘superconductivity’ when they are cooled below a certain temperature. Even lead is a superconductor at around −256.8°  C. At the critical temperature, electrons can pass through the material with seemingly zero resistance. Other materials, mostly pure metals and some special alloys, have different critical temperatures but exhibit the same total lack of resistance below that temperature. Since a superconductor has no resistance, once a current flow is initiated, the current will continue to flow at the same value without an applied potential. If a conductor has no resistance, then current flow through it generates no heat. If no heat is generated in a conductor, the amount of current passed through it can be increased far beyond normal values. 65

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The current flowing through a superconductor creates a magnetic field that becomes equal and opposite to any applied magnetic field, with the result that extremely powerful electromagnets can be constructed. Research has been carried out for many years to try to produce a superconductor effect at higher temperatures. Although breakthroughs could occur at any time, at the time of writing superconductors still need to be chilled to temperatures well below freezing point, below the temperatures where most gases become liquids. Although materials may be made superconductive, it has been discovered that their current capacity is not unlimited and current over a certain level destroys the superconductivity.

1.38.7  Superconductor applications Magnetic levitation  Japan and other countries are investigating the use of superconductors to levitate electric trains. The use of ceramic magnets operating in liquid nitrogen allows very strong electromagnetic fields to support the trains so that they float above their tracks. With no friction, they can travel much faster and more quietly than conventional trains.

Magnetic resonance imaging (MRI)  Powerful electromagnets are used to excite atoms, which then give off tell-tale radio frequencies that are used to generate images of the human body in far greater detail than any X-ray technology.

Particle accelerators  Extremely strong magnets are used to accelerate atomic particles to very high speeds and energy levels, in order to smash atoms into their parts for study by physicists.

1.39  Effects of resistance on the current-carrying capacity and voltage drop in cables 1.39.1  Current-carrying capacity

ρl For each size of conductor, there is a value of resistance ( ​​ R = ​__ ​ )​​, so the power-loss-per-unit length will depend on A the current passing through the cable. The heat produced causes the conductor temperature to rise and if it exceeds the temperature rating of the cable, the insulation can be damaged. Depending on the installation, heat may not be dissipated and a fire could result. As the current flowing through the conductor generates heat, standards have been determined which govern the maximum amount of current that can be allowed to flow in a conductor in an installation. A conductor in the open air can lose heat more readily than if it were one of several conductors in a conduit, all generating heat. Standards Australia recommends current-carrying values for conductors, and these are listed in the Australian Wiring Rules, which are generally adopted throughout Australia.

EXAMPLE 1.17 If 1000 m of copper cable has a resistance of 1.35 Ω, what is the resistance of 100 m of the same cable? R is proportional to length, 1000 m is 10 × 100 m, 

(1)

R​  2​​ is 10  × 1.35 Ω  (2)​​​ ​​∴ ​      ​  ​  ​     = ​13.5 Ω   ​ (3) ¯¯ 66

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1.39.2  Voltage drop in conductors In Example 1.16, power loss due to conductor resistance was mentioned. Associated with this is a voltage drop (Ohm’s Law, V = IR). Standards Australia publication AS/NZS 3000 stipulates the maximum conductor voltage drop. The rule states that it is not to exceed 5% of the supply voltage. This means that, on a 230 V supply, 11.5 V is the maximum allowable voltage drop.

EXAMPLE 1.18 In Example 1.16, where the conductor resistance is 0.43 Ω and the current is 15A. V = IR, the voltage drop is equal to 15 × 0.43 or 6.45 V (less than 11.5 V so the circuit is acceptable). If the circuit run is 25 m long, what is the voltage drop per metre? How long could the cable run be before the allowable voltage drop was exceeded on a 230 V supply? ​V​  d​​ ​V​  dm​​ = ______ ​     ​  Length

(1)

6.45   = ____ ​   ​    25

(2)

  = 0.258 V/ m

(3)

​ ​  d​​ = ​V​  dm​​  × Length V (4)       ​​               ​  ​  ​  ​  ​  ​  ​  ​  ​  ​  ​​​ by transposition : ​ ​ (5) ​V​  ​​ Length = ____ ​  d  ​  ​V​  dm​​

(6)

11.5   = _____ ​     ​  0.258

(7)

  = 46.5 m

(8)

1.39.3  Resistance tables Conductor resistance can be established comparatively easily by reference to appropriate tables such as those found in AS/NZS 3008.1. Nominal resistance is given in ohms per 1000 metres of cable and, by proportionate scaling either up or down, the resistance of any particular length of conductor can be obtained. For example, for 10 mm2 cable, the resistance of 1000 m is 1.79 Ω. The resistance of 100 m would then be 0.179 Ω. Do not identify the values expressed in AS/NZS 3008.1 with the value given for the resistivity of copper in Table 1.5. The resistivity value given in the table is for 100% pure copper, while the purity of commercial copper conductors is in the region of 95%. Effectively, the resistance of electrical cables is about 4 to 5% higher than that of pure copper at the same temperature.

1.40   Selecting an appropriate meter 1.40.1  Selection of instruments Electricians’ instruments must be rated for the type of work they intend to use them for. It is pointless buying an instrument intended for use on model aeroplanes as a hobby or for automotive use on 12 V systems if you are working on 230/400 V distribution systems. Electrical technicians working in rough environments such as mining or other tough industries should obtain a pouch and/or protective shroud to protect their instruments. A broken $1000 (or more) instrument is worthless, especially when someone’s life is at stake. 67

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1.40.2 Accuracy One of the first decisions to make in selecting an instrument is the accuracy required. Precision instruments are excellent but the extra cost and care required does not always justify their use. Most meters have their accuracy inscribed on their face and, when in use, this is a ready reference for the reliability of any readings indicated.

1.40.3 Sensitivity A meter with high sensitivity is not necessarily an ideal meter for all situations. For example, consider a 10 kW three-phase motor that refuses to start. Using a multimeter with a sensitivity of 20 kΩ/V on the 300 V scale, a check at the starter for voltage has been known to yield the following results:

∙ Phase 1: 230 V to earth (or neutral) ∙ Phase 2: 200 V to earth ∙ Phase 3: 230 V to earth.

An obvious conclusion would be that while Phase 2 is low on voltage and therefore suspect, the circuit is complete. A ‘volt stick’ non-contact voltage tester would simply glow and indicate that all three phases were present and correct. Further checks could reveal the cause of the fault as a blown fuse and that the voltage found on Phase 2 (200 V) was the result of feedback through electrical components of the starter circuit. Less sensitive equipment such as a pair of test lamps could have indicated a loss of voltage at the 1 mA (a) 50 kΩ beginning. In many a.c. circuits where substantial currents may be drawn, less sensitive test equipment has many advantages. R For electronic circuits where the currents 200 kΩ L 250 V drawn are often measured in milliamperes (or even microamperes), a sensitive meter must be used to avoid loading the circuit and thus obtaining misleading results. There can be no hard and fast rule regarding test V = 250 = I= 1 mA R total 250 kΩ equipment, but the technician must be alert to the 200 kΩ : V = IR possibilities that data obtained may be incorrect if = 1 mA × 200 KΩ = 200 V the wrong equipment is used.

1.40.4  Internal impedance

1.84 mA

(b)

50 KΩ

250 V

200 KΩ RL

Multimeter : 500 Ω/V on 300 V range = 150 KΩ

R total = 135.7 KΩ ∴I

=

V = 250 = 1.84 mA 135.7 R

V50k = IR = 1.84 × 50 = 92 V Vm= 250 − 92 = 158 V

Figure 1.48  Loading a circuit with a voltmeter

V

On most power circuits internal impedance is of minor importance, but in some circumstances it can affect instrument readings considerably. Any current drawn in the meter must be very small in relation to any current flowing in the circuit being measured. In the circuit shown in Figure 1.48 (a), the current flowing is 1 mA and the voltage across the load RL is 200 V. In Figure 1.48 (b), a voltmeter is connected across the load. Calculations will show that the circuit current increases to 1.84 mA and the voltage across the parallel section drops to 158 V. The result is a misleading value, some 21% lower than the true value. The incorrect reading is not due to the meter but to an incorrect application.

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1.40.5  Reading position If a meter is calibrated to be read in a horizontal position, it should be read in that position for the best results. When the readings are read in any other position, they must be treated with caution. Similarly, the same conditions apply where meters are calibrated to be mounted on magnetic or nonmagnetic panels.

1.40.6  Meter ranges Where possible, meters should be chosen so that indicated values are read well up the scale. A Figure 1.49  Type A probe leads 2% tolerance in accuracy is proportionately a far greater value at a lower scale reading than at full scale. An additional consideration is the linearity of the scale. Lower-scale values can be read reasonably well on the linear scale of a moving-coil meter, but on the movingiron or dynamometer movements, the lower part of the scale is suspect in its accuracy. Because of this, it is often left blank.

1.40.7 Probes Good quality probes, sometimes referred to as ‘Type A’ probes, have the following features: silicone insulation on the highly flexible leads; shrouded connectors that cannot allow contact with live parts, even when partially withdrawn; a guard ring to prevent fingers from slipping down the barrel to live parts being measured; and HRCfused probes to prevent fault current flashovers on switchboards (see Figure 1.49).

1.41  Measuring resistance using direct, volt-ammeter and bridge methods 1.41.1 Ohmmeters There are two basic types of ohmmeter circuits: series and parallel. Their name relates to the position of the unknown resistance in the circuit. A series circuit has the unknown resistor connected in series with the meter. A parallel ohmmeter circuit has the unknown resistor connected in parallel with the meter. Each connection has its own advantages. Both circuits can give continuity checks as well as indicate relative values of resistance. Unlike the continuity testers mentioned above, no audible or visual indication is given. A meter scale has to be read.

Ω 50 µA 5 kΩ

30 kΩ

25 kΩ

3V

(a) Circuit

Test probes

300 kΩ

60 kΩ

∞

0Ω

Ω

1.41.2  Series ohmmeters The series circuit type is the more common ohmmeter and is shown in Figure 1.50 (a). It consists of a battery, a fixed resistor and an adjustable resistor.

(b) Meter scale

Figure 1.50  Simplified circuit for a series ohmmeter

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The fixed resistor is a current-limiting resistor to provide some form of protection for the meter. It is often called a ‘ballast resistor’. Figure 1.50 (b) shows that the meter scale is the reverse of that of a normal scale. Zero ohms (0 Ω) is indicated at full-scale deflection and infinity at the zero end. The scale is non-linear. In use, the meter must be adjusted to indicate zero before switching on, and then the probes joined together and the meter adjusted to read full scale. When the probes are open-circuited, the meter reading will fall to zero again. The unknown resistor is then placed in contact with the probes and the value read against the meter scale. For the values shown in Figure 1.50, the meter would indicate a resistance of 60 kΩ at half-scale or 25 μA meter current. At 10 μA, the indicated resistance would be 300 kΩ. Both values are shown on the meter scale.

1.41.3  Parallel ohmmeters A typical circuit for a parallel ohmmeter is shown in Figure 1.51 (a). It includes a switch to ensure that the battery is not left on when the meter is not in use. This is usually done with some type of trigger or finger-operated switch. The idea is that, when the leads are put down, the battery is automatically switched off. The same operating adjustments have to be made as for the series meter to ensure that zero and full-scale deflections occur at the correct scale positions. When the probes short out the meter, it should indicate zero. When the probes are open circuited, the meter should read full-scale deflection. The meter scale is shown in Figure 1.51 (b). It is also non-linear but the values progress across it in the normal manner. For comparison purposes, the indicated position for the 60 kΩ resistor is marked on the scale at a position corresponding to 46 μA. Half-scale or 25 μA then corresponds to 5 kΩ. The 300 kΩ position is not shown but corresponds to a current of 49.2 μA. This would be indistinguishable from a full-scale reading. If the two half-scale values are compared, it can be seen that the parallel-type circuit is better suited to lower values of resistance than the series-type circuit. The parallel-type circuit is less popular and is used for measuring lower values of resistance than the series-type circuit. It does not readily lend itself to being part of a multimeter circuit as the series-type resistance circuit does.

1.41.4  Resistance-measuring circuits In Section 1.53, both parallel and series ohmmeter circuits will be introduced as a means of determining values of resistance. But both circuits have limits beyond which their accuracy is questionable. Parallel ohmmeter circuits perform better than series circuits for low values of resistance, but as 50 µA 5 kΩ resistance values get lower still, errors can creep in. The resistance of the terminal connections and the 30 kΩ 25 kΩ leads connecting the resistor under test begin to have Test probes an appreciable effect. 3V Similarly, the series ohmmeter circuit outperforms the parallel circuit for higher values of resistance, but (a) Circuit as resistance values increase, the current flowing through the resistor and the meter decreases. A point 5 kΩ 60 kΩ is eventually reached where the meter is no longer 0Ω ∞ able to indicate a value accurately. Ω

(b) Meter scale

Figure 1.51  Parallel ohmmeter

1.41.5  Volt-ammeter testing For most purposes, a resistance measurement can be obtained with sufficient accuracy by passing current through the resistor under test and simultaneously measuring both the current through and the voltage

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A

A

V

Rx

(a)

Rx

V

(b)

Figure 1.52  Volt-ammeter circuits for determining an unknown resistance

across it. The resistance is then calculated by applying Ohm’s Law. For greater accuracy, care must be taken in the connection of the circuit. Figure 1.52 shows two possible circuits. In Figure 1.52 (a), the ammeter will measure the current flowing through the voltmeter as well as that through the resistor. If the resistor has a comparatively low value of resistance when compared to the voltmeter resistance, the discrepancy in ammeter reading can be ignored. For example, if the current flowing through the resistor is, say, 1 A and the current flowing through the voltmeter is 50 μA, the ammeter is unable to discriminate between readings of 1 A and 1.00005 A. On the other hand, if the current flowing through the resistor is 100 μA, a suitable ammeter would read a current flow of 150 μA (IR + Im) and an error of appreciable percentage would result. Figure 1.52 (a) is therefore a more suitable circuit for measuring low resistance values. Figure 1.52 (b) shows the voltmeter connected across the supply source. The ammeter now reads only the current flowing through the resistor. With this circuit, the voltmeter reads the supply source or the sum of the voltage drops across the resistor and the ammeter in series, that is, V = Vm + VR. For accuracy, with this circuit the voltage across the resistor must be far greater than the voltage drop across the ammeter. Assuming that the ammeter has a 50 μA movement and the internal resistance is 5 kΩ, the voltage drop across the meter is V = IR = 50 μA × 5000 = 0.25 V. For best results, the potential difference (pd) across the resistor has to be many times this value, that is, a value around 60 V or more. For lower voltage values, the error increases considerably. These methods for obtaining resistance values have serious limitations in both accuracy and versatility. Two meters are employed, which greatly increases the possibilities for introducing errors. Voltages and currents also have to be adjusted to suit resistor and meter ratings. The diagram in Figure 1.52 (a) shows the circuit in general use, provided a good-quality analogue multimeter with a high internal impedance is used. Some analogue multimeters have input impedances of 10 MΩ or higher, and as a consequence the loading on the circuit is minimal. A good-quality digital multimeter can be substituted if it is of sufficient accuracy.

1.41.6  The Wheatstone bridge circuit The Wheatstone bridge circuit was first described by SH Christie in 1833, but was virtually ignored until it was adopted by Sir Charles Wheatstone a decade later. Originally intended for accurate measurement of values of resistance, it was adapted and modified to suit many different circuits that are able to measure other values. Figure 1.53 (a) illustrates the original circuit. It comprises three known resistors with the unknown resistor making up the fourth arm of the bridge. Figure 1.53 (b) shows one modification for measuring inductance and Figure 1.53 (c) is a modification for measuring capacitance. There are many variations of these three circuits, usually named after the people who developed them. All are based on the original bridge circuit. 71

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I2 Rx

Lx R3

R4

Cx

L1

G

G

R1

R2

C1

G

(I 1 + I 2)

I1 R (a) Resistance measurements

(b) Inductance measurements

(c) Capacitance measurements

Figure 1.53  Wheatstone bridge circuits

With good quality equipment, the bridge circuit will measure accurately down to 0.01 Ω. For the standard bridge circuit, this is about its lower limit. Further modifications to the original circuit enable the bridge to be used to measure accurately down to 0.001 Ω. Altering the ratios of resistors R1 and R2 in the arms of the bridge enables resistances of much higher or lower values to be measured. The value of voltage used to supply the bridge is immaterial because the circuit is adjusted correctly when the meter indicates a null, that is, when the meter pointer remains stationary on zero. The bridge is then said to be ‘balanced’. Higher or lower values of voltage mean only that the higher or lower values of current flow through the bridge and make the meter susceptible to possible overload and damage in the unbalanced state. The meter used in the circuit is usually a sensitive moving-coil meter with a centre-zero scale. It is sometimes referred to as a ‘galvanometer’. When the bridge is balanced, the voltage drop across the unknown resistor (Rx in Figure 1.53 (a)) is equal to the voltage drop across resistor R1. This also means that the potentials across resistors R2 and R3 are also equal to each other, that is: At null:

I1R1 = I2Rx

Similarly:

I1R2 = I2R3 I1R1  ____ IR  Dividing (1) by (2): ​​____ ​​ = ​​  2 x     ​​  I1R2  I2R3 Then, cancelling the Is, the equation becomes: R R ___ ​​  1  ​​ = __ ​​  x ​​ R2 R3 R R Rx = _____ ​​  1.  ​​3    R2 In practice, resistance arms R1 and R2 are usually made adjustable in ratios of 0.1, 1, 10, 100 and 1000. This approach enables the bridge circuit’s range to be expanded to cover a wider range of values. It also means that, when using the bridge to measure resistances, multiplying factors might have to be taken into account for calculation purposes. In real-life Wheatstone bridges, the actual values of R1 and R2 might not be known. It is usual to have them labelled as a switch, with its position indicating the ratio between them. Rx is read directly off the values set by the adjustable resistor R3. The value obtained by R3 at the null position is then multiplied or divided by the indicated ratio. The following two examples illustrate the calculations involved in using a bridge circuit. 72

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EXAMPLE 1.19 The resistances on a bridge read R1  =  10  kΩ,  R2  =  1  kΩ and R3  =  3.95  kΩ. Find the value of the resistance being measured. R1 × R3 Rx = ______ ​​  ​​    R2 3950 = 10000 × _____ ​​    ​​  1000 = 39.50 kΩ

EXAMPLE 1.20 The resistances on a bridge read R1 = 100 Ω, R2 = 1000 Ω, and R3 = 68.4 Ω. Find the value of the resistance being measured. R1 × R3 Rx = ______ ​​  ​​    R2 68.4 = 100 × _____ ​​    ​​  1000 = 6.84 kΩ

1.42  Instruments used to measure voltage, current, resistance and insulation resistance This section looks at the principles of operation regarding electrical test instruments and compares analogue instruments with digital instruments. Power measurement was also discussed without explaining how wattmeters (or for that matter ammeters and voltmeters) actually work. Other instruments were barely mentioned because much of the knowledge gained from your studies thus far is required to fully understand the concepts of measuring instruments. With technological advances and a reduction in the cost of reliable digital test devices and instruments, the use of older-style basic indicators has largely been forgotten. However, as they are still available and are, arguably, suited to risky field work, they are discussed in this chapter.

1.42.1  Circuit indicators The simplest form of indicator, or annunciator, is usually a light or lamp, perhaps even an LED that simply glows to show that power is present. An indicator with a flashing function is intended to attract attention and might indicate a problem. In some cases, even a flashing light might not draw enough attention, so an alarm is sounded. This usually announces that something is happening that requires immediate attention, such as a fire or flood, or perhaps an overheating bearing.

1.42.2  Lamp and sound annunciators Examples of the use of a lamp annunciator include a steady glowing-red indicator showing that power is available at the associated equipment, while a beeping sound may tell you that your coffee has been heated in a microwave oven. 73

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A modern motor vehicle is fitted with many indicator lights (and some with sounds such as the turn indicator). Indicator lights provide a visual confirmation of power, while other lights indicate such circumstances as lack of oil pressure, high oil or water temperature, loss of brake fluid and so on. In an aircraft, indicator lights show green when its landing gear is fully up or down and red when in between. Below a critical height, or slower than a critical speed, they flash red and are often accompanied by an audible warning noise. Other indicators announce that the aircraft is close to stalling and thus requires pilot action. These indicators are all meant to attract a pilot’s attention and warn that all is not well and a landing should not be attempted. However, indicators alone cannot prevent an aeroplane landing. They can only warn that a problem exists, for example:

1. 2. 3. 4. 5.

A fuse or circuit breaker has operated. An unsafe condition has occurred. A part, such as a shear pin, has been broken. A level such as oil level is low. Necessary oil pressure is low.

In industry, indicators may be fitted onto an annunciator panel, where all of the potential problems can be monitored with a quick look. Indicators may indicate good conditions as well, such as:

1. 2. 3. 4.

Power is available. The machine is safe to start. A working temperature or pressure has been reached. A motor is running at the correct speed.

Many modern test instruments employ one or more forms of annunciation.

1.42.3  Non-contact testing equipment Electricians often need to know whether power is energised at a location so they can then safely isolate before working on the equipment. While test equipment that connects directly to live circuits must comply with stringent safety guidelines, the industry uses a selection of non-contact testers that can establish when power is an issue.

1.42.4  Electrostatic field detector One form of non-contact detector takes a signal from the electrostatic field generated when a voltage is present. It is therefore more suitable to finding cables and connections that are energised but not taking current.

1.42.5  Electromagnetic field detector Another form of non-contact detector takes a signal from the electromagnetic field generated when current flows. It is therefore more suitable to finding cables and connections that are taking current.

1.42.6  Electromagnetic combined detector A combined detector is the most likely type that the lay person will find today. It uses both methods so it can pick up both voltage and current signals, thus increasing its reliability.

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These types of non-contact test devices typically incorporate either a light or beep function (or a combination of both) to indicate when power is present. But it is important to remember that while a light or beep indicates that power is present, no light or beep may mean that the battery is flat. An electrical technician should always check that the tester is working before relying on it and always treat bare conductors as alive. It is vital to work safely and use gloves. The devices mentioned are commonly referred to as ‘volt sticks’ (see Figure 1.54). Other types of non-contact current instruments will be discussed in detail in Section 1.50.

Figure 1.54  Non-contact volt sticks

1.43   Contact testing equipment 1.43.1  Series test lamps A test lamp is an elementary device that tests for the presence of voltages. It can indicate that the circuit voltage is present and the probability exists that the circuit is intact up to the test point. Series test lamps are antiquated and are not considered to be a safe voltage testing apparatus. However, some older and more experienced electrical workers may still prefer them. Since two different voltages (230 V and 400 V) are often encountered by technicians, the test lamps must be capable of working satisfactorily on the higher voltage. The arrangement is shown in Figure 1.55, where two 230 V, 15 W lamps are connected in series. Occasionally, when 480 V supplies are encountered, the two-lamp unit will still be satisfactory. As these devices are purely a voltage indicator, they are preferred by many older electricians. It is important that the two lamps be identical in both wattage and voltage. When non-identical lamps are used, the smaller wattage lamp is in danger of failing, owing to excessive voltage (the smaller wattage lamp always has the highest voltage across it). As one probe lead is an integral part of the lamp housing, the unit can be held in one hand and only one wandering lead is required (it should be HRC fuse protected). Since potentially lethal voltages are being tested, the leads must be insulated accordingly. Bared ends stripped for actual contact with live terminals should be kept as short as possible to prevent accidental contact with other live terminals. To protect the lamps, they are mounted back-to-back inside a short length of hard opaque plastic. The ends of the tube can be covered or otherwise, as dictated by the user. However, the lamps need to be visible to the user because no audible indication is given. The essential components are lamps made of thin glass with enclosed filaments. To ensure reliability, Figure 1.55  Test lamps consisting of 230 V they must be protected against mechanical damage.

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It is also good practice to test the lamps on a known source of power before accepting that a circuit has no power applied. On 230 V, the lamps will not shine with full brilliance, but for all practical purposes they will be at almost full brilliance on 400 V. With experience, a technician can use lamp brilliance as a rough guide for determination of single and three phase (1 or 3 ). While test lamps are simple and practical pieces of test equipment, their fragility makes them vulnerable and their reliability rather questionable, so always test them on a known source before and after use. As these devices are current-operated, it is advisable to place the first probe lead on what is considered a dead source, for example, earth or neutral; if it is placed on an active, the other probe lead is live and there is a risk of a shock hazard if the operator comes into contact with it. Gloves should be used where necessary.

1.43.2  Single-filament test lamps It is worth mentioning another version of the test lamp, the single-filament test lamp mounted in a protective housing (similar to series test lamps, with a HRC-fused probe lead). These are typically used with 100 W lamps in order to draw sufficient current to prove correct meter rotation on consumers’ premises. They are also used to prove that the correct meter is on the appropriate tariff. The same safety precautions that apply to in-series test lamps should be adhered to.

1.43.3  Vibrating testers Commonly called ‘Wigger’ or ‘Wiggy’ testers, these have been adopted by several manufacturers and made commercially. Rather more substantial and slightly more complex than a pair of lamps in series, they can withstand far rougher handling. Treated correctly, their life expectancy is many years. The construction of one version is shown in Figure 1.56. The coil wound on the spool has an impedance of approximately 2500 Ω and limits the current to less than 100 mA on 230 V. As with low-wattage test lamps, this can be a limiting factor in some circuits. A high seriesresistance fault can easily be missed when testing circuits and equipment with such low currents. With the version shown in Figure 1.56, the test leads and probes are loose and can be easily damaged. In a later model, the body of the tester is rectangular in cross-section. Provision is made for tucking the leads into the body of the unit when it is not in actual use. A third version has one probe built into the body of the unit so that only one probe is free to be shifted from contact point to contact point.

d.c.

a.c.

110

110

220

220

440 500

380 500

Return spring

Window indicator Soft-iron core

Spool

Solenoid coil

(a) Complete assembled unit

(b) Internal construction

Figure 1.56  Vibrating-type voltage tester

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The vibrating tester is relatively small and portable. Its vibration can be both felt and heard. It also gives a visual indication against a scale. In terms of voltage, the reading is only approximate and by no means accurate. It is rugged and reliable, particularly for those engaged in maintenance work where the technician must travel from job to job. The tester reads both a.c. and d.c. up to voltages of 500 V, usually on different scales moulded in its body.

1.43.4  Electronic-based voltage detectors With the advent and development of modern electronics, the vibrating tester has been almost completely superseded by a more compact, battery-powered design that is lighter and small enough to fit comfortably into a shirt pocket. Many later designs do not even have an on/off switch. By touching the ends of the probes together or putting the probe onto a voltage source, they automatically turn themselves on. After a set period of inactivity, they turn off. While not voltmeters, these devices indicate the level of voltage that might be encountered. Generally, they need to be connected to the voltage source, so technically they require gloves if the voltage is expected to be greater than 50 V a.c. Made by several manufacturers, the testers mostly cover both a.c. and d.c. voltages to about 600 V. There are as many variations in design as there are manufacturers. Some register a voltage as a digital readout and might indicate voltage polarity, while others may have different-coloured LED diodes that light up in sequence, according to the approximate voltage. It is important to remember that they indicate, not measure, and should not be used when fault conditions require a higher-category meter. A typical device is shown in Figure 1.57. It is advisable to refer to the manufacturer’s instructions before use as some devices will trip RCDs when testing active to earth. A tester such as the one in Figure 1.57 requires an active-to-neutral test for a short period of time before going active to earth to avoid doing this.

1.43.5  Plug-style testers The plug-style tester is designed for Australian-type standard three-pin sockets. Three neon lamps are mounted in a protective package of hardened plastic. It simply plugs into a three-pin socket, which is then switched on. Various combinations of neon lamps illuminate, indicating the condition of the circuit and the connections to the socket. Figure 1.58 shows some typical lamp conditions when undertaking GPO polarity testing. Since one neon lamp indicates the earthing system, the unit cannot be used in those rare situations where power is supplied through an isolating transformer. At least one model has a push-button installed which, when pressed, activates a leakage current to test any residual current devices installed.

Figure 1.57  Typical electronic-based voltage detector

Correct Faulty earth Live/neutral reversed Neutral fault Faulty live Off

Illuminated

Figure 1.58  Lamp conditions for a three-pin socket tester

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Many instruments used today incorporate a multitude of different test functions that include a plug-style tester. One type of tester that is used commonly by technicians for simplicity as it has a key ring is shown in Figure 1.59. Technicians should always be aware of instruments’ limitations. These devices will not identify a reverse neutral earth because of the MEN system. Therefore, proving correct earthing continuity is essential before placing full trust in observation of the neon lamp indicators.

Figure 1.59  10A socket-outlet

1.44   Neon testers 1.44.1 Screwdrivers Neon testers are antiquated and are not considered to be a safe voltage testing apparatus. However, some older and more experienced electrical workers may still prefer them. Screwdriver neon testers vary in style and size, according to manufacturers’ preferences. Probably the best-known version is the small neon tube with a series resistor moulded into the handle of a screwdriver. Some models have a metal cap on the end of the handle; others do not. The metal end of the screwdriver is placed in contact with the circuit to be tested and the capacitive effect of the user’s hand on the handle provides the return path to earth. The current through the lamp is so small that no electric shock effect is felt. The neon tube will either glow or not. There are no degrees of brilliance and no way of estimating a voltage at the point of contact. In bright sunlight, it is difficult to determine if the neon is glowing at all. As with other neon tube voltage testers, screwdriver neon testers are subject to capacitive and inductive effects. They will occasionally glow in the presence of a radio frequency field radiating from a transmitter without actually being in contact with a circuit.

1.44.2  Other neon light versions Several other variations of the neon tester are available, most using two leads. One model has a neon lamp built into each probe. Under certain conditions, the lamps will light, indicating a voltage when there is merely an inductive or capacitive effect present. Some versions also have fuses built into the probes.

1.44.3  Neon voltage indicators A neon tester comprising four neon lamps was manufactured in an attempt to provide a more accurate voltage indication. The neon lamps had different value series resistors and the tube that emitted light indicated an approximation of the line voltage present. The range was 50 V to 500 V. For example, if two lamps glowed, the indicated voltage would be between 50 V and 250 V. Again, it is worth observing that the makers recommend that the unit is tested on a known power source before relying on its readings.

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1.44.4  Logic probes Another form of voltage tester is the logic probe. With more and more logic circuits being used to control electrical power systems, logic module repair work is becoming more common. The probes are made for specific purposes and cannot be used in general electrical maintenance work as voltage testers. A logic probe can be self-powered with batteries or can be powered by the circuit under test via flexible leads and alligator clips. In general, the probe consists of circuitry driving two light-emitting diodes. One is coloured green, the other red. Logic circuits derive their output voltage from either having a voltage or not having a voltage at specific points in their circuit. These points are classified as being high (logic 1) or low (logic 0), without a specific voltage being meant. For example, the green diode in the probe might glow, indicating that the circuit is low at the point the probe is touching. This simply means that the voltage at that point will be in the range 0.8 V to 1.0 V. The value may be positive or negative. If the probe is touched at a point in the circuit and the red diode glows, then that point in the circuit is classed as high and indicates a voltage of between 2 V and 5 V. The logic probe will operate satisfactorily at 20 MHz, which is a far higher frequency than power line frequencies. The maximum voltage that can be applied to a probe is usually about 100 V.

1.45   Hazards involved in using electrical instruments 1.45.1  Use, selection and category of instruments Modern instruments are far more flexible, robust and reliable than the old analogue ones. They are also generally more frugal on batteries and may be rechargeable. But there are always cheap, alternative-brand instruments on the market. Some barely meet standards, and others do not reach them at all. If it looks cheap, it probably is. Remember, your life may depend on the quality of the instrument. In all cases, make sure that the instrument you intend to use on live equipment has an Australian certificate of approval. It should be tested by a reliable organisation and have a nameplate that says something like ‘complies with IEC 61010’.

1.45.2  Care and protection of instruments In the physical sense, care and protection of instruments implies careful handling, cleanliness and protection from knocks. But in the electrical sense the challenge is more complex. In general, any instrument that is correctly and permanently installed can be expected to operate correctly and have a lengthy service life. Portable meters are subject to possible damage during transportation, and each time they are connected into a circuit, they face possible electrical damage. The permanently installed meter is usually installed only once, while the portable meter is effectively installed each time it is connected into a circuit. Possible causes of damage are:

1. 2. 3. 4.

overload—either current or voltage ranges being exceeded wrong connections—e.g. an ammeter connected across a voltage source d.c. meters connected to an a.c. power source Some meters need a separate power source for their operation and often one of the instrument’s test terminals is permanently earthed. The application of this terminal into a circuit at a point that is not earthed can cause damage to its internal connections. The correct approach is to earth that terminal to the test circuit’s earth and use only one test lead.

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Multimeters are light, compact and have a variety of ranges. These advantages alone explain their popularity as a portable test meter. Because of their portability and number of different ranges, they are susceptible to misuse and damage. Some precautions to take with multimeters are:





1. When checking an unknown voltage (or current), always start with the highest range. If the reading is too low, a quick check will soon show if a lower range is more suitable. The most common reason for damage to multimeters is connecting them into a circuit without prior inspection of their range setting. Many operators disconnect a multimeter from a power source before changing ranges because of the possibility of arcing occurring between contacts during the changeover. 2. Never attempt to take a resistance reading in a circuit that has power applied to it. Similarly, capacitors in a circuit often hold a charge that can damage a meter. They should be short-circuited temporarily after the power source is removed, to discharge them, before using the ohmmeter. 3. A similar problem exists for insulation testers, continuity testers, bridge IR testers and later-model batteryoperated insulation testers. Each has its own inbuilt power supply and any connection to an external power source can lead to destruction through excessive current flow.

1.45.3  Category of use—Cat I to IV CAT IV

CAT III

CAT II

Consumer Figure 1.60  Categories of use of electrical measuring instruments

Voltage transients

Nominal Voltages 3-phase 4 wire systems

3-phase 3 wire systems

Phase to Neutral

Transient stresses estimated within the installation without any over-voltage limiting devices

CAT II 66/115 120/208 120/240 230/400 277/480 400/690

CAT III

CAT IV

50

500

800

1500

120

100

800

1500

2500

240

150

1500

2500

4000

500

300

2500

4000

6000

600

4000

6000

8000

1000

6000

8000

12000

1000

Figure 1.61  Typical voltages and voltage transients of category of equipment

A test lamp was, until recent times, one of the most traditional devices used by electrical technicians. Although they are simple to make, there have been many accidents resulting from inappropriate materials or use. Only test equipment compliant with IEC 61010 (AS 61010) should be used, as recommended by AS/NZS 4836 Safe working on or near lowvoltage electrical installations and equipment. These require instruments that are used on electricity to comply with the standards for one of several levels of safety, Categories I to IV (1 to 4), and for this to be known and written on the instrument as ‘Cat II’, ‘Cat III’ and ‘Cat IV’. Cat I does not require the instrument to be marked, but unmarked instruments must not be used on live low-voltage circuits. Cat II is to be used on final sub-circuits and testing of line voltage appliances. Cat III is suitable for most circuitry within a domestic installation up to the main switchboard. Cat IV is to be used wherever a substantial fault current is possible, in distribution lines and consumers’ mains (see Figure  1.60). Electricians and people employed in other electrotechnology areas where high fault currents are present should always use Cat IV meters. This is mandatory in most industrial sites. Each category can have various voltage limits (generally 600 V or 1000 V), but instruments must be used according to the conditions of the installation. Refer to Figure  1.61 for correct category of use.

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1.46  Operating characteristics of analogue and digital meters 1.46.1  Analogue instruments Analogue meters were invented in the early 1920s as devices that could read multiple functions were required. They usually have a moving needle and can measure continuously changing values quickly and easily.

1.46.2  Moving needle meters Basically, these meters have a needle mounted on the shaft of what is essentially an electric motor that is turned against a restraining spring. The angle the needle reaches on the face of the instrument is proportional to the torque the electric motor produced to turn on its shaft, as a result of the current flowing in the meter. Therefore, the face of the instrument is calibrated to reflect the torque value caused by a certain voltage or current. These meters are discussed in further detail in Section 1.47.

1.46.3  Digital instruments Once transistorised instruments became possible, integrated circuits followed; then computers, or ‘microcontrollers’ as they are known, were used to make even better instruments. Most modern electricians and electronics technicians use electronic instruments, particularly digital multimeters (DMMs). The impedance of older analogue instruments rarely went above 10  MΩ, but even basic digital instruments start at 10  MΩ and go up to 200  MΩ. Some may go much higher. Even at 400 V, a 200 MΩ digital multimeter draws only 2 mA from the circuit. At typical electronics voltages, that would be around 10 to 20 nA, which produces a negligible effect upon the circuit under test.

Figure 1.62  Digital power meter

CPU and LCD driver

1.46.4  A/D or ADC All DMMs require a circuit to convert the analogue value or the real value to a digital measurement of that value. The circuit that does this is called an analogue to digital converter, or A/D converter (ADC for short). There are many ways that this conversion can be done, but essentially the analogue signal is sensed, compared against a table of values and the matching value is sent to the readout or computer. Some instruments have a dedicated integrated circuit that does it all, such as the LM7106 IC found in many DMMs. Others have specially designed and manufactured ‘chip sets’ that may include a computer

ADC Analogue to digital converter

Ohms current source

Rectifier Range switch 10A shunt 200 mA

10 A 200 mA Com 1000 V

Figure 1.63  Block diagram of a typical DMM

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chip. Figure  1.62 shows a typical digital readout display, while Figure  1.63 shows a block diagram of a typical DMM with its various functions. Among the issues associated with DMMs is that they are based on steps, or resolution, so the smaller the resolution, the more values are required to reach a given range. Some of the first ADC devices had 4 bits resolution (24) so could only read 16 different values. A 12 V meter would probably have had a resolution of 1 V. An 8 bit ADC (28) has 256 values, so a voltmeter for the same job would have a resolution of 0.1 V or better. Many common instruments use 12 bit and 14 bit ADCs providing resolutions of 1/4096 of the range, or 1/16384 respectively.

1.46.5  Microprocessor-based instruments Microprocessor-based instruments allow many more functions to be added to the multimeter. These include frequency counters to give frequency measurements up to about 20 MHz, transistor test modes, capacitance measurement, temperature measurement and conversion and many others not generally available to analogue instruments. Microprocessor instruments can often save measurements, pop them up later, send them to a computer or perform data logging functions. Modern microprocessor instruments can also have the ability to connect wirelessly via Bluetooth, Wifi or mobile data. This allows data to be accessed and recorded safely without the need to access live equipment. The data can then be shared with others in both a historical and live format.

1.47  Techniques for reading the scale of an analogue meter 1.47.1  Reading a needle-type meter—parallax error Analogue instruments required a person to be knowledgeable in their use. This was partially because there were often numerous scales whose reading required some mental arithmetic to calculate. It was also due to something called ‘parallax error’. To avoid this, when the operator was taking a reading (especially a reading of a dangerous voltage), they had to read the number that the instrument gave while positioning their eyes so the needle was square to the instrument face. Otherwise, as the needle was (Correct C A B Pointer viewing not actually touching the face but was in front of it, Direct angle) the scale would seem to move as the reader moved Top their head from side to side over the meter. views To establish accuracy, it is necessary to make sure that the reading of a meter scale is taken with the eye vertically above the pointer. Figure 1.64 shows how errors can be made in reading meters by reading the Front views scale from one side or the other. This can also be clearly seen from Figure  1.65, which shows an instrument face photographed from either side and directly in front. It illustrates how the Apparent Apparent Correct reading 5.1 reading 4.9 reading 5.0 reading changes, depending on where the operator is situated. Note the highlighted circles and the Figure 1.64 Parallax readings, from 6.6 V to just over 6.7 V. 82

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Most analogue instruments did not require batteries to read voltage or current but took all the power from the circuit to work. Later instruments used valves, transistors or field-effect transistors (FETs) driven by batteries to reduce the loading on the circuit but loading was still an issue. Analogue instruments were also fragile, and even a slight bump could cause their calibration to change. In addition, their scales had to be examined for the reader to be able to distinguish between major and minor divisions. Figure 1.65  Analogue instrument parallax error

1.48  Types of voltmeters used in the electrotechnology industry 1.48.1  Analogue multimeters An analogue multimeter is a single meter with switching arrangements to connect it as voltmeter, ammeter or ohmmeter. The normal practice is to provide several ranges for each function. Analogue multimeters are known by several names: ‘volt–ohm meter’ (or ‘VOM’), or an ‘ammeter, voltmeter, ohmmeter’ (or ‘AVO’, which is also a registered trade name).

1.48.2  The voltmeter section Figure  1.66 shows a moving coil 50  μA meter with an internal resistance of 5  kΩ connected to a five-position switch. Each switch position connects a different value resistor in series (a multiplier) with the meter 19 995 kΩ to provide a range of voltages. The moving-coil meter movement can only 9995 kΩ read d.c., so some means of rectifying a.c. must be 1000 V 500 V provided. The current trend is to provide half-wave 4995 kΩ 250 V rectification only, so it is imperative to have a second Range + set of meter scales calibrated for half-wave-rectified switch 995 kΩ 50 V alternating voltages. This type of circuit will also read d.c. voltages, so for accuracy it is essential that 10 V 195 kΩ the meter be set on the correct range and voltage. Red probe A circuit showing a meter circuit with five voltage ranges and half-wave rectification is shown in Figure 1.67. For comparison purposes, the same type 50 µA Black of meter is used in both circuits. 5000 Ω V probe

1.48.3  The ammeter section Figure 1.68 shows the same 50 μA meter connected to a five-position switch so that different values of

meter

–

Figure 1.66  Simplified VOM schematic diagram

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shunt resistance can be connected in parallel with the meter. Again, it can operate on only d.c., because of the type of movement.

1.48.4  The ohmmeter section Figure 1.69 shows the 50 μA meter connected in a series ohmmeter circuit. (The circuit from Figure 1.66 has been modified slightly.) The meter still includes a series current-limiting resistor, but meter shunts are incorporated into the switching arrangements. As the resistance range to be used increases in value, so does the 4 987 500 Ω value of the resistor shunting the meter. 1000 V Assuming that the meter is provided with 1 237 500 Ω only one resistance scale, a reading of 2  Ω 250 V while the meter is switched to the ‘R  ×  1’ 237 500 Ω scale will be just that: 2  Ω. If the meter is 50 V AC switched to the ‘R  ×  100’ scale, when the 37 500 Ω volts 10 V scale indicates 2  Ω, the actual value will be 2 Ω × 100 = 200 Ω. 2.5 V The change in values of the shunt resistors Red probe has one important effect on the measuring D1 D2 current. On the lower resistance ranges, the current flowing through the unknown 11 250 Ω 12 500 Ω resistor is much higher in value. On the scale ‘multiplied by one’ or ‘R  ×  1’ range, Black probe for example, the measuring current is well 50 µA V 1666 Ω 5000 Ω in excess of 100 mA. On the ‘R  ×  10  000’ meter range, the current through the resistor being measured is reduced to 15 μA plus the meter Common current, which the meter demands to be a maximum of 50 μA at all times. Figure 1.67  Multi-range a.c. voltmeter The variation in measuring current has both advantages and disadvantages, depending on the circumstances in which the meter Red is being used. Trying to measure a lowprobe resistance semiconductor on the ‘R × 1’ scale, for example, can destroy the device. +

Black probe

Figure 1.68  Multi-range ammeter

1.48.5  The complete multimeter

1 mA 10 mA

A 525.36 Ω

50.25 Ω

100 mA 2.501 Ω

0.500 05 Ω

2

0.050 00 Ω

10 A 500 mA

50 μA 5000 Ω meter

For a complete multimeter, all components are assembled in a container with meter and batteries. In the units described in the three previous sections, the rotary switch would have a minimum of 20 positions. That is, five each for the d.c. volts, a.c. volts, d.c. current and resistance ranges. In this particular case, there would be a need for only two terminals (positive and negative), although the negative terminal is sometimes labelled ‘common’.

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High current ranges can be a cause for concern. 100 000 Ω The meter’s components such as shunt resistors and the 1 R x 10 000 rotary switch must be capable of carrying the current, 10 000 Ω and alternative arrangements are sometimes made R x 1000 by using an extra shunt and terminal (appropriately Red 1000 Ω probe labelled). R x 100 Manufacturers of multimeters make many 100 Ω R x 10 different models, and individual instructions are Runknown supplied with each type. It is a good idea to read and 10 Ω Rx1 absorb these instructions carefully. The most obvious precaution to take with any 50 mA meter is to ensure that it is set to the correct scale for 5000 Ω 15 kΩ the values to be measured. For example, to measure Ω a domestic supply voltage, the meter needs to be set Black probe to a scale that can handle 216.2 to 253 V a.c., and at the same time have an upper scale reading in excess 1.5 V of this figure. 2 100 Ω 1 If the value of the voltage is not known, the meter 2 Radj should be set to the highest possible a.c. scale and only brought down to lower scales after each test, until an adequate reading is obtained. Always leave a meter on Figure 1.69  Typical ohmmeter circuit used in VOMs the highest a.c. voltage scale when it is not in use. Under most conditions, an electrical worker does not need to consider the polarity of ohmmeter terminals. However, those working in the renewable industry, where solar panels and batteries are installed, should ensure that the appropriate d.c. voltage scale is used and polarity is correct. Many meters reverse their polarities when switched to the resistance scales. That is, the red or positive terminal becomes the negative supply lead and the black lead becomes the positive supply lead. This does not apply to all meters so it is essential that the user check the characteristics of the particular instrument. Modern multimeters are quite sensitive and often give a full-scale deflection with a current of microamperes. As a consequence, the resistance of the meter on the voltage ranges is so high that the loading on the circuit being measured can be ignored. Typically, a cheap multimeter on a 200 V d.c. range has a resistance of 20 000 Ω / V so that, on a 300 V full-scale deflection setting, the meter resistance between probes is 6 MΩ. On an a.c. range it is around 10 000 Ω / V. Better meters have resistances on d.c. of 10 MΩ / V and 1 MΩ / V. Figure 1.70 shows a commercially available multimeter. Figure 1.70  Sanwa 460-ED multimeter Range and function selection is with the aid of one rotary switch (sometimes two), usually electrically interlocked.

1.48.6  Digital reading meters With an analogue meter, accuracy depends on the user’s ability to interpret the position of the pointer on the readout scale. Accuracy can be higher with larger meter scales than with smaller scales. On more expensive analogue meters, a mirror scale is provided to help align the eye vertically with it, reducing the possibility of parallax error. 85

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A digital meter gives greater resolution, removes possible doubts about the correctness of a reading and provides excellent accuracy. (An analogue meter will respond more quickly to a change in values.) Digital meters can be read accurately by untrained people, and this avoids the confusion that is possible with the multiple scales on an analogue multimeter. A digital multimeter is similar to an analogue multimeter, the only major difference being that the meter movement is replaced with a digital converter. This is an electronic circuit that replaces the meter function and drives the components that make up the digits.

1.48.7  Digital voltmeters The basic digital meter always responds to a voltage. A typical range might be 0 to 200 mV. To use it as a multimeter, the appropriate multipliers and shunts are connected around the converter and the digital readout. Figure 1.71 shows the circuit for an elementary digital voltmeter in block diagram form. The probes are placed across a voltage, and multiplying resistors reduce the voltage according to the values selected by the range switch. The output is connected to a converter, which processes the voltage value and sends output signals to the appropriate bars of the display.

1.48.8  Readout display In most digital multimeters, each numeral in a display group is made up of a maximum of seven bars. However, more expensive graphical displays (with multiple pixels) are available. These allow for a greater diversity of information, including words and diagrams, to be displayed. Full scale is usually specified as 199 or 1999 and increases in multiples of 10 (‘decades’) as the number of digits is increased. A 199 display can also be described as a ‘2½-digit display’. Similarly, the 1999 display is sometimes called a ‘3½-digit display’. Originally, the range required had to be selected, and the decimal point shifted itself along the display accordingly. Figure 1.72 illustrates the circuit in a meter of this type. Modern digital displays are auto-ranging and the decimal point shifts along to suit the input, making the electronic circuits more complex. The only adjustment is to select the resistance, current or voltage function; everything else is done automatically. Even the polarity of d.c. voltages and currents is catered for with suitable indicators. Digit sizes can range from 5 mm to 12 mm or larger, depending on the manufacturer and the targeted use of the meter. Display size can be important, for example, when a reading has to be made from a distance. The LCD display generally has a back-lit function to allow it to be read in low light. The screen is temperature dependent, and if the display gets too hot in direct sunlight, the whole screen goes either blank or black and cannot be read. Permanent damage can occur under these conditions.

×1000 200 V ×100 20 V

1.48.9  Digital multimeters

Voltmeter Module 200mV 10 MΩ

ADC

×10 2V ×1 200 mV

X1 Buffer

Isolation

Figure 1.71  Digital voltmeter circuit principles

Modern digital multimeter circuits are far more complicated than analogue meter circuits, so only a basic circuit has been shown in Figure 1.72. With this circuit, the range and type of measurement has to be selected by the user. However, it illustrates the principles behind the operation of this kind of meter. Digital multimeter inputs are made up by an input attenuator and a function selection switch. The attenuator is sometimes automated and combines with the auto-range function. The converter and digital readout

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100 mV

+

1V Voltmeter 10 V attenuator 100 V

Input amplifier

Rectifier circuits

1000 V 100 μA 1 mA a.c. / d.c. ammeter 10 mA shunts 100 mA 1A 100 Ω 1 kΩ Ohmmeter 10 kΩ circuits 100 kΩ

Analogue-to-digital converter

1 MΩ

Figure 1.72  Digital multimeter circuit principles

are not always sensitive enough for multimeter use, so an amplifier is often provided. It serves the additional function of providing isolation between the converter and the attenuator. This prevents possible loading of the circuit being tested.

1.48.10  Comparison of digital and analogue meters

1. For normal operation, the digital instrument is more accurate. The more expensive the meter, the greater the accuracy. 2. Both types need an internal battery source of power. 3. Both types use a rectifier to convert a.c. to d.c., but the analogue meter has to use a separate scale for a.c. voltages. The digital meter has to have a correcting circuit to compensate for this. 4. Ohmmeter functions in an analogue meter use a non-linear scale. The digital meter has no scale and its nonlinear tendency has to be corrected with a special constant-current circuit. 5. The input impedance of a digital meter is far higher than that of an analogue-type meter circuit; for an analogue meter it may be 20 kΩ / V, while for a digital meter it may be 20 MΩ / V. This means less interference or effect on the circuit being tested. 6. A digital multimeter is subject to large errors in the presence of a radio-frequency field. Usually, this has minimal effect on an analogue meter. 7. The digital meter is far more sensitive to circuit conditions than the analogue meter. In some circumstances, this can result in misleading readings. 8. Analogue meters used on resistance readings can have negative polarities (from the internal battery) on the positive probe. This has to be checked before use because of possible directional errors in current-sensitive devices such as diodes. Digital meters on the other hand have constant polarities on the resistance ranges and cause no confusion. 9. An analogue meter is more responsive to changing values than a digital instrument. Because of its circuit configuration, the digital device takes an appreciably longer time to respond to the new value and settle again. 87

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1.49   Non-contact testing instruments Meters have been made for testing for voltages and currents that make no electrical contact with the circuit under test. Several versions are available.

1.49.1  Voltage testers A commercially made unit that senses voltage and does not rely on lamps or vibrating solenoids is a device sensitive to the electrostatic fields produced by the circuit voltage. It is the basis of the finder used to locate live conductors buried in walls up to a depth of 2.5 cm. Most units give both audible and visual signals. (These were shown earlier in Figure 1.54.)

1.49.2  Current testers Current testers are marketed under various names, including ‘tong testers’, ‘clamp meters’, ‘clip-on testers’ and ‘link test meters’. Clamp action meters are generally used to measure currents without having to interrupt the circuit being tested. Most meters have accuracies within 1% of full-scale deflection and on frequencies ranging from direct current (f = 0) to about 1 kHz. Originally there were only two types. One worked on the repulsion principle of the movingiron meter while the other used a transformer combined with a switch to select the desired current ranges. These can still be obtained, but many other versions are now available.

1.49.3  Repulsion-type movement (a.c. and d.c.) The operating principle was that of the moving-iron meter. A variety of current ranges was catered for with plugin modules. When placed around the conductor to be measured, the magnetic field created by the current set up repulsion between the meter elements and caused the moving section with the pointer attached to rotate. They could be used on both a.c. and d.c..

1.49.4  Transformer operated (a.c. only) Different current ranges were catered for by using a transformer with tappings connected to a range switch. The basic principle is shown in Figure 1.73. The transformer prevented it being used on d.c.. The indicating meter could be a d.c.-operated meter if a rectifying unit was connected between the transformer output and the meter movement. With a d.c. meter, the scale became linear. With a moving-iron meter, the scale was non-linear. The instrument’s jaws were opened with a lever, placed around the chosen conductor and then allowed to close. The magnetic field around the conductor entered the low permeability path of the iron and the meter movement responded according to the strength of that magnetic field. A

Figure 1.73  Internal circuit arrangement of a current transformer

1.49.5  Modern versions Modern versions can be switched to indicate peak, RMS and average values for many different waveforms, as well as d.c. values. Some models will also indicate circuit voltage by measuring the strength of the electrostatic field around the conductor (the ‘Hall effect’).

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The number of available functions on any one meter has a considerable influence on its price. The range of options is impressive, and instruments with digital readouts and auto-ranging facilities are popular. Two testers are illustrated in Figure  1.74, both with a finger-operated trigger. In Figure 1.74(a), a digital readout model is illustrated. It is auto-ranging and will read currents in the range 2 A to 2000 A a.c. It can also be used to measure voltages, both a.c. and d.c., and resistance values of 40  kΩ with a pair of plug-in test leads. The unit in Figure 1.74(b) has an analogue readout and a pointer that has to be read against a scale. Varying ranges are provided by a series of scales, Figure 1.74(a)  Non-intrusive ammeter—digital clamp meter which are rolled around in a window. It is an a.c.only instrument and reads up to a maximum of 500 A. To read voltages or resistance values, test leads are plugged into the base of the unit. A replaceable battery is enclosed and the meter is protected by a fast-acting fuse. Other clamp-on meter movements use a Halleffect device to detect the presence and quantity of current flowing. This phenomenon was first recorded in 1879, but its use has only become practical with the development of integrated-circuit modules. When a current is passed through the opposite Figure 1.74(b)  Non-intrusive ammeter—analogue clamp meter edges of a thin piece of foil, a magnetic field applied at right angles to the current will produce a voltage across the remaining two edges. This voltage is proportional to the current flow through the piece of foil. By maintaining a constant current flow, the voltage produced is directly proportional to the strength of the magnetic field. When the magnetic field is the result of a current flowing through a conductor, the device effectively becomes an ammeter. Electronic circuitry has to be employed to maintain a constant current flow and to measure and amplify the voltage produced. A separate power supply (usually batteries) must also be used. The method is an excellent and accurate one, but the additional components tend to make a meter of this type expensive. Models can be obtained in current ranges from milliamps to 2000 A. Their sensitivity to low values of current and their accuracy make them ideal for measuring leakage currents. Some clamp meters can also measure extremely high currents via a flexible cable current probe which wraps around large conductors. This allows for current readings greater than 1 kA to be measured.

1.50   Using and selecting an appropriate meter 1.50.1  Use of instruments Only use instruments as their manufacturer intended. A 600 V-rated meter might mean 600 V peak. The peak of 400 V is around 695 V. Check relevant information and only use instruments within their safety limits and tolerances. 89

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The measurement of any quantity consists basically of its comparison with a known value. The comparison also means that the value is being compared either directly or indirectly with a standard whose accuracy is known. The degree of accuracy of an instrument generally falls into one of two categories.

Precision instruments Sometimes known as ‘reference instruments’, precision instruments are usually kept in laboratories and other instruments are taken to them for calibration purposes. As a general guide, errors are of the order of ± 0.5% or less of the full-scale deflection (FSD) reading; but they can be many times less than this, and can approach ± 0.000 01%, depending on the degree of accuracy required. Every precaution is taken to minimise error and maintain high standards of accuracy.

Industrial instruments With industrial instruments, the object is to secure results that are reliable and reasonably accurate. The error is usually greater than 0.5 per cent and up to 2.5 per cent. Modern trends and production methods are gradually reducing this value.

1.51   Resistance measurement 1.51.1  Insulation resistance In practical terms, a battery-operated circuit as described in Example 1.20 is not convenient, accurate or practical for measuring very high values of resistance. A high voltage is required to ensure that a reasonable amount of current can flow in the circuit being tested. This is necessary to enable a meter to give a more positive indication. Australian Standards specify minimum voltages for testing circuits, which approximately equates to double the operating voltage of the circuit. That is, on a 230 V circuit, the specified test voltage is 500 V. If testing between phases, 1000 V should be applied. Probably the first maker of an instrument for tests of this nature was an English firm known today as Megger Instruments Ltd. (The original name was Evershed and Vignoles and the trade name for the unit was ‘Megger’. This trade name has become a generic term for instruments of this type.) Other firms manufacture similar test instruments and all should be considered as insulation testers. There are two general arrangements for obtaining the necessary voltages: a hand-cranked generator, or dry cells and an electronic circuit.

1.51.2  Battery-powered insulation testers (IR testers) Modern instruments use a bank of dry cells to energise an electronic circuit. The output from this circuit is highvoltage, high-frequency a.c., which is then rectified and used to operate the instrument. The complete unit is usually much smaller and lighter than a generator-powered instrument, but care must be taken to ensure that the batteries are in good condition for satisfactory operation of the tester. Once a suitable value of d.c. voltage is obtained, the operation of the unit is much the same as that of the generator-powered model. The normal operating resistance range is 0 to 200 MΩ. Standard models are available in voltages of 100 V, 250 V, 500 V or 1000 V, and accuracy is equivalent to that of the hand-cranked IR tester. As the instruments are battery powered, it is normal for one of the test probes to include a switch that must be held down while the instrument is actually in operation. On release of the probe, the battery is disconnected. The voltage in modern insulation testers is generated by an internal switched power supply (or inverter circuit), which can generate high voltages from a set of 1.5 V cells. Later models of the battery-powered insulation testers have digital readouts. The readout is supplied directly with power from the batteries. 90

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It is the responsibility of the person undertaking the test not to damage any vulnerable equipment, particularly items with electronic components. As there is such a variety of these testers, the type used is usually a matter of personal preference.

1.51.3  Bridge meggers

Control coil circuit

R

Deflection coil circuit

N

R

R

G

Several variations of the basic IR tester circuit have Test Rx been produced. One includes a built-in bridge circuit S terminals for measurement of lower values of resistance. The instrument is much larger, heavier and more expensive than the IR tester described previously. A circuit of a bridge IR tester is shown in Figure 1.75. Figure 1.75  Basic bridge IR tester circuit It can be seen that adjustable resistors are connected into the circuit. This is achieved with the aid of the switches on the side of the instrument housing (see Figure 1.76). On the top surface are the four rotary switches. These operate the resistance box component of the bridge-measuring circuit. When used as an insulation tester, the bridge IR tester is a direct-reading series ohmmeter for high resistance values. When switched to the bridge configuration, the circuit has to be balanced by adjusting the rotary switches. The infinity end of the scale is taken as the null or balanced position. In the bridge-balanced position, the pointer rests directly above the infinity symbol. One of the major applications of a bridge IR tester instrument is the location of cable faults. The resistance between the ends of cables and the fault can be accurately measured and, by calculation, the distance to the location of the fault can be obtained. Figure 1.76  A 500 V bridge IR tester The circuit connection most often used is known © Richard Allan, www.richardsradios.co.uk as the ‘Varley loop’, after the person who first proposed it. More modern instruments, called Time Domain Reflectometers (TDR), are used to locate cable faults in either communication cable or power cables. They typically identify open circuits, short circuits, crossed pairs and so on.

1.51.4  Continuity testing Another variation of the IR tester circuit tests the continuity and resistance of conductors in an installation. While the standard IR tester operates as a series ohmmeter for resistance ranges of 0 to 100 MΩ, 0 to 200 MΩ or 0 to 550 MΩ in some instances, the continuity tester operates like a parallel-connected ohmmeter. Its normal resistance range depends on the manufacturer. The continuity part of an IR tester is typically used for earth continuity tests.

1.51.5  Hi-pot testing Just as the Australian and international standards require a higher current for low ohms tests, insulation tests under these standards are often performed at 1500 V, or up to 4500 V. Insulation, clearance and creepage distances are 91

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expected to be sufficient to prevent 1 mA from flowing, even at such high voltages. As this type of testing requires a high voltage or potential difference, it is referred to as ‘hi-pot testing’.

1.51.6  Care in the use of insulation resistance testers A 500 V IR tester can cause an electric shock unless care is taken. Inadvertent contact with the test leads can give rise to an electric shock, which could affect other technicians handling the same conductors. Underground cables are often tested with higher voltages, often by IR testers generating 3000 V. Apart from direct electric shocks from the instrument, there is an additional danger created by the capacitance effects of the cable. This applies particularly to armoured or metal-sheathed underground cables as well as to metal-insulated and metal-sheathed (MIMS) cables. The capacitance created by the method of construction of the cable enables an electric charge to be stored on the cable. The charge is created from the d.c. of the IR tester and generally exists between the conductor and the armoured metal sheath protecting the cable. Because the actual capacitance can vary widely from cable to cable, it is usually expressed in microfarads per unit length. One typical cable has a capacitance of approximately 0.2 μF / 300 m. Others may have higher or lower capacitances. At 3000 V, this capacitance relates to an energy storage of around 9 J. This quantity of charge at this voltage can cause enough of a shock to immobilise a technician for a time. Sometimes medical attention is needed, and this is a reportable incident by law. On an aerodrome, for example, there can be many kilometres of underground cable, so the scope for an electric shock is considerable. Even with a comparatively short length of underground cable, this equates to an energy content at a voltage that can kill. This is why it is a good idea to discharge the cable after testing. Typically, electricians will do this by shorting a screwdriver or something similar across the sheath and conductor. However, care should be taken in doing this as it may present other risk hazards, and so a slower discharge method such as using a high ohm value bleed resistor with a high wattage rating, is a safer method. Before relying on readings taken by an IR tester on an installation that contains capacitance, the operator should ensure that the installation is charged up to the voltage of the IR tester. This is generally done by extended testing on any one conductor for a period of time. The meter reading usually indicates that this has been achieved when the reading stabilises at one value. For example, when reading the resistance of one conductor in an underground cable to its sheath, the IR tester may show a reading which indicates a low resistance path to earth. On persisting with the test, the IR tester reading will generally climb to a much higher, more satisfactory, reading.

1.52   Continuity and resistance testing The testing of electrical circuits requires measuring instruments to be able to cope with very high and very low values of resistance. What may be suitable for measuring high resistances is not necessarily suitable for measuring low resistances. High-value resistors and insulation testing need one type of device, while low values of resistance and continuity testing need another type. To check a circuit, two factors must be taken into account: continuity and resistance. The test required determines the type of testing device to be used.

1.52.1  Low-value resistance and continuity testers Low-value resistance testers can range from elementary to quite complex. The choice often depends on the degree of accuracy required. For simple continuity testers, all that is required is a low-voltage source of power and an indicator, for example, a 6 V battery and a 6 V lamp or buzzer. Two test leads, the lamp and the battery are connected in series and, when testing a circuit, the continuity of a conductor is indicated when the lamp lights. This type of tester has the advantage of being simple, easily made up when required and inexpensive. The disadvantages are that regular battery replacement is required and the low voltage will not provide sufficient power to 92

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give a positive indication when the circuit is complete but contains an appreciable amount of resistance. For example, if a circuit is complete but has a series coil resistance of 100 Ω, the lamp will not light, falsely indicating an open circuit. Whenever circuits and test equipment indicate a possible fault is present, further testing is necessary. More sophisticated equipment might have to be used to indicate the extent and type of the problem. It may well be that a resistance is present in the circuit, giving the doubtful indication. The fault might be more extensive than that, and establishing what it is, of course, is the purpose of the testing function. One attempt to get around this problem was the introduction of small hand-cranked generating sets that were used in conjunction with a suitable bell. When the crank was turned and the test leads touched together, the bell would ring. The voltage was often around 150 V but was also a.c.. More costly than a battery and a buzzer, the system was rugged, still relatively simple to use and operated on low resistances. It was excellent for checking out multiple conductors in a new installation but had one big disadvantage: as it worked on a.c., its indication was subject to high inductances in the circuit path. No indication would be given under some circumstances. On the other hand, with very long runs it would give a false indication of continuity because of the capacitance between adjacent conductors in the circuit.

1.52.2  Continuity testing AS/NZS 3000:2018 requires that all parts of the earthing system must be installed and tested to ensure that protective devices (such as circuit breakers and RCDs) operate in the event of a fault and exposed conductive parts (such as the enclosures on electrical equipment and plumbing pipework) do not reach unsafe voltage levels when these faults exist. The requirements for earth continuity are listed in clause 8.3.5. The acceptable values of resistance are 0.5 Ω for the main earth and any bonding earths and the Re values listed in AS/NZS 3000:2018 Table 8.2 for the protective earth conductor size of the circuit. The values in Table 8.2 are low enough to ensure the operation of the circuit’s protective device.

1.52.3  Insulation resistance AS/NZS 3000:2018 requires the insulation resistance on all parts of an electrical installation be high enough to prevent electric shock from contact in normal use, fire hazards from short circuits and equipment damage. To check that the insulation of an installation (including all wiring and equipment insulation) has not been damaged during installation or deteriorated over time, an insulation resistance tester should be used. The requirements of this test are noted in clause 8.3.6. When applied between live conductors (all active and neutral conductors) and earth, the insulation tester must be able to output 500 d.c. to stress the insulation. The result when testing between live conductors and earth must be greater than 1 MΩ. The exception to this measurement is when testing sheathed heating elements, such as those used in hot water systems and ring-type cook tops, which can have a measurement of 0.01 MΩ. This only applies to the elements; the rest of the appliance still needs to be greater than 1 MΩ to ensure that no faults are present in the wiring that connects up the elements.

1.53   Capacitors and capacitance 1.53.1 Introduction A capacitor is a sandwich consisting of an insulator between two conductors. If a voltage is applied, electrons from one conductive side are transported to the other conductive side via a circuit. (This is called ‘charging’ the capacitor.) When the capacitor has been charged, the leads may be removed and the charge will remain in place until leakage causes it to drain away. In real circuits, the capacitor acts like a very fast battery, storing electrical energy when there is an excess and giving it back when the voltage falls. Capacitors can appear to have no resistance when a sudden high voltage 93

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appears on a circuit and, if correctly placed, the capacitor can safely dump the current from surge voltages to ground. In other words, capacitors can be very important components.

1.53.2 Capacitors A capacitor consists of two conducting surfaces called plates, separated by an insulating material called the dielectric. Each of the plates has a separate conductor connecting it to a set of connecting leads. A capacitor stores energy in the form of an electric charge contained by an electrostatic field. This is like a magnetic field, except that a magnetic field results from current and an electrostatic field results from potential difference.

1.53.3  Capacitor types Many specialised capacitors exist, and they are too numerous to detail in one chapter. The most common capacitor types are described in Table 1.7. Many older types have been replaced in the past few decades by modern plastic-insulated types that are both more reliable and smaller for a given value. As well as the commercial capacitor types, the ‘capacitive effect’ is commonly used in measuring instruments. Capacitance is also an unwanted byproduct in other components. Table 1.7   Examples of capacitor types Capacitor type

Description

Application

Ceramic

Ceramic capacitors are made by silverplating both sides of a ceramic insulator, which is usually a circular disc or square ‘chip’. The capacitor is then ‘encapsulated’ or enclosed in an insulating material such as ceramic, enamel or epoxy resin. Encapsulation protects the conducting surface and reduces leakage between the conducting surfaces. Ceramic capacitors have values from 0.5 pF to 0.1 μF and voltage ratings exceeding 6.0 kV.

Ceramic capacitors are often constructed for low-capacity high-voltage use in electronic circuits. They are common at very high frequencies that other types cannot handle. For electrical work, the main uses of ceramic capacitors are voltage-surge suppression and arc suppression. Some ceramic capacitors are quite large, and some are meant for very high voltages and very high surge currents. Capacitors for distribution systems are often tubular ceramic.

The conductive plates and dielectric insulators are stacked in a pile, and alternate plates are joined to form two large surface areas. Mica capacitors are a common example of stacked-plate capacitors (and are so named because of the mica dielectric material).

Stacked silver-mica capacitors are good for high-stability, high-voltage, low-capacity applications such as radio transmitters and medical equipment. In the electrical field, their main use is for the suppression of voltage surges and contact arcing.

Figure 1.77  Ceramic capacitors Stacked-plate

Figure 1.78 Stacked-plate capacitors

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Capacitor type

Description

Application

Rolled

An insulating material such as polyester or polycarbonate is made into a thin sheet which is then ‘aluminised’ on one side by exposure to an aluminium plasma cloud. Two sheets are rolled together to make the double layer conductor/insulator/ conductor/insulator set. This roll is then cut into sections, wires are attached and the whole assembly encapsulated to make a tightly bound small capacitor with medium-size capacitance from 1 pF to several μF.

The main uses of large rolled capacitors are in motor starting and running capacitors, as well as for general powerfactor correction purposes. Small polymer (plastic) capacitors have replaced paper in most applications, especially in electronics. Polyester, polycarbonate, polypropylene or mylar capacitors are used extensively in electronics and consumer products, as well as in industrial instrumentation and control.

Electrolytic capacitors are similar to rolled capacitors, except that the dielectric is an absorbent material impregnated with a borax electrolyte solution. The plates are etched to increase their surface area. Electrolytic capacitors provide a very large capacitance in proportion to physical size but are polarised because of the electrolyte. This is a disadvantage in that a voltage of the wrong polarity can destroy the capacitor. Electrolytic capacitors range from 1 μF to 1 F. Voltage ratings are generally from around 10 V to 500 V.

Electrolytic capacitors have the greatest capacity of all capacitor types and are therefore popular as d.c. filters in power supplies and large amplifiers. Electrolytic capacitors are used in switch-mode power supplies that power most consumer electronics and an increasing number of industrial applications. Electrolytic capacitors also find use in audio and lower-frequency circuitry. Electrolytic ‘super-capacitors’ are available with 25 F capacity, which is sufficient storage to replace batteries in electronic circuits.

Variable capacitors are rarely used today, but at one time all radios were tuned by one or more variable capacitors. In the normal variable capacitor, one set of capacitor plates can be moved within the other set so the surface area between the plates changes. Other variable capacitors are adjusted by changing the space between the plates or by sliding a dielectric in or out of that space. Most variable capacitors range from several pF to perhaps 1000 pF.

Variable capacitors were traditionally used in the electronic communications industry to tune radios, antennas, amplifiers and test equipment. However, the variable capacitor has largely been replaced by ‘voltage-variable’ capacitors or by digitally tuned phaselocked loop circuits.

Figure 1.79 Rolled capacitors Electrolytic

Figure 1.80 Electrolytic capacitors Variable

Figure 1.81 Variable capacitors

1.53.4 Capacitance Capacitance is the measure of the ability of a capacitor to hold an electric charge. The size of a capacitor is known as the ‘capacity’. In the automotive world, capacitors are often called ‘condensors’, harking back to a time when they were thought to ‘condense’ electricity.

Unit of capacitance The unit of charge is the farad (F), which is defined as the capacity of a capacitor that stores a charge of one coulomb at a potential difference of one volt. 95

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A coulomb (represented by Q) is defined as the charge that passes a point in one second when a current of one ampere flows.

i.e.: Q = VC      (1) and Q = It     (2) ∴ Q = VC = It   (3) where: Q = charge in coulombs V = voltage C = capacity in farads I = current in amperes t = time in seconds

This is a very important set of relationships. Up until recently, the farad was considered a very large unit (sub-multiples were, and are still, commonly used). Advances in technology have made capacitors of up to several thousand farads possible. The two most common sub-multiples of the farad are:

∙ Microfarads, 1 μF = 1 × 10−6 F ∙ Picofarads, 1 pF = 1 × 10−12 F

The quantity of charge held in a capacitor is dependent on both capacitance (as defined above) and the voltage across the capacitor. The same quantity of charge can be held in a large capacitor at a low voltage and in a small capacitor at a high voltage.

EXAMPLE 1.21 (a) A 10 μF capacitor is charged to a potential difference of 100 V. Calculate the charge. Q = VC

 (1) −6

​ = 100 × 1 × 10

 (2)

​​ ​      ​  ​  ​  10 ​  ​  ​​​ ​ = 100 × ​ ________    ​   (3) 1000000 ​ = 0.001 C​

 (4)

(b) A 1000 μF capacitor is charged to a potential difference of 1 V. Calculate the charge. Q = VC

   (5)

​ = 1 × 1000 × 10−6

   (6)

​      ​​ ​  ​  ​  1000 ​  ​  ​  ​ ​ = 1 × ​ ________   ​     (7) 1000000 ​ = 0.001 C​

   (8)

1.53.5  Capacitance parameters Capacitance varies according to the following physical parameters: 1. The effective area of the plates. Capacitance is directly proportional to the effective area and is increased by increasing the number of plates (e.g. stacked plates) or the total area of the plates (e.g. rolled capacitors). 96

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  ‘Effective area’ means the surface area adjacent to a plate of the opposite polarity. The outsides of the plates at either end of the stack do not count. (Actually, what is known as ‘stray capacitance’ exists between any two conductors, but this is not generally considered in calculations.)   Electrolytic capacitors are etched to increase their surface area via the bumps and hollows that are formed. 2. The distance between the plates. As the separation decreases, the electrostatic field strength increases, so more charge can be maintained, thus increasing the capacitance. 3. The permittivity of the dielectric. Capacitance is affected by the type of material used as the dielectric. For example, if glass is used instead of air, the capacitance increases approximately six times. Glass also increases the breakdown voltage of the capacitor considerably, so much higher voltages can be used. The ratio by which the dielectric can increase the charge, relative to air, is called the ‘dielectric constant’. The measure of the dielectric effect is known as ‘permittivity’. Even a vacuum has permittivity (known as ‘the permittivity of free space’ or ‘absolute permittivity’). For a capacitor consisting of two parallel plates, the capacitance can be found from the following equation: ϵoϵrA ​C = ​ _____  ​​    d where: C = capacity in farads ϵo = absolute permittivity (= 8.85 × 10−12) ϵr = relative permittivity A = area of plates in square metres d = distance between the plates in metres Today, 2.5 V, 25 F ‘super-capacitors’, although still rare, can be bought from electronics suppliers. The value of most electrolytic capacitors is usually expressed in microfarads, even when the figure is 10 000 microfarads. The terms ‘farad’ and ‘millifarad’ are still not commonly used, presumably due to tradition.

1.53.6  Dielectric constants The dielectric constant signifies the degree to which capacitance can be increased by replacing the air between the plates with a dielectric. For example, if two parallel plates in air had a capacitance of 120 pF and then the air was replaced with glass (the area and distance between the plates being unchanged), the capacitance would increase to 720 pF. An insulating material with a high dielectric constant is used to increase capacitance without an increase in physical size. To increase capacitance further (or to reduce physical size), the dielectric is made very thin. However, if the voltage across the dielectric material is increased beyond the material’s breakdown voltage, the insulation fails and becomes useless as an insulator between the plates. The same result occurs in variable capacitors if the voltage is kept constant and the thickness of the material is reduced. Table 1.8   Dielectric constants Dielectric

Dielectric constant (er)

Dielectric strength (kv/mm)

Air/vacuum

1

3

Paper

2

40

Transformer oil

4

15

Mica

5

100

Glass

6

30

Porcelain

6

7

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The voltage per unit thickness necessary to cause breakdown is called the ‘dielectric strength’ of the insulating material. Selected values of this are shown in Table 1.8. The maximum voltage applied across a dielectric depends on both the type of material and its thickness.

1.54   How a capacitor is charged in a direct current circuit 1.54.1  Capacitors in direct current Figure 1.81 illustrates a capacitor connected to a battery. When first connected, the capacitor would have no charge, meaning that the number of free electrons on either side of it would be approximately equal. The capacitor would begin to charge, with the positive plate of the battery attracting some of the free electrons from the capacitor, thus causing the connected capacitor plate to become positively charged. The other plate of the capacitor, connected to the negative of the battery, would receive the free electrons displaced from the other side of the capacitor and therefore become negatively charged. Capacitors are insulators, so the current measured in any circuit containing them is the movement of the free electrons from the positive side of a capacitor to the negative side of that capacitor or another capacitor. The current does not flow through the capacitor, as current does not flow through insulators. When the capacitor voltage equals the battery voltage, there is no potential difference, the current ceases to flow and the capacitor is considered to be fully charged. If the voltage is increased, a further migration of electrons from the positive to negative plate results in a greater charge and a higher voltage across the capacitor.

1.54.2  The time constant The rate at which a capacitor is charged depends on its capacitance and the circuit resistance. The formula has already been used several times: Q = CV = It CV V Therefore t = ​​___  ​​  and you know that R = ​​__ ​​  I I Therefore t = RC where: t = charge time for the capacitor in seconds (one ‘time constant’) R = resistance in ohms C = capacitance in farads

Battery

+ve −ve

Wire Wire

+ve

Capacitor

−ve

Atom Electron

The battery electrolyte becomes ionised by drawing electrons from the positive plate and depositing electrons in the negative plate. The potential difference between the battery plates can then cause electrons to flow to and from the external circuit. That is, a wire connected to the positive terminal will also become +ve, and a wire connected to the negative terminal will become –ve. Similarly, the plates of a capacitor will also become +ve and –ve according to the terminal they are connected to. The difference between the wires and the capacitor is that the narrow insulating gap between the capacitor plates allows the electrons in the negatively ionised plate to be electrostatically attracted to the positively ionised atoms in the positive plate. The attraction is strong enough to keep the charge in place when the wire is disconnected.

Battery

Current (and electron) flo Wire e– +ve

Capacitor

+ve

Electrolyte Dielectric −ve

−ve e–

Wire

Figure 1.82  Capacitor connected to battery

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Vi = Vm(1 – e–t/RC)

95.0%

98.2% 99.3%

86.4%

63.2% Voltage

In terms of what kind of time is t, the time constant is usually denoted by the Greek letter ‘tau’ or τ (pronounced ‘tow’, to rhyme with ‘cow’). This is the time the capacitor takes to charge up to 63% of the applied voltage. (This comes from a formula that uses exponential maths, Vt  =  Vmax(1  −  e(−t/RC)), which is not essential for the electrical trades.) Example 1.22 shows the type of calculation you might commonly need to learn for the electrical trades.

Even at 10τ, Vi = 99.995%Vm

Time

τ = RC

2τ

3τ

4τ

5τ

Figure 1.83  Capacitor charging voltage

EXAMPLE 1.22 A circuit consists of a 100 kΩ resistor in series with a 500 μF capacitor. How long would it take for the voltage across the capacitor to reach 63% of the value of the supply? τ = RC

 (1) 3

−6

=​ ​  100 × 10  × 500 × 10 ​   (2)​​​​ ​​ ​ ​     ​  ​  ​ = 50 s  (3)

Therefore, to increase the charging time, either the capacitance or the resistance need to be increased. Likewise, decreasing either value decreases the time constant. Notice that the formula does not include voltage or current. The supply voltage does not affect the charging time for any given capacitor. Doubling the supply voltage doubles the charging current, but the quantity of electric charge being pushed into the capacitor is also doubled, so the charging time remains the same. Plotting the values of voltage against time for any capacitor charging from a constant voltage results in an exponential Vmax, Imax Voltage Switched curve increasing towards the applied voltage. Discharging a charged capacitor into a fixed VC resistance creates another exponential curve, this time Current reducing towards zero. Time The discharge current is shown as a negative value because of the reversal of current flow. The charge is IC now flowing out of the capacitor. The curves show that the current is at a maximum –Imax when the voltage is changing most rapidly (i.e. at the start of charging and discharging). Charge The current is zero when the voltage is steady, but R1 Discharge technically the voltage never quite reaches maximum, as exponential curves continue to rise for infinity (i.e. C1 the voltage never reaches a steady value). When the circuit resistance value is very small, extremely high values of current can result and the Figure 1.84  Capacitor charge/discharge 99

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charging time may be reduced to millionths of a second. By Q  =  VC  =  It, when the discharge +ve High voltage time is small, high currents must flow. This high Bleed battery Capacitor resistor discharge current can be dangerous. (DC supply) C1 RB EHV As no dielectric is a perfect insulator, a –ve charged capacitor will slowly lose its charge as current leaks from one plate to another. However, a really good capacitor may hold its charge for a Figure 1.85  Capacitor charging circuit very long time. Therefore, to reduce the risk of an electric shock, many high-voltage, high-power circuits have a high-value ‘bleed resistor’. This is a resistor connected across the capacitor to reduce the charge to a safe limit (within perhaps ten seconds). See Figure 1.85.

1.54.3  Harnessing the time constant As the time a capacitor takes to charge (or discharge) to a set voltage can be calculated from resistance and capacitance, a circuit can be designed that operates at that value, perhaps to turn a light on or off or to control how long a motor runs or takes to start. In electronics, the circuit known as a ‘voltage comparitor’ is used and, although an electrician may never need to design or build one, they may fail or behave erratically, requiring the electrician to remember and understand time constants in order to repair them.

1.55   Calculation of quantities from given information 1.55.1  Energy stored in a capacitor When a capacitor is charged, a static electric field exists between the plates. This is a result of the electrons being pumped from the positive plate to the negative plate, and of the attraction between these electrons and their counterpart positive ions. The actual value of stored energy depends on the capacity of the capacitor and the voltage on the capacitor. Unlike an inductor, which must have a dynamic flow of electrons (a current) to maintain its charge, a capacitor needs only a stored (static) charge of electrons. The attraction between the electrons and the positive ions keeps the electrons in place and the capacitor remains charged until leakage allows the charge to escape. The actual value of energy stored in the field depends on the applied voltage and the capacitance of the capacitor. The energy stored in a capacitor can be found from the formula: 1 2 W = _​​ ​​C   V 2 where: W= work or energy in joules C = capacitance in farads V = voltage in volts

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EXAMPLE 1.23 A 1 μ F capacitor is charged from a 300 V d.c. supply. Find the energy stored in the capacitor. 1 W = ​ __ ​  C​V​​  2​  (1) 2 ​​ ​     ​  1 × 10​  −6 × ​300​​  2​  ​​  ​ ​ = ___________ ​     ​    (2) 2 ​ = 0.045 J (45 mJ )​

 (3)

1.56  Hazards and safety control measures involved in working with capacitance effects 1.56.1  Dangers of a charged capacitor The value of energy stored in the capacitor in Example 1.23 is certainly low but, because the potential difference across the terminals is 300 V, an unpleasant (if not dangerous) electric shock can be given to an operator. Also, capacitors can store the charge for a long time after the supply has been disconnected. A capacitor that has been used on three-phase line voltages can have a charge exceeding 500 V. Electric circuits such as modern switch-mode welders can have large capacitors that are charged to well above the supply voltage and still very much alive, even after the plug has been removed from the socket. Electrical workers should always take care when dealing with capacitors. Depending on actual circumstances, a high discharge current can flow from a charged capacitor. To illustrate this point, consider Example 1.24.

EXAMPLE 1.24 If a resistor of 0.4 Ω is connected across the terminals of a 1 μF capacitor while it is charged to 300 Vd.c., what current will flow through the capacitor and resistor? From Ohm’s Law: V I = __ ​   ​  R

 (1)

​​     ​    ​  300 ​  ​  ​  ​​​  ​   (2) Therefore I = ____ ​  0.4 ​ = 750 A​

 (3)

This current lasts for only a very short period of time before deteriorating to a much lower value, but it can cause damage to a circuit if the circuit or the capacitor are not built to withstand such current surges. A circuit of this type is the basis of photographic flash guns, which generate a high current for a few milliseconds to generate the bright electric arc which is seen as a camera flash. A capacitor is charged up to between 200 and 500 V and discharged into a xenon gas-filled tube. Before handling capacitors or working on circuits where they are used, it is a sensible precaution to ensure that they have been discharged. Capacitors with a small value of capacitance can be discharged directly with a short circuit but, where there is a safety issue, larger values might need a discharge (bleed) resistor to control the value of the current during discharge.

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As mentioned earlier, some circuits have high-value ‘bleed’ resistors permanently connected across a capacitor to ensure discharge occurs when the power goes off, and avoids the dangerous possibility of a handler touching a charged capacitor. This applies particularly in higher-voltage circuits.

1.56.2  Capacitor faults As capacitor size decreases and greater capacity is expected from them, greater stress is placed on both the insulation and the conductive foils. If any point in the insulation should fail, there is no insulation and the whole capacitor fails. The applied voltage, which causes great stress on the insulation, might be better appreciated when it is considered that a voltage of 100 V applied across an insulator just 0.1 mm thick represents a voltage gradient of 100/0.1 × 10−3 =  1 million volts per metre. Current flow can also be a problem, as capacitors discharge at a rate determined by the resistance of the circuit and sudden discharges, such as the shorting of the terminals of the capacitor, result in very high internal currents. A short is theoretically zero ohms, so the current would theoretically be infinite. Thankfully, capacitors have internal resistance, although the value may still be milli-ohms. The resulting current can easily fuse the thin foil conductors. For example, a 1000 microfarad capacitor charged to 1000 volts represents a charge of 1 coulomb. If that charge is discharged in 1 millisecond, up to 1000 amps would flow internally.

1.56.3  Dielectrics drying out Electrolytic and oil-filled capacitors can leak or dry out and then the capacity of the capacitor will be less than designed. Eventually the capacitor will fail to meet its design criteria. Electrolytic capacitors in switch-mode power supplies reach higher temperatures than the same capacitors on d.c. or 50 hertz. The higher temperature is the result of dielectric heating, which occurs in most capacitors, especially at higher frequencies.

1.56.4  Testing capacitors To test a large capacitor, an ohm-meter is placed across the terminals of a known discharged capacitor. If the resistance is low at first but increasing, there is capacity in the capacitor. However, to know whether there is enough capacity, a good capacitor should be checked on the same resistance range and the result compared to the suspect capacitor. For small capacitors, multimeters often have a capacitance range which will actually measure the capacitance, up to perhaps 200 microfarads. The testing procedure will be given in the instruction book for that instrument. An instrument that is currently gaining favour is the Effective Series Resistance (or ESR) meter, which measures the internal series resistance of electrolytic capacitors and some other components. The reading gives an indication of the condition of the electrolyte within the capacitor. Another simple method requires the capacitor to be removed from the circuit and placed in series with a resistor of known value across a d.c. power supply. The capacitor is charged to 63% of the applied voltage and the charge time noted. Using the time constant and the resistance value, the capacitance can be calculated. Small capacitors may be tested at their expected operating frequency against a known good capacitor in a circuit called a ‘capacitance bridge’ or an ‘LCR bridge’. Capacitors with a bulging bottom or leaking electrolyte should be replaced, even if they are still working.

1.57   Effects of capacitors connected in parallel 1.57.1  Capacitors in parallel Placing two or more capacitors in parallel is the same as increasing the area of the plates. As each capacitor is added in parallel, the effective capacitance of the group is increased as if by simply adding more area. The actual dimensions do not matter, but the method of calculating parallel capacitors is easy—simply add them up. The total 102

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capacitance in a parallel circuit is the sum of the individual capacitances, as shown in Figure 1.86. Capacitors in parallel are subject to the same rules as other components in parallel circuits. They have the same voltage across them. Since the voltage is the same across each capacitance, the total charge can be calculated from the capacitances and the applied voltage.

... Cparallel

C1

C2

...Cn

C3

Cparallel = C1 + C2 + C3 + ... Cn Figure 1.86  Capacitors in parallel

EXAMPLE 1.25 A 4  μF and an 8  μF capacitor are connected in parallel across a 100  Vd.c. supply. Find (a) the total capacitance, (b and c) the charge on each capacitor, and (d) the total charge. Step 1. The total capacitance is found as: ​C​  Total​​ = ​C​  1​​  + ​C​  2​​

 (1)

=​  4μF + 8μF  (2)​​​ ​ ​     ​  ​  ​ 

 ​​

​ = 12μF​

 (3)

Step 2. For the 4 μF capacitor, the charge will be found from Q = VC; that is: ​Q​  C1​​ = 4 × 10−6 × 100         (4) ​      ​  ​  ​  ​​​ ​ = 4 × 10−4 coulombs​         (5)

​​

Step 3. Similarly for the 8 μF capacitor: ​Q​  C2​​ = 8 × 10−6 × 100        (6) ​      ​  ​  ​  ​​​ −4 ​ = 8 × 10  coulombs​        (7)

​​

Step 4. The total charge is found by addition; that is: ​Q​  Total​​ = ​Q​  C1​​  + ​Q​  C2​​ ​​

  (8)

−4 ​ ​     ​  ​  ​  =​  4 × 10−4 + 8 × 10   (9) ​​​

​ = 1.2 × 10−3 coulombs​

     (10)

1.58  Effects on the total capacitance of capacitors connected in series 1.58.1  Capacitors in series When capacitors are connected in series, as shown in Figure  1.86, the effect is the same as adding the distances between the plates of each capacitor. The total distance between the plates is greater, therefore the total capacitance is less. This can be proven with maths (the formula has been used for over a century). The total series capacitance is found by using the formula shown in Figure 1.87.

Cseries

C1

C2

C3

...

...Cn

1 1 1 1 1 = + + + ... Cseries C1 C2 C3 Cn Figure 1.87  Capacitors in series

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The total capacitance in Example 1.26, 5.3 μF, is less than those of either of the capacitors in the circuit. Also, the potential differences across the two capacitors must add up to the applied voltage according to Kirchhoff’s Voltage Law.

EXAMPLE 1.26 A 16 μF and an 8 μF capacitor are connected in series. Find the resulting capacitance. 1  1 1 _____ ​    ​  = ___ ​    ​  + ​ __ ​   ​C​  Total​​

16

 (1)

8

=​  0.0625 + 0.125  (2)​​ ​      ​​  ​  ​    ​  ​  ​  ​  ​ = 0.1875

 (3)

∴ ​C​  Total​​ = 5.3 μF​

 (4)

(To be more exact, the resultant capacitance in this example is 5.333 μF with a recurring decimal figure. Generally, though, capacitors can only be bought with a value of two significant figures.)

Remember that, by Kirchhoff’s Current Law, the current in each of the capacitors is the same as the total circuit current. Charge is dependent on current and time by the formula Q = It. Therefore, the charge in each capacitor (and in the whole circuit) is the same; only the voltage across each capacitor changes. If an applied voltage of 100 V were to be placed across these two capacitors in series, the charge present in the whole circuit would be found by applying the formula Q = VC. In this case, the overall quantity of charge is: Q = VC −6 ​​     ​   ​​ ​​  =​  100 × 5.33 × 10  coulombs​ ​ = 533 × 10−6 C Again, remember that the same current flows for the same time in every component in a series circuit. The charge must be the same in each component. Since the capacity of each capacitor is different, the voltage across each will Q also be different. By transposing the formula Q = CV to V = ​​__ ​​ , the voltages across each capacitor can be established. C

EXAMPLE 1.27 Find (a) the voltage across the 16 μF capacitor in Example 1.26. Q V = __ ​   ​  C

 (1)

​​     ​     ​  533 × 10 ​  ​  −6​  ​ ​ = _________ ​   ​   (2) −6 16 × 10 ∴ ​V​  C1​​ = 33.31 V​

 (3)

​​Repeating this for (b) the voltage across the 8 μF capacitor gives: Q V = __ ​   ​  C

     (4)

−6 ​​     ​     ​  533 × 10 ​  ​  ​  ​ ​ = _________ ​   ​          (5) −6 8 × 10

∴ ​V​  C2​​ = 66.625 V​

     (6)

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​​The total voltage (c) would be: ​V​  Total​​ = ​V​  C1​​  + ​V​  C2​​ ​​

 (7)

​ ​    ​  ​  =​  33.31 + 66.651  (8)​​​ ​ = 99.935 V​

 (9)

Kirchhoff’s Voltage Law tells us that the sum of the individual voltage drops must add up to the total applied voltage, in this case 99.935 V, a figure that compares well to the applied voltage of 100 V. If more decimal places were used throughout the calculations, the final figure would be even closer to 100 V. Capacitors therefore have to be selected not only by capacity, but also by the voltages expected to exist across them—that is, their working voltages. Where the capacitors in series are of equal capacitance, the potential differences will divide equally between them. From Ohm’s Law, if one capacitor becomes short-circuited, then other capacitors in series with it will be subjected to higher than normal voltages.

1.59  Application of capacitors in the electrotechnology industry Capacitors serve many functions in the electronics industry, including coupling (blocking d.c. from a.c. signals) and decoupling (separating signals from other circuits), high- and low-pass filtering (allowing only certain audio such as bass or treble or radio frequencies through), noise filters, oscillators (that produce sound and radio waves) and radio tuning circuits. In the electrical part of the electrotechnology industry, capacitors can be used for energy storage (especially super capacitors > 1F), power factor correction, motor starting and ‘snubbing’ relay circuits (especially d.c.), where opening the relay results in arcing across the contacts. As capacitors have the ability to discharge a large amount of energy in an almost instantaneous time, they are also used in many types of weapons, ranging from tasers to railguns.

Summary ∙ Electricity is a naturally occurring phenomenon found in nature, and is explained in biology, chemistry and physics. ∙ All the materials in the universe are known as matter. Matter has mass. ∙ Matter is made up of compounds, whose basic components are molecules. ∙ Molecules are constructed from atoms of different elements. ∙ An atom is the smallest part of an element that maintains all of the characteristics of an element. ∙ Atoms can be further divided, with protons, neutrons and electrons the parts most important to electrical studies. The main body of an atom is called the nucleus. ∙ Protons are positively charged atomic particles contained in the nucleus of an atom. ∙ Neutrons are non-charged atomic particles that are also contained in the nucleus of an atom. ∙ Electrons are negatively charged particles roughly 1000 times smaller than a proton. They orbit the nucleus of an atom. ∙ Electricity will flow through a liquid if the liquid is ionised. 105

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Electrical Principles ∙ The positive connection to a liquid is called an anode. ∙ The negative connection to a liquid is called a cathode. ∙ The liquid through which a current flows is called an electrolyte. ∙ Two dissimilar metals in a conducting medium (an electrolyte) form a voltaic cell. ∙ When a load is connected to a voltaic cell, chemical energy is converted into electrical energy. As the process continues, at least one of the metals is eaten away by being transformed chemically into a different compound. ∙ Different metals produce different voltages. ∙ Primary cells are cells that, once depleted, cannot be renewed without replacing the two constituent parts. ∙ Primary cells cannot be economically recharged by reversing the chemical process. ∙ Secondary cells have an easily reversible chemical process. ∙ Secondary cells can be recharged. ∙ Electrolysis can be used in manufacturing to coat metals with other metals, to build up or to erode away at metals. ∙ Metals can be polished by electrolytic action. ∙ Electroplating is a technique whereby chemical changes that take place in the electrolytic process can be put to good use. Material can be given a decorative finish, built up or reduced in size and made resistant to corrosion and/or staining. ∙ Electrolytic corrosion is created by contact between two different metals in a damp atmosphere with dust or pollution of a type that will dissolve in water. Precautions may have to be taken to ensure that the join between two different metals is kept dry. ∙ Electrolytic corrosion can be reduced by providing sacrificial anodes. ∙ Corrosion can also be reduced by applying a reverse voltage to neutralise stray ground currents.

Questions Exercises 1.1 What is the difference between static and current electricity? 1.2 List three different means for producing electricity from renewable sources and three different means of producing electricity from non-renewable sources and briefly explain each one. 1.3 State the five main components that are required to construct a basic electrical circuit. 1.4 Explain what is meant by ‘open circuit’, ‘closed circuit’, ‘short circuit’ and ‘fault’. 1.5 State Ohm’s Law in your own words. 1.6 If the voltage in a basic d.c single path circuit is increased the current will : increase / decrease / stay the same. 1.7 Explain what is meant by the power rating of a device and what effects exceeding this value would have. 1.8 If the resistance of a basic d.c. single path circuit was reduced the output power of the circuit would: increase / decrease / remain the same. 1.9 Explain the terms ‘Basic protection’ and ‘Fault protection’ as described in AS/NZS 3000. 1.10 What are the two effects of electricity that are always present when an electrical current is flowing? 106

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Solve problems in d.c. circuits  Chapter 1 1.11 What effect of electricity causes metal to corrode? 1.12 What is the difference between a primary and secondary cell? 1.13 The output power of an electrical device is equal to the input power plus / minus the loss power. 1.14 List two fixed and three variable types of resistors used in the electrotechnology industry. 1.15 What does the term ‘preferred value of resistance’ mean and what device is required to match the circuit to the required resistance? 1.16 In a series circuit what is the relationship between the voltage drop across all of the components and the supply voltage? 1.17 Give an example of where a series circuit is used in the electrotechnology industry. 1.18 In a parallel circuit what is the relationship between the current in each parallel branch and the current drawn from the supply? 1.19 Give an example of where a parallel circuit is used in the electrotechnology industry. 1.20 Give an example of where a series/parallel (compound) circuit is used in the electrotechnology industry. 1.21 Explain why the length of a conductor affects its resistance. 1.22 What four factors affect the resistance of a conductor? 1.23 Why does an ammeter have to be connected in series in a circuit? 1.24 Why does a voltmeter have to be connected in parallel in a circuit? 1.25 What is the purpose of an insulation resistance tester? 1.26 When using an analogue ohmmeter to measure the resistance of an earth connection what must be done to ensure the measurement is accurate before taking the measurement? 1.27 Describe the construction of a capacitor. 1.28 What three factors affect the capacitance of capacitor? 1.29 State two applications for capacitors in the electrotechnology industry. 1.30 What are the hazards associated with capacitors in electrical circuits and how can they be minimised?

Calculations 1.31 Given that 1 Amp is equal to 1 Coulomb of electrons (6.24 × 1018 electrons) flowing per second (I =Q/t) how many Coulombs of electrons would flow in a circuit of 2A for 20 seconds? How many electrons pass though the conductor in the period? 1 .32 Express the follow large and small units in multiple or submultiples of the S.I. units (a) 2450 m (b) 33  000 V (c) 0.03 A (d) 0.000023 F (e) 0.3 m (f) 1 × 10E6 Ω 1 .33 Using Ohm’s Law, calculate the missing numbers from the following list: (a) 12 V, 1 A,? Ω (b) 6 V, 0.5 A,? Ω (c) 24 V,? A, 100 Ω (d) 12 V,? A, 10 Ω (e) ? V, 100 mA, 240 Ω (f) ? V, 3 A, 8 Ω 107

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Electrical Principles 1 .34 Calculate the power used by each of the following: (a) 12 V, 1 A (b) 6 V, 0.5 A (c) 24 V, 100 Ω (d) 12 V, 10 Ω (e) 100 mA, 240 Ω (f) 3 A, 8 Ω 1.35 How much power is required to run an electric motor if the motor requires 4 amps at 230 volts? How much energy would the motor use in a week if it runs for 8 hours per day? 1.36 A motor draws 15 A from a 2.5 mm2 cable of route length 40 m (note that total conductor length is 80m, taking into account positive and negative conductors). If the resistance of a 2.5 mm2 conductor is 6.88 Ω/km, how much energy is lost in the cable over a 24-hour period? 1.37 An electric heater is rated at 3.6 kW when used on 230 volts. How much current will it take? 1.38 What is the resistance of the heater in question 1.37? 1.39 Define a ‘series circuit’, a ‘parallel circuit’ and a ‘series/parallel circuit’. 1.40 A simple circuit has a 12 volt battery supplying current to a 20 Ω resistor. Calculate the current drawn and the power used by the resistor. 1.41 What value resistor must be added in series with a 12 Ω resistor to give the circuit a total resistance of 28 Ω? 1 .42 Find the total resistance of each of the following groups of resistors, each connected in series: (a) 12 Ω, 15 Ω & 21 Ω. (b) 6 Ω, 7.5 Ω, 10 Ω & 13.5 Ω. (c) 25 Ω, 22 Ω, 42 Ω & 55 Ω. (d) 1.8 kΩ, 2.7 kΩ, 3.3 kΩ & 4.7 kΩ. (e) 900 Ω, 1.2 kΩ, 82 kΩ & 1.5 MΩ. 1 .43 Find the total resistance of each of the following groups of resistors, each connected in parallel: (a) 180 Ω, 150 Ω, 120 Ω & 100 Ω. (b) 6 Ω, 8 Ω, 12 Ω & 15 Ω. (c) 9 Ω, 9 Ω, 12 Ω & 12 Ω. (d) 36 Ω, 24 Ω, & 18 Ω (e) 1.2 MΩ, 1.8 MΩ & 820 kΩ. 1.44 (a) In a series circuit as shown in circuit (a) in the figure below, the four resistors are 2 Ω, 4 Ω, 6Ω and 8 Ω. If the potential difference across the 4 Ω resistor is 10 V, find:   (i) the current in the circuit   (ii)  the p.d. across the other resistors and the supply voltage (iii)  the power consumed by each resistor and the total power used. 1.44 (b) The parallel circuit in circuit (h) below has the following values known. The resistance of the first branch is 12 Ω. The current in the second branch is 300 mA. The power taken in the third branch is 1.5 W and the fourth branch has a voltage of 10 volts. Calculate all the VIRP values in the circuit if the total current is 1.5 A.

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Solve problems in d.c. circuits  Chapter 1 In questions 1.44 (c) to (i) that follow, assume the resistor values remain as calculated or given.

1.44 (c) Referring to circuit (b) above, calculate the VIRP values from the values given. If R1 is short circuited, will Itotal increase or decrease? 1.44 (d) Referring to circuit (e) above, calculate the VIRP values from the values given. If R3 is open circuited, will Itotal increase or decrease?

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Electrical Principles 1.44 (e) Referring to circuit (f) above, calculate the VIRP values from the values given. If R1 is short circuited, calculate the new Itotal. 1.44 (f) Referring to circuit (g) above, calculate the VIRP values from the values given. Recalculate the voltage values if R4 is open circuited. 1.44 (g) Referring to circuit (d) above, calculate the VIRP values from the values given. If R1 is open circuited, what else will be changed? 1.44 (h) Referring to circuit (c) above, calculate the VIRP values from the values given. 1.44 (i) Referring to circuit (g) above, calculate the values if the applied voltage is changed to 18 V. 1.45 A 1mm2 TPS cable has a resistance of 1.7 Ω per 100 m per conductor. If a load takes 10 A, what voltage would you estimate is lost per metre of cable, remembering that 1 m of cable is 2 m of conductor? 1.46 What three values are specified when resistors are ordered? 1.47 What is the resistance of a full roll (100 m) of 2.5 mm2 copper cable based on a resistivity of 1.72 m Ωm? 1.48 How much cable is left of that 2.5 mm2 roll when the resistance of the conductor is only 0.1032 Ω? 1.49 Find the resistance and tolerance of each of the following resistors.

1.50 Name the components shown here. (a)

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Solve problems in d.c. circuits  Chapter 1 (b)

1.51 Find the equivalent capacitance of a 7 μF capacitor and a 33 μF capacitor connected in series. 1.52 Find the equivalent capacitance of a 7 μF and a 16 μF capacitor connected in parallel. 1.53 Determine the amount of charge held in a 100 μF capacitor at a voltage of 100 V d.c.. 1.54 If the quantity of charge held on a 1000 μF capacitor is 1 coulomb, what would be the voltage across its terminals? 1.55 Calculate the energy stored in a 33 μF capacitor at a voltage of 100 V. 1.56 Which type of ohmmeter circuit would be best suited for measuring a resistance of 0.9 Ω? Draw the circuit and give a short explanation to justify your answer.

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Solve problems in electromagnetic circuits

2

CHAPTER OBJECTIVES • • • • • • • • • • • • • • • •

understand natural magnetism use fields to predict reactions between magnets apply magnetic principles to simple machines relate magnetic effects to electric current predict magnetic fields around conductors apply right-hand grip rule to determine polarity calculate electromagnetic values understand the characteristics of magnetic materials compare magnetisation and hysteresis curves for various materials describe the effects of Lenz’s Law explain inductance as an electrical effect explain time constant describe inductor types describe a magnetic circuit, magnetic leakage and magnetic fringing describe the construction and operation of moving-coil and moving-iron meters explain how to extend the range of meters and calculate the component sizes

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Electrical Principles

2.0  Introduction Magnetism was one of the first effects of electricity studied by physicists. Magnets were considered magic, the words ‘magnet’ and ‘magic’ both being derived from the ancient Greek word ‘magus’. Magnetism was originally considered to be a mechanical property of a material which caused it to attract, or be attracted to, other materials with similar properties. The study of electricity, and then atoms, has changed this thinking to the current belief that magnetism is an electric effect of an atomic particle, such as an electron, moving at a very high velocity. In fact, following discoveries by Einstein, scientists continue to pursue what is called the ‘Unification Theory’, which suggests that electromagnetism, nuclear weak force, nuclear strong force and gravity may all be related in physics. Every electric motor, generator, alternator, transformer, relay and contactor relies on magnetism to work. In fact, most of today’s most common electrical or electronic products would not exist without the physicists who discovered and learned about magnetism.

2.1   Magnetism 2.1.1  Magnetic field pattern of bar and horse-shoe magnets When iron filings are sprinkled around a magnet, a strange pattern appears which looks like lines coming from one pole and going towards the other pole. These lines appear to spread out from the first pole and converge again at the other pole. Early experimenters called this pattern made up of lines of force a ‘magnetic field’. Iron filings are elongated particles of iron, whereas iron powder particles are spheroidal; iron filings produce better field patterns. (Magnetic field patterns can be made by placing a sheet of paper or thin card over the magnet to prevent the filings sticking to it. This also proves that magnetic fields pass straight through materials such as paper.) Figure 2.1 shows the magnetic field produced by a bar magnet. The filings arrange themselves in a series of lines that commence and end near opposite poles of the magnet. Magnetic fields become weaker as they expand away from the magnet, but may expand to infinity. It is the close magnetic field that electricians are concerned with. A magnetic compass is a magnet which is either suspended or mounted in such a manner that it can rotate freely, often above a dial marked with the Figure 2.1  Iron filings in a magnetic field

N

S

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Solve problems in electromagnetic circuits  Chapter 2

points of the compass or from 0° to 360°. In magnetic N S Free swinging compass needle experiments, a compass may simply be a magnetised needle balanced on a point to allow it to rotate. If a magnetic compass is slowly moved along a line of force, Magnetic ‘line of force’ the North pole of the compass will indicate the path in forming a loop which the magnetic force is acting. S N Scientific convention states that a magnetic force always Bar magnet acts outwards from the north-seeking pole of a magnet and inwards at the south-seeking pole (see Figure 2.2). Figure 2.2  Line of force in a magnetic field The magnetic field tends to take the path of least magnetic resistance, which means that the field will take the shortest possible path between the north and south poles of a magnet (see Figure 2.3). The field will pass directly through materials that cannot be magnetised (non-magnetic materials). However, when a material that can be magnetised (a magnetic material) is placed within the magnetic field, the field is distorted—and perhaps even lengthened— in order to pass through this magnetic material. This is because a magnetic material offers much less opposition to the field than a non-magnetic material.

2.1.2  Magnets’ attraction and repulsion when brought in contact with each other If two straight (bar) magnets are placed with their unlike poles together (N–S and N–S), the magnets will attempt to click together and remain attached due to the attraction between their poles. The field pattern between Figure 2.3  Magnetic fields—single magnet the magnets, if kept apart, will show a magnetic ‘fringe’ between their co-joined poles, which means that the magnetic field spreads out between the poles (see Figure 2.4). If two bar magnets are placed alongside one another with their like poles together, the magnets will tend to move apart, owing to the force of repulsion between their like poles. The two fields will remain separate, unable to form a single magnetic field (see Figure 2.5).

2.1.3  Common magnetic and nonmagnetic materials and groupings (diamagnetic, paramagnetic and ferromagnetic materials) The three most important magnetic materials are iron, nickel and cobalt, together with their alloys. Of these, iron produces the greatest magnetic effect and is therefore the most widely used magnetic material. Iron Figure 2.4  Magnetic field—unlike poles and iron alloys are termed ‘ferromagnetic’ materials. 115

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Figure 2.5  Magnetic field—like poles

Figure 2.6  Magnetic induction

Alloys of magnetic materials have produced permanent magnets of superior properties; for example, an ‘Alnico’ magnet is an alloy of aluminium, nickel and cobalt, with a few minor impurities. Ferromagnetic materials, which are easily influenced, are called ‘magnetically soft’; but those materials whose magnetic properties are difficult to alter are said to be ‘magnetically hard’. Soft magnetic materials such as iron or steel can be machined with little difficulty and may be rolled into a sheet from which shapes can be punched and stacked to form what is known as ‘laminations’. Laminations are usually made from an alloy of silicon and iron called ‘silicon steel’. Magnetically soft materials are easily magnetised; however, when the magnetising force is removed, the material tends to demagnetise itself. Any magnetism that remains is called ‘residual magnetism’. A magnetically hard material is, almost without exception, a mechanically hard material. Some modern magnetically hard materials cannot be machined with any degree of success, although others can be surfaced by grinding. To manipulate the shapes of these materials, they are usually cast into the required shape and magnetised while still above their Curie temperature. Some modern magnetic materials are formed by placing a mixture of powdered magnetic materials and a ceramic binder under high temperature and pressure to form ferrite, a very highpermeability magnetic material. This process is known as ‘sintering’ and produces sintered ferrite cores. Many of the materials used today are called ‘rare earth materials’—not because the material they are made from is rare, but because of the difficulty in isolating the element from the surrounding material. There are several of these elements, all of which come from the lanthanide (or lanthanoid) group of the periodic table. Many of these elements have been experimented with, but the most promising appears to be element number 60, neodymium. Neodymium appears to make the strongest magnets currently available. It has a very high melting point, which adds to the difficulty of working it. Neodymium requires an extremely high magnetic force to magnetise it, but has the advantage of requiring a much higher magnetic force to de-magnetise it. Neodymium magnets tend to be rather brittle and can shatter if roughly handled. Rare earth magnets can be manufactured in any shape by casting or sintering. Applications for these magnets include electric motor fields for permanent magnet motors such as those used in cordless tools.

2.1.4  The principle of magnetic screening (shielding) and its applications Magnetism cannot be stopped and there are no magnetic insulators. Instead, when a device needs to be protected from a magnetic field, a magnetic shield is used (see Figure 2.7). Magnetic shields divert the magnetic field by 116

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providing a path of much greater permeability than free space or the material normally surrounding the device to be protected. The magnetic field therefore flows around the device instead of through it. Magnetic shields in sensitive instruments are often made of a material known as ‘Mu-metal’, which is a nickel–iron alloy (There are several compositions of ‘Mu-metal’. One is Ni 77%, Fe 14%, Cu 5% and MO 4%.).

2.1.5  Practical applications of magnets Probably the most common application of permanent magnets is the magnetic compass. Permanent magnets are also used to provide a constant magnetic flux for some analogue meters and other instruments used in industry. Today, the permanent magnet is used for a wide variety of purposes ranging from the magnetic tape used in credit cards, fridge door seals, proximity relays, alarms, small generators, debris-collecting sump plugs and printed-circuit motors. In the past, the permanent magnet was also used in video tapes. A common and important application in modern machining practices is the magnetic chuck (shown in Figure 2.8). This uses the holding power of magnets to retain magnetic materials firmly in position on the work table of a machine during machining processes. No electrical connections are needed and, therefore, in the event of an electrical failure, the material being machined is not accidentally released or allowed to move or cause damage. Because it is not possible to ‘switch off’ the magnetism of a permanent magnet, some other means must be used to release articles held by the chuck. This is achieved by shunting (bypassing) the magnetic flux through low-reluctance bridges.

2.1.6  Construction, operation and applications of reed switches

Figure 2.7  Watch protected by a magnetic shield

Figure 2.8  Magnetic chuck

Figure 2.9  Normally closed reed switch Shutterstock/Darkdiamond67

Reed switches consist of two ferromagnetic wires and specially shaped contact blades enclosed in a hermetically sealed glass capsule with a gap between them. The glass capsule is filled with inert gas to prevent activation of the contacts (see Figure 2.9). They are operated using a magnetic field created by either a permanent magnet or current-carrying coil located close to the switch. The magnetic field will force the reed contacts to close. When the magnetic field is removed, the switch will open. 117

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2.2  Electromagnetism When current travels along a conductor, a magnetic field surrounds the conductor. This magnetic field increases if the current increases and decreases if the current decreases. If the conductor is made into a loop, the magnetic field increases inside the loop and decreases outside the loop, due to compression of the field inside the curve and stretching of the field outside the curve. Multiple turns further increase the field strength, as if greater current flows within the single loop.

2.2.1  Conventions representing direction of current flow in a conductor A single conductor, passing vertically through a flat plane (provided by a sheet of cardboard or clear plastic, maybe), is given a large current of perhaps 100 amps. If iron filings are sprinkled on the plane, a pattern appears, circling the conductor. That pattern is the magnetic field that surrounds every conductor-passing current.

2.2.2  Magnetic field pattern around a single conductor and two adjacent conductors carrying current A compass placed near the conductor will align on a tangent to the conductor, with the polarity of the compass aligned to the direction of the induced field (see Figure 2.10). If the direction of current in the conductor is reversed, the pattern of the filings remains unchanged, indicating that there is no change in the position or strength of the magnetic flux. However, the compass will now point in the opposite direction, indicating that the lines of force are now acting in the reverse direction around the conductor.

2.2.3  Using the right-hand (grip) rule to determine the direction of magnetic field around a current-carrying conductor There is a simple rule to help determine the direction of the field for a given direction of current flow—the ‘righthand (grip) rule’. In the context of a straight conductor, if the conductor is grasped (only if it has been established that it is not energised) in the right hand with the thumb pointing in the direction of the current flow, the fingers point in the direction of the magnetic field. The strength of the magnetic field around a straight conductor depends on the value of the current in the conductor. Doubling the current results in double the field strength—the field strength is proportional to the current.

2.2.4  Direction of force between adjacent current-carrying conductors Two symbols are commonly used to indicate the direction of current flow in any conductor seen end-on. A circle with a dot in the centre represents a current flowing towards the viewer, as if it were the point on the end of an arrow. A circle with a cross inside it represents a current moving away from the viewer, with the cross as the feather flights of the arrow. A magnetic field as a whole extends to infinity; however, a portion of the field may be of particular interest. In that Current flow case, the ‘magnetic flux’ (meaning the magnetic field at some particular location) is referred to. Figure 2.11(a) shows the flux around two straight conductors carrying current in the same direction. The flux of each conductor unites to form a single flux around both conductors. A flux tends to take the shortest possible N S path, which in this case will tend to pull the two conductors together. Figure 2.10  Magnetic field around a straight conductor 118

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If the current in each conductor flows in opposite directions, as shown in Figure 2.11 (b), the flux between the two conductors is acting in the same direction. Flux in the same direction tends to spread out, forcing the two conductors apart.

2.2.5  The effect of current, length and distance apart on the force between conductors (including forces on bus bars during fault conditions)

(a) Conductors carrying current in the same direction

Figure 2.11(b) shows a cross-sectional view of two conductors carrying currents in opposite directions. The lines of force between the two conductors act in the same direction and therefore tend to repel each other. Conductor movement will occur when the magnetic force of repulsion exceeds the physical forces holding the conductors in position. This situation can occur in (b) Conductors carrying current in opposite directions practice with heavy-current switch gear and machinery, and the effects are not always undesirable. Conductors Figure 2.11  Flux around straight conductors within electric motors and measuring instruments, for example, depend on these forces for their operation. The force between conductors carrying current in the same direction causes an attraction between the conductors (see Figure 2.11 (a)). The ampere is defined as the current that would cause a force of 2 × 10−7 newtons per metre between two conductors placed one metre apart. Therefore, the force between two conductors with a known current flow in each conductor and with a known distance separating the conductors can be calculated from: 2 × 10−7  × ​I​  1​​​I​  2​​  ​F  = ​ ___________     ​​   s where: F = force between conductors in newtons I1 = current in the first conductor in amps I2 = current in the second conductor in amps s = distance separating the conductors in metres

EXAMPLE 2.1 Two long parallel conductors 0.1 m apart each carry a current of 100 A in opposite directions. Calculate the force between them. 2 × 10−7 ​I​  1​​ ​I​  2​​ F = __________ ​​     ​​ (1)   s 2 × 10−7 × 100 × 100 = _________________ ​​        ​​ (2) 0.1 Press the following buttons on your calculator: 2

×

˘ 0x

(–)

7

×

1

0

0

×

1

0

0

÷

.

1

=

= 0 ​ .02 N​ (3) 119

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Electrical Principles

2.2.6  Magnetic field around an electromagnet Figure 2.12 shows how the current in each adjacent turn of a coil flows in the same direction. The magnetic fields around each loop will combine to form a single magnetic flux embracing all the turns of the coil. The strength of the resultant flux will be equal to the total of all the separate fields set up by each coil turn. As a result, the flux inside the coil is proportional to the number of turns in the coil. Figure 2.12 shows that the flux flowing through the centre of the coil establishes a north pole at the end where it leaves the inside of the coil and a south pole at the end where it enters the coil. The field around the outside of the coil is similar to the field around a bar magnet. Such a coil is commonly referred to as an ‘electromagnet’, because a magnetic field is produced by the current flowing through the coil.

2.2.7  Using the right-hand (grip) rule to determine the direction of magnetic field around a current-carrying coil The magnetic field generated by a solenoid can also be determined by the right-hand (grip) rule. When the right hand is placed over a solenoid coil so that the fingers point in the direction of the current flow, the thumb points in the direction of the magnetic field (see Figure 2.13).

2.2.8  Magnetomotive force (MMF) and its relationship to the number of turns in a coil and the current flowing in the coil If a straight conductor is bent to form a loop, the strength of the flux inside the loop is due to the magnetic field generated by each side, and therefore the total field is doubled. By winding the conductor into a coil of many turns, the field strength is increased in proportion to the number of turns in the coil.

2.2.9  Practical applications of electromagnets Electromagnets can replace permanent magnets or temporary magnets in most applications, with the advantage that electromagnets can be turned on and off and varied in magnetic strength. Electromagnets can also have alternating fields when an alternating current is applied. Permanent magnets cannot be made to alternate, especially at the line frequency of 50 Hz or 100 times per second. Electromagnets are used in motors and generators, transformers, microphones, loud speakers, indicators such as doorbells and car-ignition coils. The electromagnetic effect is used in the operating coils of devices such as contractors, relays, inductors, solenoids, chokes and ballasts.

S

N Current flow

Figure 2.12  Flux in a solenoid

Magnetic N flux

S Right hand Current direction −

+

Figure 2.13  Right-hand (grip) rule

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2.3  Magnetic circuits 2.3.1  Magnetic characteristic curve for various materials and identifying the various regions Non-magnetic materials The reluctance of non-magnetic materials is not affected by the density of flux in those materials. Flux (Φ) therefore will vary directly with the MMF (IN), and flux density (B) will consequently vary directly with the magnetising force (H). For non-magnetic materials, B varies directly with H and therefore the graph of B against H will be a straight line.

Magnetic materials When values of B are plotted against values of H for a magnetic material, the resulting graph is in the form of a curve. Table 2.1 shows figures for an iron sample. A graph plotted from these figures is shown in Figure 2.14. Since values of B are plotted against values of H, the graph is known as a ‘B/H curve’. These curves are commonly used as a means of comparing the magnetic characteristics of different types of magnetic materials.

Magnetic saturation Reference to the B/H curve in Figure 2.14 shows that, when the value of H is low, small increases in the value of the magnetising force (H) will produce large increases in the value of the flux density (B). This is shown by the section of the curve that slopes steeply.

Table 2.1   Magnetisation curve for a magnetic material Flux density B (Wb/m2)

Permeability µ = B/H

Relative permeability µr = µ/µo

100

0.04

0.00040

318

200

0.12

0.00060

477

300

0.40

0.00130

1058

400

0.90

0.00225

1790

500

1.00

0.00200

1591

600

1.06

0.00177

1408

700

1.11

0.00159

1265

800

1.15

0.00144

1146

900

1.18

0.00131

1042

1000

1.21

0.00121

963

1200

1.25

0.00104

828

1400

1.29

0.00092

732

1600

1.32

0.00083

660

2000

1.36

0.00068

541

Magnetising force H (At/m)

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Electrical Principles

1.8

1600 B/H Curve

1.4

1400

1.2

1200

1.0

1000 800

0.8 Value of B at which µr is at maximum

0.6 0.4

600

Relative Permeability µr

1.6

Flux Density B (Teslas)

For higher values of H and B, it can be seen that increases in H will produce progressively smaller increases in B. Further increases of H to the value H3 will result in an even smaller increase in B from B2 to B3. As the magnetisation increases towards 2000 At/m, the flux density increases less and less. This indicates that magnetic saturation is taking place. Saturation is said to occur at a flux density near the centre of the ‘knee’ of the B/H curve. In practice, it is not economical to magnetise steel to a flux density much beyond the point of magnetic saturation. A large increase in magnetising current produces only a small increase in flux density, resulting in a waste of electrical power without achieving any useful increase in flux. The permeability of ferromagnetic materials changes with differing values of flux density. For a given flux density, permeability (μ) is equal to the ratio B/H. This can be proved by applying the basic magnetic equation in the following manner:

1800

µr /H Curve

400 200

0.2

0

0.0 0

400 800 1200 H1 H2 H3 Magnetising Force

1600

2000

H (At/m)

Figure 2.14  Flux—magnetisation curve



IN Φ = ___ ​    ​   ​R​  m​​

(1)



and Φ = BA

(2)



lN ∴ BA = ___ ​    ​   ​R​  m​​

(3)

l ​also R​  m​​ = _____ ​     ​   ​μ​  o​​ ​μ​  r​​  A

(4)

lN ___ ​   ​ 

l By substitution: BA = ______ ​     ​   ​μ​  o​​ ​μ​  r​​  A lN ​μ​  o​​ ​μ​  r​​  A = _______ ​   ​     l

lN ​μ​  o​​ ​μ​  r​​ ∴ B = ______ ​   ​     l IN also H = ___ ​   ​   l

By substitution: B = H × ​μ​ o​​ ​μ​  r​​

(5) (6) (7) (8) (9)



and  :  μ = ​μ​  o​​ ​μ​  r​​

(10)



B ∴ μ = __ ​    ​ H

(11)

Table 2.1 gives typical values of B and H for iron. Therefore, it is possible to calculate permeability for each particular flux density and magnetising force. In columns 3 and 4, values for μ and μr have been calculated from the given values of B and H. 122

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Comparison of B/H magentisation curves

1.8 1.6

Saturation is the portion on the curve at which an increase in magnetising force produces less of an increase in flux density, after the point of maximum permeability. Silicon steel

1.4

Flux Density B (Teslas)

The values of μr have been plotted against the values of H in Figure 2.14 to give the μr/H curve. The graph shows that the permeability curve rises steeply to a peak. Beyond this point of maximum permeability, the curve slopes away quite rapidly. This indicates that permeability becomes progressively less as H is increased beyond the value that causes magnetic saturation.

Figure  2.15 illustrates the magnetisation curves for

1.2 1.0

n

r

tu

Sa

io at

t

Sa

Cast steel

0.8 0.6

Cast iron ion urat

0.4

silicon steel, cast steel and cast iron. The following points should be noted:

n

tio

a ur

Sat

0.2

1. The materials tend to become magnetically 0.0 saturated in the region that corresponds with the 400 800 1200 1600 2000 2400 0 centres of the ‘knees’ of the respective curves. Magnetising Force H (At/m) 2. When the value of H is in the lower ranges, Figure 2.15  Magnetisation curves much greater flux density will be produced in silicon steel, compared with cast steel or cast iron. 3. Silicon steel saturates at a slightly lower value of flux density than cast steel. 4. Cast iron saturates at much lower values of flux density than either silicon steel or cast steel. It is also much harder to magnetise than either of the above materials.

2.3.2  Identifying the various conditions of a magnetic material from its hysteresis loop The term ‘hysteresis’ means lagging behind. In electrical terminology, it describes the lag between a change in value or direction of the magnetising force and the resulting change in value or direction of flux. Residual magnetism is that portion of the magnetic flux that remains in a ferromagnetic material when the magnetising force is removed. In other words, the material remains partially magnetised because it has some permanent magnetic properties. In order to remove residual magnetism, it is necessary to use a force that acts in the opposite direction to the original magnetising force. The force that is used to overcome residual magnetism is known as the ‘coercive force’—the force required to coerce the magnetism from the material. When a ferromagnetic material is magnetised first in one direction and then in the other, it is necessary to +B use coercive force to overcome the effect of residual A B magnetism. The amount of coercive force required Residual flux (Br) depends on the type of magnetic material. The energy required for the coercive force is wasted and therefore Coercive force (Hc) considered to be a loss, resulting in lower efficiency O F and heating of the magnetic core. −H +H C

Hysteresis loops If the magnetising force is plotted against the flux density in the classic B/H graph, the hysteresis can be clearly seen in both directions. In Figure 2.16, the initial magnetisation curve OA is of note. It begins at the origin (O) when no magnetic

D

E -B

Figure 2.16  Magnetic hysteresis

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force or flux exists, and increases to point A which is well into the saturation region, or past the knee of the curve. The magnetising force (+H) results in a flux (+B) that is saturated. As the magnetising force is reduced back to zero, the flux density reduces as well, but not to zero. The part of the curve AB represents the removal of the magnetising force and the resulting reduction in flux, but point B shows the flux density that remains, the residual flux (Br). In order to remove the residual magnetism, a reverse magnetising force is required, called a ‘coercive force’ (Hc), that causes the flux density to be reduced to zero. Part BC of the curve shows the coercive force in effect. The negative magnetising force now continues to increase to point D, which is the maximum negative magnetising force and a point equal but opposite to point A on both axes. Curve DEFA is an exact reflection of ABCD. Thus the combined magnetisation curves form a closed loop, ABCDEFA. This loop is commonly known as a ‘hysteresis loop’ for a ferromagnetic material. OB and OE indicate the values of residual flux density at zero magnetising force, while the value of the coercive force required to remove that residual flux is indicated by OC and OFAL.

2.3.3  Factors which determine losses in magnetic material Reversing the magnetic field requires a coercive force to reverse the residual magnetism, and this requires a current flow. This results in the generation of heat within the magnetic material, which represents a loss of energy, known as ‘hysteresis loss’. How much energy is lost depends on the amount of coercive force required to reverse the magnetic dipoles within the material, and this is directly proportional to the area within the hysteresis loop for that material. The hysteresis loop determines the suitability of a magnetic material for a particular application. In equipment that is subjected to a rapidly changing flux, it is important that the material used in the magnetic core has a hysteresis loop with a small area. The maximum height (B) is the designated flux that must be reached, but the width of the loop (H) must be as narrow as possible to reduce losses. Permanent magnets, however, should require a very large coercive force to be de-magnetised, and therefore the hysteresis loop should be very wide, with a large loop area. Hysteresis loss appears in the form of heat in the magnetic cores of equipment; these are often iron, particularly in older equipment, and so it is known as ‘iron loss’. Electrical power has to be consumed to make up for iron loss, and it is therefore usual to give values of iron loss for a particular material in watts per kilogram at a given frequency—50 Hz, for example.

2.3.4  Methods used to reduce electrical losses in a magnetic circuit The area of hysteresis loops obtained from tests on samples of magnetic materials give important information about the suitability of a material for a particular application. Figure 2.17 compares the hysteresis loops of transformer steel and carbon steel. It shows that the hysteresis loop for Transformer steel transformer steel is comparatively small in area, which +B indicates that transformer steel will give a relatively Carbon steel lower iron loss. This is an important factor in the choice of core material for transformers, because rapidly reversing fluxes occur in this application. Carbon steel would not be suitable because of the large iron loss −H +H that would occur; however, permanent magnets may be made from carbon steel.

2.3.5  Magnetic flux −B

Figure 2.17  Hysteresis losses in materials

So far, magnetic fields have been considered in terms of the total flux. The unit for flux is the weber (Wb, after Wilhelm Eduard Weber), which refers to the

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total flux generated by a magnetic source. The SI defines the weber as the unit of magnetic flux, equal to the flux that produces in a circuit of one turn an electromotive force of one volt, when the flux is uniformly reduced to zero within one second.

2.3.6  Reluctance as the opposition to the establishment of magnetic flux Some materials require high magnetising forces to align their atomic dipoles in the same direction, while others are readily magnetised by small forces. All materials offer some opposition to being magnetised, and the term used to describe this opposition is ‘magnetic reluctance’. Reluctance is comparable with resistance in an electric circuit.

2.3.7 Permeability The permeability of a material is defined as the ease with which a flux can be created in that material. If there is no material, such as in a vacuum, the value can be shown to be 4 × 10−7π (or 4π × 10−7). That is the permeability of free space (a vacuum), which has the abbreviation μo. The permeability of free space is the reference against which the permeability of other materials is compared. To compare the permeability of any given material with the permeability of free space, it is necessary to use a ratio μr which is known as the ‘relative permeability’ of the material. For air and other non-magnetic materials, μr has the value of unity (μr = 1). If the non-magnetic core of a solenoid is replaced with a magnetic material, the flux produced by the same number of ampere-turns may be greatly increased. The ratio of the flux produced by the magnetic core to that produced by the non-magnetic core is a direct result of the relative permeability of the magnetic material. For some magnetic materials, μr can have a value in the thousands. For any one magnetic material, the relative permeability value can vary considerably, being dependent on the flux density in the material. Relative permeability is higher at low values of flux density. To find the actual permeability of a material, the permeability of free space is multiplied by the relative permeability of the material: ​μ  = ​μ​  o​​ ​μ​  r​​​ where: μ = actual permeability μ ​​         ​​ o​  =​ ​  permeability of free​ space​ μr = relative permeability

2.3.8  Difference for magnetic and non-magnetic materials with regard to reluctance and permeability The reluctance of a material depends on a number of factors:

1. Length of a magnetic circuit—reluctance varies directly with the mean length of a magnetic circuit and is similar in this respect to electrical resistance: ​Rm ∝ l (as R ∝ 1)​

2. Cross-sectional area of a magnetic circuit—reluctance varies inversely with the cross-sectional area of a magnetic circuit: 1  1 ​Rm ∝ ​ __  ​  (as R ∝ ​ __  ​)  ​  A A 125

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3. Permeability of the circuit material—permeability is used as a measure of the ease with which materials may be remagnetised. Reluctance, on the other hand, is a measure of the opposition to flux. Permeability is analogous to the resistivity of an electric circuit: 1  Rm ∝ ​ ____    ​  (as R ∝ ρ) ​​   ​  ​   ​μ​  0​​ ​μ​  r​​  ​​​ Rm =  ​μ​  o​​ ​μ​  r​​  A where: Rm = reluctance in ampere-turns per weber l = length of circuit in metres A​      square ​​ metres​​ ​​              ​  =​ ​  cross-sectional area in  ​​ μo = permeability of free space μr = relative permeability

EXAMPLE 2.2 The total mean length of the path of an iron core is 200 mm. The core is rectangular in cross-section, with dimensions 15 mm × ​ ​ 10 mm. If the core has a relative permeability of 830 at the designed flux density, calculate the reluctance of the core. (Remember to convert to base units.) l ​R​  m​​ = _____ ​     ​  (1) ​μ​  o​​ ​μ​  r​​  A ​​

200 × 10−3 ​​         =​  _____________________________ ​           ​​  (2)​​​ ​    ​ 4 × 10−7 × π × 830 × 15 × 10−3 × 10 × 10−3 1.278 × 106 At  ​ = ____________    ​    ​  Wb

(3)

Ohm’s Law, when applied to electrical circuits, gives the following formula: V  ​I  = ​ __ ​​   R where: I = current flow in amperes ​  =​  electromotive force​ ​​ ​​ V        ​ R = circuit opposition to flow or resistance A similar rule can be applied to magnetic circuits, that is: IN  ​Φ  = ​ ___  ​​   ​R​  m​​ where:

Φ = magnetic flux (webers) IN = magnetomotive force (ampere-turns) ​ ​​      ​​      ​  ​  ​ IN Rm = magnetic opposition or reluctance ​ ___ ​    ​  ​ (Wb)

From the above equation, it can be seen that increasing either the current or number of turns of a solenoid will increase the flux. A decrease in Rm also increases the flux. 126

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Ohm’s Law for magnetic circuits may be given in three variations to suit particular problems: IN  Φ = ___ ​    ​  (webers)  ​R​  m​​    ​​     ​  ​  IN   ​​​ ​ Rm = ___ ​   ​  (At/Wb)  Φ IN = Φ​R​  m​​(At)

EXAMPLE 2.3 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 IN/Wb. Calculate the flux produced when 10 A flows through the coil. Using the magnetic law in the form: IN Φ = ___ ​    ​      (1) ​R​  m​​ ​​ ​      ​  10 × 600 ​  ​  ​  ​ ​ = ________ ​   ​         (2) 800 ​ = 7.5 Wb     (3)

EXAMPLE 2.4 A contactor coil has 7200 turns, which are wound on an iron core, rectangular in section and having dimensions of 20 mm × 30 mm. If the flux density in the magnetic circuit is 1.2 T, find the reluctance of the magnetic core. The current drawn is 0.1 A. Step 1. Calculate flux from flux density: ​ Φ​= BA (1) = 1.2 × 20 × 10−3 × 30 × 10−3 (2) = 720 × 10−6Wb (3) Step 2. Calculate reluctance: IN ​ R​  m​​ = ___ ​    ​ (4) Φ 0.1 × 7200 = _________ ​     ​ (5) 720 × 10−6 1  × 106 At  = ________ ​        ​ (6)  Wb

2.3.9  Calculation of MMF, flux or reluctance, given any two values The force required to create a magnetic field is called the ‘magnetomotive force’. This is abbreviated to MMF and has a general symbol—Fm. The magnetomotive force is the force that creates the magnetic field. It acts like the electromotive force in an electric circuit and is the force necessary to set up a magnetic flux in a magnetic circuit. The MMF is dependent on the current flowing in a conductor, and the magnetic field of a solenoid is dependent on the number of turns of the solenoid. The field strength of a coil is therefore proportional to the product of the current and the number of turns in the coil. In pure SI units, the MMF unit is the ampere, because the number of turns in a coil or solenoid is considered dimensionless. In calculations, however, the number of turns has to be included. In this book and generally within the electrical trades, an MMF quantity will be given directly as ampere-turns (abbreviated as IN), and the units will be specified as ampere-turns (At). 127

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​Fm = IN​ where: Fm = MMF (or magnetomotive force) in ampere-turns ​​      ​​ ​ ​  =​  current flowing in amperes ​ I     N = number of turns in coil

EXAMPLE 2.5 If a current of 5 A is flowing in a coil of 120 turns, find the value of MMF creating a magnetic flux. Fm = IN (1) = 5 × 120

(2)

= 600 At (3)

2.3.10  Flux density In many instances, it is helpful to know the density of the flux rather than its total strength. (Density refers to the quantity of flux per unit area.) The general symbol for flux density is B and the unit is the weber per square metre (Wb/m2). One weber per square metre is called a tesla (T), after Nikola Tesla. (An older term for flux, the ‘gauss’, is still occasionally used, as is a gaussmeter. One tesla is equal to 10 000 gauss. In other terms, one gauss is equal to 10−4 tesla.) If both the total flux and the area of the magnetic path are known, the flux density is found from: Φ  ​B  = ​ __ ​​   A where: B  = flux density in teslas (Wb/m2) Φ = total flux in webers A   = area in m2

EXAMPLE 2.6 A magnetic circuit has a cross-sectional area of 100 mm2 and a flux density of 0.01T. Calculate the total flux in the circuit. Φ = BA (1) = 0.01 × 100 × 10−6 (2) = 1 × 10−6 Wb (3) The answer is expressed in webers and not in lines of force.

2.3.11  Magnetising force The MMF required to magnetise a unit length of a magnetic path is termed the ‘magnetising force’ for that portion of the magnetic circuit. The magnetising force is applicable only to that section of the magnetic circuit, made of the one material and with a constant cross-section. The unit is expressed in ampere-turns per metre and the symbol is H. 128

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In a similar fashion to that for magnetomotive force, the ‘turns’ part of the expression is dimensionless and in pure SI units should be omitted, leaving it as amperes per metre. For all practical purposes, however, the more descriptive term is ampere-turns per metre, which is what is used in this book. That is: ​H  =  IN / l​ where: l = length of magnetic circuit in metres It is important to convert length into metres. Magnetising force must not be confused with magnetomotive force.

2.3.12  Common magnetic circuit types As a magnetic field may be induced into magnetic materials, the path of the magnetic circuit is important in maximising the efficient use of the magnetic force. When inductance is the only requirement of a coil, a closed magnetic circuit confines the magnetic field and results in minimal losses. Such a closed magnetic circuit is often made of a toroid of iron or ferrous materials. A toroid is a shape similar to a doughnut or car tyre, being a circle of iron, usually of square section with radiused corners, as shown in Figure 2.18. Traditional laminated core or shell-type cores may also be used, but the trend today is toward toroids—they are generally simpler to manufacture (by modern machines) and have a better efficiency and lower weight.

Figure 2.18  Toroidal core

2.3.13  Effect of an air gap in a magnetic circuit The magnetic field will attempt to take the shortest possible path while spacing the ‘lines of force’ into whatever space is available. That means that the lines of force tend to spread out sideways while taking the shortest path around the circuit. As iron or similar ferrite materials have a lower resistance to the magnetic field, the lines of force will tend to take a path through the iron core rather than air, which is the non-magnetic path of the circuit. Due to the high reluctance of air, the lines of force will try to shorten the air, which provides the basis of magnetic switching.

2.3.14  ‘Magnetic leakage’ and ‘magnetic fringing’ In practical magnetic circuits, it is often desirable to have the maximum value of flux in a particular section of the circuit. Unfortunately, the flux tends to spread out, particularly when the flux density is high. There is a tendency for some of the flux to leak through the surrounding air, bypassing the intended path. Therefore, the flux density in the intended path of the magnetic circuit is reduced to a lower value. The magnetising force must be increased to allow for the losses but, when the core becomes saturated, the amount of energy required to increase the magnetic flux may become uneconomical, or even impossible. Figure 2.19 illustrates a magnetic circuit for an instrument in which the source of MMF is a strong permanent magnet. In this particular circuit, the maximum possible flux is desirable at the air gap, evenly distributed in the gap between the soft iron pole pieces and the armature. The total flux of the magnet does not reach the air gap as some of it leaves the iron poles prior to the gap and passes through the surrounding air. The flux which leaves the main path is known as the ‘leakage flux’. The tendency for the leakage flux to stray from the desired path is known as ‘magnetic leakage’. When designing magnetic circuits, engineers allow for magnetic leakage when calculating the values of flux required. 129

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Fringing

Leakage

Figure 2.19  Armature relay/contactor showing leakage flux

As there are no magnetic insulators, there is no means of retaining the magnetism within the magnetic conductor. Figure 2.19 also shows the magnetic field that exists across an air gap in a magnetic circuit. The lines of force near the centre line of the flux path are straight. Lines of force at the edges of the field tend to curve outwards in the air gap and spread according to the rule that flux travelling in like directions repels. As a result, the area of the flux path is greater in the air gap than in the material of the magnetic circuit. The flux density of the air gap will in consequence be less than that in the magnetic material on either side of the gap. This effect is known as ‘magnetic fringing’ and must be allowed for when designing magnetic circuits in which there are air gaps. Some magnetic leakage also occurs at the sides of the air gap, but this is normally counted as a part of the fringing.

2.4  Electromagnetic induction 2.4.1  Principle of electromagnetic induction (Faraday’s Law of electromagnetic induction) When a magnet is attracted to a piece of magnetic material, the magnetic field passes through the material, turning it into a temporary magnet. This is easily proved by placing a piece of non-magnetised material, such as a mild steel bolt, above a collection of small iron nails or washers. The bolt will not pick up the small items by itself, but placing a magnet above it will induce a magnetic field into the soft iron bolt, causing it to pick up the small items. The magnetic field is said to be induced into the material and this action is called ‘magnetic induction’. When a material has been induced by an external field, the magnetic flux passes through the material in the same direction as in the magnetising source. This means that the magnetised material will have a complementary pole next to the permanent magnet pole—that is, if the permanent magnet pole is north, the induced magnet pole it is connected to will be south. In all magnetic materials, the magnetising force induces an unlike polarity at the surface of the material nearest the point where the magnetising flux enters (see Figure 2.6). Magnetic induction always takes place when attraction occurs between a magnet and a material that is not magnetised. The green items in Figure 2.6 are both ferromagnetic while the yellow item is diamagnetic, which means that its permeability is less than that of free space.

or

ct du

n

Co

2.4.2  Applying Fleming’s righthand rule to a current-carrying conductor under the influence of a magnetic field Symbol ‘B’ signifies current flow towards viewer

Symbol ‘A’ signifies current flow away from viewer

Figure 2.20  Current flow convention

Fleming’s right-hand rule helps to determine the direction of the induced current in a conductor if the direction of the magnetic field around the conductor is known. If the conductor is grasped (only if it has been established that it is not energised) in the right hand with the thumb pointing in the direction of the current flow, the fingers point in the direction of the magnetic field. The convention to represent current flow is shown in Figure 2.20.

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2.4.3  Calculation of induced EMF in a conductor, given the conductor length, flux density and velocity of the conductor

For a conductor rotating at a fixed velocity in a uniform magnetic field

The formula for the EMF generated in a coil is:

At 0° between path and flux, V = Vmax sin0° =0V

At 270° between path and flux, V = Vmax sin270° = −1 v

​e = Blv sinθ​

Rotational velocity is constant

At 90° between path and flux, V = Vmax sin90° = 1v

While the average electrician may not use this formula to calculate the EMF generated in a coil, it At 180° between is important in establishing (and remembering) that path and flux, V = Vmax sin180° the voltage is proportional to the number of turns, At 135° θ V = V sin135° =0V max the field density, the relative velocity between the = 0.707 V conductor and the field, and the angle that the motion makes with the axis of the field. Figure 2.21 shows Figure 2.21  Conductor path through a magnetic field the path a conductor takes in one revolution. Example 2.7 shows that, for a given conductor length and velocity in a given field, all of which remain constant, the voltage generated is directly proportional to the sine of the angle between the conductor path and the axis of the magnetic field. When the path is parallel with the magnetic field, at θ = 0°, no voltage is generated as the conductor does not cut across the magnetic field. When the path is at right angles to the magnetic field, at θ = 90°, the full voltage is generated; in Example 2.7 this is 1 V.

EXAMPLE 2.7 A 10 cm conductor is rotated within a magnetic field of a constant density of 1 tesla. If the velocity relative to the field is 10 m per second, what voltage will be generated at each of the angles: 0°, 30°, 45°, 60° and 90°? 10 cm = 0.1m

(1)

e = Blv sinθ

(2)

Blv = 1 × 0.1 × 10

(3)

= 1 V (4) ∴ @ 0°,  e = 1 × sin(0°)

(5)

= 0 V (6) @ 30° ,  e = 1 × sin (30° )

(7)

= 0.5 V (8) @ 45° ,  e = 1 × sin (45° )

(9)

= 0.707 V (10) @ 60° ,  e = 1 × sin (60° )

(11)

= 0.866 V (12) @ 90° ,  e = 1 × sin (90° )

(13)

= 1 V

(14)

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At any angle between 0° and 90°, the voltage will be between 0 V and 1 V. The actual value is calculated using E = Emax × sin(θ). The value increases from 0° to 90°, then reduces again to 0 V at 180°. The voltage then becomes negative from 180° to 270°, when it is –1 V, and returns to 0 V at 360°.

2.4.4  Calculation of induced EMF in a coil, given the number of turns in a coil and the rate of change of flux An EMF can be induced in a conductor if the conductor cuts across (or is cut across by) a magnetic field. That is to say, when there is a relative movement between a conductor and a magnetic field, a current will be induced in the conductor if there is a complete circuit. Michael Faraday found that the voltage generated in a coil due to a changing magnetic field is directly proportional to the change in flux and inversely proportional to the change in time. He also noted that increasing the number of conductors, or turns of a coil, is equivalent to increasing the current.

Faraday’s Law The value of the EMF induced in a circuit depends on the number of conductors in the circuit and the rate of change of the magnetic flux linking the conductors. In mathematical terms: ΔΦ ​V  =  N ​ ____ ​​   Δt where: V = induced voltage N = number of turns ΔΦ = flux change in webers Δt = time change in seconds In engineering and science, the generated voltage is often denoted by the symbol ε for ‘EMF’, so the following formula represents the same law: ΔΦ ​ε  =  N ​ ____ ​​   Δt

EXAMPLE 2.8 A coil of 600 turns has a flux of 80 μWb passing through it. If the flux is reduced to 30 μWb in 15 ms, find the average induced voltage.

ΔΦ ε = N ​ ____ ​   Δt

(1)

80 × 10−6 − 30 × 10−6 = 600 × ​ _____________        ​ 15 × 10−3

(2)

50 × 10−6 = 600 × ​ ______  ​   15 × 10−3

(3)

= 2 V (4) 132

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EXAMPLE 2.9 A coil of 500 turns has a permanent magnet moved into it such that 0.2 Wb cuts across the coil in four seconds. ΔΦ E = N ​ ____ ​   Δt

(1)

0.2 = 500 × ​ ___ ​    (2) 4 = 25 V (3)

The parameters that determine the magnitude of the generated EMF are therefore:

∙ ∙ ∙ ∙

the magnetic field density (B) the length of the conductor within the field (l) the relative motion between conductor and field (v) the angle between the field lines and the path of the conductor (sinθ).

An EMF is generated by the continuous rotation of a conductor through a magnetic field; this is the most important method of generation of electricity—it is the basis of all rotating electrical machines

2.4.5  Calculation of force on a conductor, given the flux density of the magnetic field, length of the conductor and the current being carried by the conductor If two conductors have an MMF between them caused by the interaction between the flux of each, then it follows that a conductor carrying a current within a field from a permanent magnet—or electromagnet—will also have a force placed upon it that can be calculated (as shown in Figure 2.11 and calculated in Example 2.10). The value of the force on a conductor within a magnetic flux can be found from: ​F = BIl​

EXAMPLE 2.10 A conductor is placed at right angles to a magnetic field with a flux density of 0.66 T over a length of 0.1 m of the conductor. If a current of 25 A is passed through the conductor, calculate the force exerted on the conductor. F = BIl (1) = 0.66 × 25 × 0.1

(2)

= 1.65 N (3) where: F = force in newtons B = flux density I = current in amperes l = conductor length in metres 133

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2.4.6  Lenz’s Law Current flowing in a conductor generates a magnetic field, which increases as the current increases and decreases as the current decreases. When a changing magnetic field cuts across a conductor, a voltage is generated in that conductor and, if a circuit exists, a current will flow. Therefore, whenever a current in a conductor changes (either increasing or decreasing), the change in the magnetic field will generate a voltage and a resulting current in that conductor. The polarity of the generated voltage is opposite to that of the applied voltage during a current increase, and the generated current opposes the original current. As the current decreases, the field collapses, producing a voltage that assists the applied voltage. The value of the generated voltage, and therefore the current, is proportional to the rate of change of the original current. The magnitude and direction of the induced EMF is defined in Lenz’s Law. The induced current will appear in such a direction that it opposes the change that produced it. Lenz’s Law tells us three things about current in a conductor:

1. A current that is increasing produces an opposing current that causes the increase to be slower than expected. 2. A stable current in a conductor maintains a magnetic field of stored energy. 3. A current that is decreasing converts the stored energy back into a current that assists the applied voltage and current, such that any decrease in current is slower than expected.

It will be shown that in a.c. circuits the current is constantly changing in both strength and direction. Figure 2.22 represents the downward movement of a conductor through a magnetic field as a result of mechanical force acting downwards. This downward movement through the field will induce an EMF in the conductor. The resulting current, in a closed circuit, will create a circular magnetic field around the conductor. For Lenz’s Law to apply, the induced field must oppose the motion. The direction of the induced field must be such that the following reaction will occur between the main and induced fields: Direction of current flow due to induced EMF

Conductor motion

(NB: The circuit is complete but only a section of the conductor is shown.)

Direction of magnetic field Direction of force resulting from interaction between magnetic field and field surrounding conductor.

Figure 2.22  Forces on a conductor in a magnetic field

Figure 2.23  Typical brake mechanism

  1. The main field will be compressed in front of the moving conductor and expanded behind it.   2. The compressed magnetic field is a stronger force than the expanded magnetic field; therefore, the difference in the forces acts in opposition to the motion of the conductor.

2.4.7  Applications of electromagnetic induction Electromagnetic brake Electromagnets are often used in conjunction with an electric motor, especially a lifting motor as used on a crane. When the lifting motor is engaged, a solenoid releases a brake, allowing the lifting drum to rotate and wind up the load. Disconnecting the motor releases the solenoid and automatically applies the brake. The system is considered failsafe as loss of power does not permit the load to fall. Electromagnetic brakes can also be made to operate when power is applied, either when a control circuit applies energy or the operator presses a button or foot switch. Electro dynamic braking involves an electric motor connected in such a way as to make its operating speed zero, so when the motor is energised it attempts to stop whatever load it is connected to. A typical brake mechanism is shown in Figure 2.23.

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Electromagnetic clutch At times, an electric motor cannot speed up or slow down fast enough for a given load. A typical situation is a large metal-working guillotine. The electric motor runs a large flywheel up to speed, and when the press is operated an electromagnetic clutch engages the flywheel to the cutting blade for one revolution of the flywheel. The flywheel provides most of the energy for the cut and, when completed, the motor drives the flywheel back up to its idling speed. Many other machines use an electric clutch to engage or disengage various functions of the machine, often multiple functions from a single driving motor.

Figure 2.24  Electromagnetic chuck SCHUNK GmbH & Co. KG

Electromagnetic chuck An electromagnetic chuck (Figure  2.24) is an electrically operated device for holding work on a machine. On a grinding machine, for example, an iron part might be held in place by placing it on the surface of the chuck and applying power to the magnet. A disadvantage is that the power supply must be very reliable as loss of magnetism can result in major damage to the machine. The system is therefore mostly used to add security to a holding mechanism where the job is unlikely to move anyway. Often the machine is a computer numerical controlled (CNC) machine.

Lifting electromagnet Scrap metal dealers often need to move large amounts of jagged and dangerous iron and steel. To manually handle the material would be risky, and even ropes and lifting straps might be damaged by the scrap. The answer is to use electromagnets to pick it up. The magnet is lowered onto the scrap, energised and lifted away to wherever the scrap is intended to be placed, and then de-energised to drop it. Some electromagnets can lift many tonnes of iron in one lift, including large automobiles (see Figure 2.25).

Electromagnetic separator Electromagnets only work on magnetic materials, so the effect can be used to separate magnetic materials from non-magnetic materials. As shown in Figure  2.26, a conveyor belt typically carries materials to a dumping bin; but the end drum is magnetised so magnetic materials fold around to the underside of the drum, where they drop off into a separate bin. Other methods exist, depending on the type of materials being separated.

Figure 2.25  Lifting electromagnet

Scrap material

Non-ferrous is not attracted by the magnetised drum

Magnetised drum Conveyor belt Ferrous bin (iron)

Non-ferrous bin

(a) Ferrous metal separator

Non-ferrous metals such as copper, brass and aluminium are ‘levitated’ by the a.c. magnetic drum

Scrap material Alternating magnetic drum Conveyor belt Ferrous bin (iron)

Non-ferrous bin

(b) Non-ferrous metal separator

Figure 2.26  Electromagnetic separator

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Magnetic relay A magnetic relay is a switch operated by a magnetic coil. The relay switch consists of a solenoid that has a fixed iron core and a part which is movable. A spring is often used to provide the force to hold the movable portion (the armature) away from the fixed portion (the stator or core) when the solenoid is de-energised. When the coil is energised, the armature is pulled against the stator, closing the magnetic circuit and mechanically closing (or opening) one or more sets of contacts. Relay switches operate electrical contacts for closing or opening a circuit, while solenoids operate a plunger to effect a mechanical operation.

2.5  Inductance In electric circuits, ‘inductance’ is the property of a circuit which creates electromagnetic induction: it produces a voltage in a conductor that results from the magnetic field created by an electric current. That is, the voltage is ‘induced’ in the conductor as the result of an electric current in another (or the same) conductor. ‘Induction’ is the process by which this voltage is produced by the electric current. Inductance is the property itself, while induction is the process by which inductance operates. Induction is the basis of many important theories and practices in electricity, so much so that the single most common type of electric motor is called the ‘induction motor’. All transformers work through the inductance effect. The induction process can store energy when a current is first applied and return that energy after the current has been turned off. Although the property of inductance is present in all conductors, components that are called inductors usually take the form of a coil of wire, often wound around an iron or other magnetic core.

2.5.1  Construction of an inductor, including a Bifilar winding inductor An inductor is a component with inductance—it induces an electromagnetic field into the space around the conductor. The electromagnetic field is stored energy, which the inductor can later return as a current. Inductors have the effect of storing current as an electromagnetic field whenever the current increases and giving it back when the current decreases. Therefore, an inductor is often used to smooth the current value. This is called ‘filtering’, and in this case the inductor is called a ‘choke’. The Bifilar winding (see Figure  2.27) has two closely-spaced parallel windings. They are commonly used to reduce the self-inductance in wirewound resistors.

2.5.2  Australian Standard circuit diagram symbol for the four types of inductor

Figure 2.27  Bifilar winding Flickr/Windell Oskay/CC BY 2.0.

Normally, inductors are made as a coil of wire, sometimes wound around a core of a magnetic material such as iron. The symbol for a single coil is shown in Figure 2.28(a). A line drawn next to a symbol for a coil indicates that a magnetic core has been used. If there is no bar, this often means that it is an air-core coil which has no magnetic core. However, the general symbol for a coil as described in Standards Australia publications does not

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require the bar to show the type of core. The bar is included only when it is necessary, such as when some inductors in a circuit have a core and others do not. Inductors can also have multiple coils with the same symbol used for each coil, and generally a core is shown as a solid line (see Figure 2.28(b)) or as a dashed line to represent a ferrite (ceramic iron) core (see Figure 2.28(c)). The symbol for a Bifilar winding can be seen in Figure 2.29

2.5.3  Effect of physical parameters on the inductance of an inductor

(a) Air-core inductor

(b) Laminated iron-core inductor

Magnetic field density The magnetic field density (B) is determined by the total flux produced by the magnet (Φ) and the area of the magnetic field (A). As the total flux spreads out over any area available, flux density often refers to the flux in a given area, such as the area directly between two magnetic poles. The magnetic field density or flux density can be changed by changing the magnets or the magnetic path that the field passes through. An electrically produced magnetic field can be changed by changing the current flowing in the coil or the number of turns of that coil.

(c) Iron-powder core inductor

Figure 2.28  Inductor types and symbols

Length of the conductor The conductor length can be increased by increasing the area of the magnetic field that the conductor passes through, Figure 2.29  Bifilar symbol while keeping the magnetic field strength constant. However, the most common method of increasing the length of the conductor within a given space is to add more conductors. As the conductor is usually wound in a coil, the length must be multiplied by the number of turns in the coil passing through the flux (N). Therefore, the total length of a conductor is the actual length multiplied by the number of conductors.

Velocity of motion of the conductor A conductor passing through a magnetic field over a given time generates a voltage proportional to the field through which it passes. If the conductor travels faster, it will pass through more of the magnetic field in the same time and the voltage generated will be greater. The most obvious way to change the voltage, therefore, is to change the speed at which the conductor travels. This is achieved by changing the rotational speed of the machine. Traditionally, rotational speed is given in revolutions per minute (rpm), and speed is given in revolutions per second (rs−1) or radians per second (rad s−1). One revolution per second equals 2π radians per second.

Angle of the conductor path A second factor that changes the effective speed or velocity of the conductor is the angle between the magnetic field and the path of the conductor. At 90° to the field flux, the voltage generated will be the greatest, and at 0° the voltage will be zero. This is because at 0° the conductor is travelling parallel to the magnetic field and will not cut across any magnetic lines of force. The value of the voltage will therefore be between 0% and 100% of the maximum voltage generated. Those familiar with trigonometry should see that the value is proportional to the sine of the angle. 137

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2.5.4  Common types of inductor cores Air cores An air-core inductor is simply a coil of wire, sometimes wound around a plastic former, but often simply wound into a coil, as shown in Figure 2.30. Air-core inductors have no core and therefore have no appreciable core losses. They can therefore be used at any frequency. However, they can only convey a small amount of energy at lower frequencies; to convey more power at low frequencies, a magnetic core must be used.

Iron-powder cores

Figure 2.30  Air-core inductor

Sometimes called ‘ferrite cores’, iron-powder cores (see Figure 2.31) are manufactured from very fine iron powder mixed with an insulating bonding medium moulded into the required shapes. Owing to the small size of the particles, iron losses are greatly reduced. Ferrite cores can be used above 30 MHz, depending on the application. The central iron-powder core position is often adjustable so the inductor can be tuned by altering the inductance by changing the position of the core. Iron-powder cores are also used in small transformers in switch-mode power supplies and in special-purpose inductors operating at higher frequencies. As frequency increases, the size of a transformer decreases, and switch-mode power supplies use higher frequencies to allow the size and weight of power supplies to be drastically reduced.

Iron cores

Figure 2.31  Iron-powder core inductor

Iron cores are available in two types—laminated (see Figure 2.32) and solid. Solid cores are used for d.c. magnetic pole-pieces. The inductance of the coils associated with solid iron poles is usually so high that solid iron poles are restricted to frequencies below about 5 Hz. The iron losses are prohibitively high if the magnetic polarity of the pole changes at any higher frequency. Laminated cores are made from stacked thin sheets of iron to reduce what are known as eddy currents and to reduce iron losses at power-line frequencies. Special types of ferrous materials have been developed to reduce these losses further. Plain iron sheeting can be used to make laminations for small, low-energy transformers; but for larger distribution transformers, a more expensive, electrical silicon-steel alloy is used. The special steel allows higher flux densities and a smaller iron core for the same power output. Lower iron losses result in less heat generated in the cores.

2.5.5  Applications of the different types of inductors Straight or line type Figure 2.32  Laminated iron-core inductor

At radio frequencies, an antenna is often a straight tube of a length that makes the inductance just right for the antenna to

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work. Inductors made from straight conductors are also used inside UHF radios. Studying the effects of a.c. on inductors shows that, as frequency goes up, so does the inductive reactance (≈ resistance).

Loop When a conductor is bent around to form a loop, the magnetic field induced inside the loop is compressed into the area of the loop, while the magnetic field outside the loop is expanded. Therefore, the magnetic effect is greater inside the loop.

Solenoid coil—air-core Adding more loops to an inductor by adding turns has the same effect as increasing the current flow—that is, adding two turns makes the current go around twice and therefore has the effect of twice the current. Often, formulas will use IN or current multiplied by the number of turns to take account of the multiple turns in a coil. Coils wound with multiple turns in one or more layers are often called ‘solenoids’.

Solenoid coil—magnetic core To further increase inductance, a coil may have a magnetic core added, such as laminated iron or even ferrite. Other man-made materials are also formed into magnetic cores to increase the inductance of the coil. Relays and plunger solenoids use a magnetic core to increase the force that can be applied, and also to reduce current flow when the relay or plunger is closed.

Toroidal core Although toroid cores have existed since Faraday made his experimental transformer from a toroidal core of iron wire, toroids came into common use in the 1970s when they were ‘rediscovered’. This was the result of needing higher efficiencies from smaller and lighter inductors. Convention Toroidal cores of ceramic materials have made Current flowing very high-value inductors easy to make, and therefore toward the viewer popular in many areas of electronics and electrical Current flowing away from the viewer engineering.

Multi-coil—transformer Whenever more than two coils are placed together, usually on a common core, their inductance interacts, causing what is known as ‘mutual inductance’, so that the rising or collapsing field in one coil causes a voltage to be generated in every other coil. This is the transformer effect—a very important effect in electrical engineering.

2.5.6  Self-inductance, inductance and mutual inductance

(a) Represents a field surrounding a conductor where the current is constant and therefore the magnetic field is stationary. Apparent conductor motion

Expanding field

(b) As current increases, a relative movement exists between other conductors and the magnetic field. The direction of the current generated is opposite the current that created the field. Apparent conductor motion

Self-inductance The term ‘self-inductance’ is used when a conductor has a voltage induced in it by its own magnetic field. Figure 2.33(a) shows the field that surrounds a conductor in which current flows at a steady value. Because the current flow is steady, the field also is steady and there is no relative movement between the field and the conductor.

Contracting field

(c) As current decreases, a relative movement exists between other conductors and the magnetic field. The direction of the current generated is assisting the current that created the field.

Figure 2.33  Field surrounding a conductor

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Electrical Principles

An increasing current will cause an expanding field, which is moving outwards in relation to the conductor. The field causes a current in the conductor opposing the existing current. As current flow in a conductor increases, the flux density of the surrounding field will also increase. This leads to crowding of the lines of force and results in a tendency for the field to expand outwards from the conductor, thus causing relative movement between field and conductor. This condition is illustrated in Figure 2.33(b). Under these conditions, the conductor is fixed but the field is moving. It is convenient, however, to consider that the conductor moves relative to the field when determining the direction of induced EMF. Relative conductor movement is therefore in the direction indicated by the blue arrow. When current flow in a conductor decreases, flux density also decreases and the magnetic field contracts. The relative movement is opposite in direction and is shown in Figure 2.33(c) by the blue arrow. The relative movement between conductor and field that results from current changes in the conductor will induce an EMF in the conductor. This induced EMF results directly from current change within the same conductor and it is therefore known as a ‘self-induced EMF’. A circuit in which self-induced voltages occur is said to have the property of ‘self-inductance’. In inductors, self-inductance is inherent in their method of construction. When power is applied, the magnetic field builds up and, in doing so, produces a generated voltage that opposes the applied voltage. When the current from the power source reaches a steady value, the relative movement of the field ceases and no induced voltage is generated. When the power is switched off, the current has to reduce to zero and so the magnetic field has to collapse. While it is decreasing, an induced EMF is produced in the opposite direction and this voltage opposes the decrease.

Inductance Magnetic inductance occurs when a magnet induces a magnetic field in another material. In an electric circuit, inductance occurs when a current in one circuit causes another current to be created in that same circuit or in another circuit via a magnetic field. An inductance coil has this property of inductance. Inductive currents can only be generated by a changing current but time is very important in determining the value of any generated EMF. Inductance coils have a wide variety of names, depending on their expected uses. For example, the inductance coil used in automotive ignition systems is known as an ‘ignition coil’. They may be known as a ‘choke’ in other circuits, but most commonly they are called ‘inductors’.

Mutual inductance The term ‘mutual inductance’ is used to describe the effect when variations of current flow in a conductor cause an induced EMF in a neighbouring conductor. It is not necessary that there is an electrical connection between the conductors. Two coils placed together on a common axis is an easy concept to imagine. However, any two coils sharing a part of a magnetic field will experience mutual inductance to some extent. Figure 2.35 shows two parallel conductors. AB is connected in series with a switch and battery. The conductor CD and a centre-zero millivoltmeter form a separate circuit. As soon as the switch is closed, current will build up in accordance with the curve shown in Figure 2.34. While current is building up in AB, the field around AB is increasing in strength, and this will produce an induced voltage in conductor CD. This induced voltage will act in the direction shown in Figure 2.35(a). Figure 2.35(b) shows the condition that applies when the current flow in AB remains at a steady value. The field surrounding AB will be at a fixed strength and no induced voltage will occur in CD. Figure 2.35(c) shows what happens immediately when the switch is opened. The current flow in AB will collapse and, in doing so, will cause the field around AB also to collapse. This will induce a voltage in CD in the direction shown. Conductor AB is termed the ‘primary winding’ because it is connected to a source of power. Conductor CD is termed the ‘secondary winding’ because it has an EMF induced in it by the magnetic flux from the primary. 140

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NOTE: Maximum value of induced voltage (V) as the current and therefore the field collapses can approach infinity limited only by the series resistance of the coil.

Voltage and Current

+

Induced current C A Switch closed

D

Applied current B (a) Current increasing, field expanding

Induced voltage (V) Applied voltage (V)

C A

No induced voltage

Switch closed 0

Current (I) Maximum value of V always less than V I increasing V opposes change in I

− Switch on

Time

I constant V zero

D

Applied current

Maximum value of V much greater than V I decreasing V opposes change in I

B

(b) Current steady, field steady

Induced current C A

Switch off

Switch open

Figure 2.34  Inductor charge and discharge

D

These terms are still applicable if multi-turn coils are used instead of single conductors. If conductor CD had the power connected to it, it would be the primary winding and conductor AB would be the secondary winding because it would then generate the induced EMF.

B (c) Current collapsing, field collapsing

Figure 2.35  Mutual inductance between conductors

2.5.7  Calculation of value of self-induced EMF in a coil The unit of inductance is the henry, which is defined as the inductance of a closed circuit in which an EMF of 1 V is produced when the electric current flowing in the circuit varies uniformly at the rate of one ampere per second. or: ΔI ​V = L ​ ___ ​​  Δt where: V = voltage generated L = inductance in henrys ΔI = change in current Δt = change in time It is common to use sub-multiples of the unit such as milli-henrys (mH) and micro-henrys (μH). Multiples of the henry are virtually unknown because of the large physical sizes involved.

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EXAMPLE 2.11 If the current through an inductor of 1.5 H is reduced uniformly from 5 A to 1 A in 0.5s, find the value of the induced EMF. ΔI V = L ​ ___  ​        (1) Δt 5 − 1 ​ = 1.5 ​ ____ ​           (2) ​​ ​     ​  ​  ​  0.5​  ​  ​​​ 4 ​ = 1.5 ​ ___   ​         (3) 0.5 ​ = 12V        (4)

EXAMPLE 2.12 An inductor of 0.5 H has a current of 2 A flowing through it. If the current is reduced to zero in 1 ms, find the induced voltage across the terminals. ΔI V = L ​ ___  ​          (1) Δt 2​  ​​ ​     ​  ​  ​  ​​​ ​ = 0.5 ​ _____  −3 ​           (2) 1 × 10 ​ = 1000 V​          (3)

EXAMPLE 2.13 The current in a 100-turn coil changes from 5 A to 0 A, causing a flux change of 300 mWb. What inductance does the coil have? ΔΦ L = N ​ ____ ​  ΔI

(1)

​​ ​     ​  ​  ​  300 × 10−3​  ​​​ ​ = 100 × ​ _______  ​     (2) 5 ​ = 6 H​ (3)

Inductance can also be expressed in terms of the change in flux linkages brought about by a change of current: ΔΦ ​L = N ​ ____ ​​   ΔI where: L = inductance in henrys N = number of conductors ΔΦ = change in flux ΔI = change in current 142

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2.5.8  Mutual induction occurring between two coils When a powered coil, called the ‘primary’ coil, is energised, a magnetic field is generated that expands through the second coil, named the ‘secondary’ coil. The flux in the field generates a voltage in the secondary coil, which causes a current to flow if the circuit is complete (see Figure 2.36(a)). It is important to note the polarities in the secondary coil. When the inductor has fully charged, the field has expanded fully and there is no longer any self-induced voltage. There will also be no secondary-induced voltage and the current in the secondary coil will fall to zero. For as long as the primary coil is energised, the field will be maintained at a steady strength, and there will be no selfinduced voltage or secondary-induced voltage, and therefore no current in the secondary coil (see Figure 2.36(b)). When the current is switched off, the primary field collapses, cutting across the conductors of the secondary coil. The relative direction of movement will be opposite to what occured during charge-up and the polarity of the induced voltage in the secondary coil will also be reversed (see Figure 2.36(c)). If the current could be continuously turned on and off, a current would continue to flow in the secondary coil, and this is approximately what happens in a transformer connected to an a.c. source.

2.5.9  Graphical relationship between load voltage, current and self-induced EMF in a single d.c. circuit which has inductance

Primary coil

Secondary coil

N

SN

S

switch closed Applied current

Induced current

(a) Current increasing Primary coil

N

Secondary coil

SN

S

switch closed Applied current

No induced current

(b) Current steady Primary coil

N

Secondary coil

SN

S

switch open Applied current

Reversed induced current

(c) Current decreasing

Figure 2.36  Mutual inductance in conductors

The value of an induced voltage in general depends on flux strength, the number of conductors and the rate of motion between them. These same factors also affect the value of a self-induced voltage. The inclusion of an iron core within a coil greatly increases the field strength produced when a given current flows through the coil. Coils with iron cores have much greater self-induced voltages than coils without iron cores. Because the value of an induced voltage is dependent on the number of turns connected in series, the self-induced voltage produced by a coil of many turns will be greater than that produced by a coil of few turns. An increase in the number of turns in a coil will give an increase in self-induced voltage for a given rate of change of current flow. The reason for this is that the flux around any one conductor cuts across not only that conductor, but also others. The value of any induced voltage depends on the rate of motion, or the rate of change of flux linkages. The rate of change of flux linkages that cause self-induced voltages depends in turn on the rate of change of current. The more rapidly current changes in value or direction, the greater will be the self-induced voltage. A good example is provided by comparing the conditions that apply during the making and breaking of an inductive circuit. The collapse of a magnetic field surrounding an inductor occurs much more rapidly at switching off than the building up does during switching on. Figure 2.34 illustrates the relative directions and values of induced voltage during ‘circuit break’ and ‘circuit make’. The following points should be noted: 143

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Electrical Principles

Relay coil

Diode

R

Relay coil

C

(b)

(a)

Relay coil

R

R Relay coil

L

Diode

   1. Self-induced voltage opposes current build-up.     2.  The maximum value of self-induced voltage during switching on is less than the applied voltage.    3.  Self-induced voltage also opposes current collapse at switching off.    4. The value of self-induced voltage is greater at circuit break than circuit make, and can be many times the value of applied voltage.    5. The greatest values of self-induced voltage occur at points where the current curves have the steepest slopes. At these points, the rate of change of current is greatest.    6. Where there is no current change, there is no self-induced voltage.

The rate of change of current or voltage has no connection with the actual value of current or voltage. In Figure 2.34, for (c) (d) instance, when the current I is at its maximum value, the rate of change is zero. Figure 2.37  Spike protection using flyback diode or The high self-induced voltage which occurs during breaking snubber circuits of the circuit will tend to maintain current flow, because its direction of action opposes the collapse of the current. There will be a tendency for an arc to form as the contacts open, and in practice it is necessary to use special devices to decrease this arcing effect. When opening highly inductive circuits, it is necessary to use a bypass circuit through which the high selfinduced voltage may be discharged. Reference to Figure 2.34 will show that this induced voltage can reach values many times the normal operating voltage of equipment. This could easily lead to failure of the circuit insulation if precautions are not taken. This bypass circuit is called a ‘snubber’ circuit. The method of switching inductive circuits is referred to as ‘commutation’. Figure 2.37(a) shows the relay with a diode connected across the coil. It is suitable only for d.c. circuits and is connected so that no current flows through it in normal operation. On switching off the relay, the self-induced voltage that attempts to keep the current flowing is shorted out by the diode. Figures 2.37(b), (c) and (d) show variations of snubbing circuits with other components such as inductors, resistors and capacitors. C

2.5.10  Practical applications for the effects of self- and mutual induction An example of practical application for the effect of self-induction would be ballasts in fluorescent lights, where the ballast is used to limit the current to the fluorescent lamp. A common application of the effect of mutual induction would be found in a transformer, where a change in flux in the primary coil induces an EMF into the secondary coil.

2.5.11  Undesirable effects of self- and mutual induction The energy that can be stored in an inductor can be calculated from the following formula. 1 ​W = ​ __ ​ ​ LI​​  2​​ 2 where: W = energy in joules L = inductance in henrys I = current flow in amperes 144

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Solve problems in electromagnetic circuits  Chapter 2

Ii = Im(1 − e–t/(L/R))

95.0%

99.3%

98.2%

86.4%

Current

63.2%

τ

Even at 10 , Ii = 99.995%Im

Time

τ = RC

2τ

3τ

4τ

5τ

Figure 2.38  The time constant

This energy is stored in the electromagnetic field while the current is flowing but is released very quickly if the circuit is turned off or power is lost. The sudden discharge can cause a very high EMF to be generated. LΔI The energy in an inductor can be discharged very fast, generating a very high voltage, as E = ​​ ____ ​​ or the EMF ΔT generated is proportional to the change in current divided by the change in time. As current goes from maximum to zero in a fraction of a second, the voltage is high for a large inductor. Large inductors driven by a source such as an automotive battery can deliver a lethal voltage across their terminals when discharged.

2.5.12  ‘Time constant’ and drawing the characteristic curve as applied to a series circuit containing an inductor and a resistor Figure  2.38 shows that the current flow takes some time to reach its maximum value. The voltage across the inductor falls as the current rises, until a value of approximately zero is reached. Similarly, when the circuit is switched off, the current does not immediately drop to zero but decreases rapidly at first and then more slowly. An inductor is therefore said to have a time constant (τ = tau) which is found from the formula: L ​τ  = ​ __  ​​ R where: τ  =  time constant in seconds L = inductance in henrys R = resistance in ohms This expression shows that a greater inductance and/or a lower resistance will cause a longer time constant. In one time constant, the current will increase to 63% of the value of the maximum current. As this increase is exponential, in theory it will never reach its maximum value, but becomes 63% closer with each time period.

EXAMPLE 2.14 A 1 H choke has an internal resistance of 25 Ω. Find the time constant of the choke. L τ = __ ​    ​  (1) R ​​ ​     ​  1​  ​  ​  ​​​ ​ = ​ ___  ​   (2) 25 ​ = 40 ms​​  (3) 145

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Electrical Principles

EXAMPLE 2.15 A 10 H electromagnet with an internal resistance of 50 Ω has a current flowing through it of 5 A. Find the energy stored in the fully charged magnetic field, and the discharge time to turn-off. (5 τ). 1 W = __ ​   ​ ​ LI​​  2​  (1) 2 1 ​ = __ ​   ​  × 10 × ​5​​  2​  (2) 2 ​ = 125 J​​  (3) ​​         ​     ​  ​  ​  ​  ​  ​  ​  ​ L __ τ = ​    ​  (4) R 10 5τ = 5 × ​ ___ ​   (5) 50 ​ = 1 s  (6)

​​

2.5.13  Time constants required for the current in an LR circuit to reach its final value In d.c., a turn on the inductor produces the greatest back EMF, which all but stops the current from flowing. It is the losses that allow the initial current flow. As the back EMF does not completely oppose the applied voltage, the current flow through the inductor will increase until the only limiting factor is the circuit resistance, and the V maximum current can be calculated by Ohm’s Law, I = ​​ __ ​​ . R The voltage drop across the inductor at this time will be zero if the inductor has zero resistance. All practical inductors will have some series resistance and so a very small voltage may be measured across them. After five time periods, the difference between the actual value and the final value will be 37% to the fifth power, 0.375, which is 0.0069 or 0.69% less than 100%, which is generally accepted as approximately the full value (see Figure 2.38). L During discharge, when the current is decreasing, it decreases at the same rate as the increase. In __ ​​    ​​ seconds it R reduces to 37% of the maximum value (the decrease is 63%). It is this rapid decrease in current (and flux) which causes induced voltages with values many times greater than the applied voltage. The voltage is high enough to jump across the opening contacts, causing sparking that can burn the contacts. Capacitors or diodes are often used to stop or reduce these arcs through methods shown in Figure 2.37.

2.5.14  Determining of instantaneous values of voltage and current in an LR circuit using a universal time constant chart When a circuit containing an inductor and a resistor is first energised, the flow of current is opposed by the back EMF created in the inductor. The expected maximum current can be calculated using Ohm’s Law, however, it will take five time periods for the current to reach a maximum. The percentage of current existing in the circuit at each of these time periods can be determined using the universal time constant chart (see Figure 2.38).

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Solve problems in electromagnetic circuits  Chapter 2

When the supply is removed, the current will take five time periods to reach 0 A. Calculating the instantaneous values of current at any of these time periods is achieved by multiplying the maximum current value by the percentage identified by the time constant chart. For example, using the time constant chart (see Figure 2.38), if the maximum current in the circuit (determined by Ohm’s Law) is 10 A, there would be 6.32 A at the first time period, 8.64 A at the second time period, 9.5 A at the third time period, 9.82 A at the fourth time period and 9.93 (or 100%) at the fifth. The voltage across the inductor will reduce as the current in the inductor increases, taking five time periods to decrease from a maximum voltage to 0 V. When the current in the circuit is at a maximum, the supply voltage will appear across the resistor.

2.6  Measurement instruments 2.6.1  Moving-coil, moving-iron, dynamometer meter movements and clamp testers Moving-coil meters Figure 2.39 is an exploded view of a moving-coil movement. It can be seen that a coil free to rotate is suspended in the field of a permanent magnet. The coil ends are connected to a suspension system so that current can be passed through the coil. The suspension system may consist of one of two methods:



1. A coiled spring as shown in Figure 2.39. Sometimes called a ‘hair spring’, the outer end is attached to an adjustable arm so that the pointer of the movement can be adjusted to align itself with the zero on the meter scale. 2. The second method is called ‘taut band suspension’ and is considered a more robust method for suspending the moving coil. With this method, the rigid coil pivot is replaced with two separate thin metal strands under tension. The hair springs are no longer necessary so are usually removed. Zero adjustment of the meter is achieved by a similar movable arm attached to one of the bands. 10

1

2

6 7 8 4 5 9

0

Figure 2.40(a) is an exploded view of a moving-iron meter to illustrate its operating principle. In practice, the construction is slightly different and is shown in Figure 2.40(b). There are two magnetically soft iron vanes in the movement. One vane is fixed and the other pivoted and free to rotate. A pointer attached to the moving vane moves across a scale as an indicator. When an electric current is passed through the coil, both the fixed and moving vanes are magnetised and have like poles at adjacent ends. Like poles repel each other and the movable vane moves away from the fixed vane. The attached pointer then indicates a value against a calibrated scale. A restraining spring provides opposing torque so that the vane movement can be stabilised.

3

Moving-iron meters

Pointer

Moving coil

Coil spring

N

S

Permanent magnet

Permanent magnet

Figure 2.39  Exploded view of a moving-coil movement

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Electrical Principles

Dynamometer meter movement 10

0

1

2

3

6 7 8 4 5 9

Pointer Spring anchor Moving vane

Coil

Coil spring

Fixed vane

Coil

(a) Exploded view

An exploded view of a dynamometer movement is shown in Figure 2.41(a). The meter has two circuits. One is for voltage, the other for current. The model illustrated has a soft iron core, around which is wound a low-resistance coil to carry the circuit current. This coil produces a magnetic flux proportional to the current flowing in a circuit. Not all dynamometer-movement meters have an iron core; some models are air cored. The meter’s second circuit consists of a coil with a series resistance of high value. This is the voltage circuit and produces a magnetic field proportional to the applied voltage. The direct multiplication of voltage and current values in an a.c. circuit to obtain a power value can at best be only an approximation. With some electrical components, the voltage and current can be out of step with each other. This type of meter construction, with its two magnetic fields, takes into account any displacement between voltage and current and gives a true power reading. With a.c. supplies, the values of voltage and current are continually changing so a true power reading indicates the average power being consumed over a finite period of time, rather than at one instant.

Clamp testers Meters have been made for testing for voltages and currents that make no electrical contact with the circuit under test. Several versions are available.

Voltage testers

(b) Practical construction

0 50

75 90 100 120 140

A commercially made unit that senses voltage and does not rely on lamps or vibrating solenoids is a device sensitive to the electrostatic fields produced by the circuit voltage. It is the basis of the finder used to locate live conductors buried in walls up to a depth of 2.5 cm. Most units give both audible and visual signals. These are shown in Figure 2.42.

Current testers

Current testers are marketed under various names, most of which are trade-related. They are called ‘tong testers’, (c) Non-linear scale ‘clamp meters’, ‘clip-on testers’, ‘link test meters’ and so Figure 2.40  Moving-iron meter on. Clamp action meters are generally used to measure currents without having to interrupt the circuit being tested. Most meters have accuracies within 1% of full-scale deflection and on frequencies ranging from direct current (f = 0) to about 1 kHz. 148

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6 7 8 4 5 9

10 Moving coil V+ Power (responds to source load voltage)

0

1

2

3

Solve problems in electromagnetic circuits  Chapter 2

Pointer

M

Coil spring

Moving coil

Fixed coil V+

M

V

R

Load

L V Fixed coil (responds to load current)

(b) Connections. The moving coil with the series resistance R carries a current proportional to load voltage. Meter deflection is proportional to the product of voltage and current, which is power. This meter may be used for a.c. or d.c. measurements

L

(a) Exploded view

Figure 2.41  A dynamometer movement

Originally there were only two types. One worked on the repulsion principle of the moving-iron meter while the other used a transformer combined with a switch to select the desired current ranges. These can still be obtained, but many other versions are now available.

Repulsion-type movement (a.c. and d.c.) The operating principle was that of the movingiron meter. A variety of current ranges was catered for with plug-in modules. On being placed around the conductor to be measured, the magnetic field created by the current set up repulsion between the meter elements and caused the moving section with a pointer attached to rotate. They were capable of use on both a.c. and d.c.

Figure 2.42  Non-contact volt sticks

A

Transformer operated (a.c. only) Different current ranges were catered for by using a transformer with tappings connected to a range switch. The transformer prevented it being used on d.c. The basic principle is shown in Figure 2.43. The indicating meter could be a d.c.-operated meter by connecting a rectifying unit between the Figure 2.43  Internal circuit arrangement of a current transformer transformer output and the meter movement. With a d.c. meter, the scale then becomes linear. With a moving-iron meter, the scale was non-linear. The jaws of the instrument were opened with a lever and then placed around the chosen conductor. The jaws were then allowed to close. The magnetic field around the conductor entered the low-permeability path of the iron, and the meter movement responded according to the strength of that magnetic field. 149

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Electrical Principles

2.6.2  Practical applications for moving-coil, moving-iron and dynamometer meter movements Moving-coil meters A current is passed through the coil—not a voltage. The current that flows through the coil is governed by the value of the applied voltage. The coil sets up its own field, which reacts with that of the permanent magnet and causes the coil to rotate. A pointer attached to the coil gives a voltage reading against a scale. The meter movement can only work satisfactorily on direct current. If a.c. is applied to the movement, it tries to turn the coil rapidly in the opposite direction, with the result that the coil effectively remains stationary. The meter can only operate on a.c. if the a.c. is rectified to d.c. before it flows through the meter. Because of these factors, the moving-coil meter always reads average values of current.

Moving-iron meters Like the moving-coil instrument, the moving-iron meter is current operated. The current that flows through the coil is governed by the applied voltage. As a voltmeter, the coil impedance is very low when compared with the required series resistance. Consequently, the meter movement can be considered as resistive only and the current through the meter is directly proportional to the applied voltage (Ohm’s Law). The meter will operate on both d.c. and a.c., although it might need to be calibrated differently. Because the two vanes are magnetised by the same current, the moving-iron meter operates on root-mean-square (RMS) values of current. The major difference in scale calibration is that the moving-iron meter has a non-linear scale. This is illustrated in Figure 2.40(c).

Dynamometer meter movements Power being consumed in a circuit is measured with a wattmeter. Wattmeters are often constructed with a dynamometer movement. This type of movement usually has two internal electrical circuits. Dynamometer movements find their greatest number of applications in a.c. work because they integrate both current and voltage values and give a true power reading with a high degree of accuracy. The meter-movement principle is also applied to other types of meters. While wattmeters can be used on d.c., it is not the usual practice. Good voltmeters and ammeters can give quite high accuracy for d.c. work by multiplying the two meter values together. Figure 2.41(b) shows how the meters are connected into an a.c. circuit.

2.6.3  Calculation of resistance of shunts and multipliers to extend the range of ammeters and voltmeters It was stressed in earlier sections that both moving-iron and moving-coil meters were current-operated and relied on magnetic effects for their operation. However, the meter scales may be calibrated as voltage because of the direct ratio between voltage and current. The basic movements of both types often have only a small voltage drop across the operating coils. Typically for a modern moving-coil meter, this voltage is in the order of a few millivolts. While the moving-iron type has a slightly higher voltage drop, it is still very low and this factor limits the uses of these meters unless steps are taken to extend their operating range.

Extending the range of a voltmeter For any given voltage, adding series resistance decreases the current flow through the meter. If a moving-coil movement with 100 Ω coil resistance has an extra 10 kΩ added in series, the total meter resistance circuit would be 10.1 kΩ. From Ohm’s Law, the current is now reduced approximately 10 times. To restore the operating current to its original value, 10 times the voltage must be applied; that is, the voltage range of the meter is extended 10 times. The full answers for voltage have been given in (b) and (c), but in normal practice they would be rounded off to 10 V and 1000 V. 150

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Solve problems in electromagnetic circuits  Chapter 2

EXAMPLE 2.16 A moving-coil meter (Figure 2.44) has an internal resistance of 100 Ω. Find: (a) the voltage drop across the meter if 1 mA gives a full-scale deflection (FSD) of the pointer (b) the voltage that would have to be applied to give full-scale deflection of the movement if a resistance of 10 kΩ is connected in series with the meter (c) the new full-scale voltage if the series resistance is replaced with one of 1 MΩ. (a) Voltage across meter: ​V​  M​​ = IR −3 ​​ ​ ​   ​   ​​ =​  1 × ​10​​  ​  × 100​ ​ = 0.1 V

(b) Rse = 10 kΩ. Maximum current of meter is 1 mA. Total resistance = 10 000 + 100 = 10 100 Ω: V = IR −3 ​​ ​ ​   ​   ​​ =​  1 × ​10​​  ​  × 10 100​ ​ = 10.1 V (c) Rse = 1 MΩ. Maximum current is still 1 mA. Total resistance = 1 000 000 + 100 = 1 000 100 Ω: V = IR ​​ ​ ​    ​  −3​  × 1  ​​ =​  1 × ​10​​  000 100​ ​ = 1000.1 V

1 mA (max)

V 100 Ω Vm

Rse 10 kΩ

Figure 2.44  Circuit for Example 2.16

In summary, for a moving-coil meter, a series resistor of 10 k Ω enables the meter to be used as a 10 V meter. Similarly, a series resistance of 1 M Ω enables the meter to have a full-scale rating of 1000 V. For moving-iron meters used as voltmeters, a similar situation applies. Once the full-scale current value and the internal resistance of the movement are known, series resistors can be added to extend the maximum voltage range of the meter. These two facts are often inscribed on the face of the meter for identification purposes. These added series resistors are known as ‘multiplying resistors’, or simply ‘multipliers’.

EXAMPLE 2.17 A moving-iron meter has the following inscribed on its face: ‘FSD 5 mA, Resis 25 Ω’. Find the full-scale voltage ranges for series resistors of 10 k Ω and 1 M Ω. Voltage across meter at full-scale deflection: V = IR ​​ ​ ​   ​  −3 ​​ =​  5 × ​10​​  ​  × 25​ ​ = 0.125 V (continued) 151

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Electrical Principles

The 10 k Ω series resistor: V = IR −3 ​​ ​ ​    ​   ​​ =​ ​  5 × ​10​​  ​  × (10 000 + 25)​ ​ = 50 V The 1 M Ω series resistor: V = IR ​​ ​ ​    ​  −3  ​​ =​ ​  5 × ​10​​  ​  × (1 000 000 + 25)​ ​ = 5000 V

Extending the range of ammeters The operating current of an ammeter is generally very low to ensure adequate sensitivity for measuring small values of current. The internal resistance of the meter is also kept as low as possible to reduce the voltage drop across the meter itself. To measure values of current higher than that required to give full-scale deflection, a resistor called a ‘shunt’ is placed in parallel with the meter. It allows some of the current to bypass the meter. Any fixed value of current flowing into a parallel circuit will divide according to the resistance of the paths. The less the resistance, the greater will be the current flow in that path. The following example explains this, using the same meter movement as that in Example 2.16.

EXAMPLE 2.18 A moving-coil meter movement has a full-scale current rating of 1 mA and an internal resistance of 100 Ω. Calculate the resistance of a shunt to be placed in parallel with it so that currents of up to 1 A can be measured. The circuit is shown in Figure 2.45. The intention is to bypass 999 mA around the meter with Rsh, so leaving only a maximum of 1 mA to flow through the meter. Meter voltage at FSD: V = IR −3 ​​ ​ ​   ​   ​​ =​  1 × ​10​​  ​  × 100​ ​ = 0.1 V Because the shunt resistor and the meter are in parallel, the voltage across the parallel section will be the same for both resistors; that is, the voltage across the shunt = 0.1 V. This means that two of the three values required to apply Ohm’s Law are known. (It has already been established that 999 mA must bypass the meter.) Thus: V  ​R​  sh​​ = __ ​   ​   I ​​ ​  ​  ______ ​   ​​​  0.1  ​ = ​    ​   0.999 ​ = 0.1Ω

Vm

A

1 mA (max) 1A

1A

Rsh

999 mA

Figure 2.45  Circuit for Example 2.18

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Solve problems in electromagnetic circuits  Chapter 2

EXAMPLE 2.19 A meter movement has a full-scale deflection current of 50  μA and an internal resistance of 40  Ω. Calculate the value of a shunt resistance to extend the meter range to 300 mA. The circuit will be similar to that of Figure 2.45, although the values will be different. Current to bypass meter: ​ = 300 mA − 50 μA −6 ​ ​ ​​​       ​ =​  (300 × ​10​​  −3 ​​ ​  ) − (50 × ​10​​  ​  ) ​ = 0.299 95 A Voltage across the meter at FSD: V = IR −6 ​​ ​ ​   ​   ​​ =​  50 × ​10​​  ​  × 40​ ​ = 0.002 V Resistance of shunt: V  R = __ ​   ​   I ​​ ​  ​  ________ ​  ​  ​​ 0.002  ​ = ​     ​   0.29995 ​ = 0.0066Ω

In practical terms, to extend the range of an ammeter 1000 times, a shunt resistor must be placed in parallel with the meter. Its resistance will be one-thousandth that of the meter movement. The values indicated on the meter scale have to be corrected for the new range of the meter; that is, at an indicated half-scale reading of 0.5 mA, the actual current would be 500 mA. For some meters, and particularly d.c. meters, shunts of very low values of resistance are required. Small errors in resistance can lead to much bigger errors in current readings. Moving-iron meters on a.c. often use a special type of transformer called a ‘current transformer’ to eliminate the possibility of shunt calibration error. Factors to be considered in selecting meters for a particular application are covered in Chapter 1: Sections 1.41, 1.46 and 1.51.

2.7   Magnetic devices 2.7.1  Construction, operation and applications of relays Figure 2.46 shows a simple attracted-armature type of relay (relay switch) used to open or close an electrical circuit. When current flows in the operating coil, a magnetic flux is created in the soft iron core and around the magnetic circuit, including the armature and the air gap. If the air gap between the core and the armature is not too large, most of the core flux will pass through the armature and induce polarities in the pole faces of the armature and core, creating a magnetic force that will attract the armature to the pole face.

Coil supply

Switched current Fixed contact

Magnetising coil Air gap Fixed iron stator

Moving contact Fixed stop Moving iron armature

Return spring

Figure 2.46  Armature relay/contactor

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Electrical Principles

The force of attraction between the armature and the core is greater than the force holding the armature in the open position (due to the spring). The armature will close and hold for as long as the magnetic flux is applied and is strong enough. The force exerted on the armature in the closed position (minimum air gap) will be many times greater than when the armature is in the fully open position (maximum air gap). For a coil connected to a direct current supply, the current will be constant for all positions of the armature, but the reluctance of the magnetic circuit will change with the length of the air gap. This is because the reluctance of air is much greater than the reluctance of the iron core. For an alternating supply, conditions are somewhat different due to the coil current being dependent on the flux and the reluctance of the magnetic circuit. If the ampere-turns are great enough to create the tractive force necessary to close the armature through a large air gap, this same force will often leave a residual flux in the magnetic circuit. This residual magnetism may be strong enough to keep the armature closed, even when the coil current is switched off. This problem can be overcome by using a non-magnetic spacing piece on one pole face to ensure that a certain minimum air gap is left in the magnetic circuit when the armature is in the fully closed position. The length of this gap must be such that the residual magnetism is not sufficient to maintain the armature in the closed position.

2.7.2  Construction, operation and applications of contactors Relays are any set of contacts operated electromagnetically by a solenoid coil. A contactor is the same mechanism, but is usually meant to operate an a.c. circuit, and particularly a three-phase or high-voltage/current circuit. There are many types of relays and contactors (see Figures 2.47 and 2.48).

2.7.3  Magnetic methods used to extinguish the arc between opening contacts An arc suppression blowout coil produces a magnetic field in an electrical switching device (contactor, circuit breaker, etc.) for the purpose of lengthening and extinguishing an electric arc that is formed as the contacts of the switching device part to interrupt the current. The magnetic field produced by the coil is approximately perpendicular to the arc. The interaction between the arc current and the magnetic field produces a force driving the arc in the direction perpendicular to both the magnetic flux and the arc current. Refer to Figure 2.49.

Figure 2.47  Typical small relays

Figure 2.48  Relays and contactors

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2.7.4  Construction, operation and applications of Hall effect devices Hall effect sensors are activated in response to an external magnetic field, characterised by flux density (B) and polarity (North and South Poles). The output signal from a Hall effect sensor is determined by the magnetic field density around the device. The sensor will detect when the magnetic flux density around it changes, generating an output voltage when it exceeds a predetermined level. Hall effect devices are used in speed control, proximity and positioning systems, as well as in currentsensing applications.

Figure 2.49  Magnetic blowout coil

From Herman. Industrial Motor Control, 7E. © 2014 Delmar Learning, a part of Cengage, Inc. Reproduced by permission. www.cengage.com/permissions

2.7.5  Operation and applications of magnetostriction equipment Magnetostriction is a process in which a ferromagnetic material changes shape when introduced to a magnetic field. It is caused by the shifting of the magnetic domains within the material. Magnetostrictive devices are commonly used in security systems where labels made of ferromagnetic material are secured to, for example, goods in shops and books in libraries. When the label signal and the transmitter pulse interact, an alarm will sound (see Figure 2.50).

2.7.6  Construction, operation and application of magnetic sensing devices Magnetic sensors are solid-state devices that have many functions and can be used in applications such as sensing position, velocity or directional movement. They have become increasingly popular for their versatility, non-contact operation, low maintenance and hardy build. Magnetic sensors are particularly useful in sensing position, distance and speed in automotive systems. They are helpful in determining the position of car seats and seat belts for air-bag control, and wheel rotation speed detection for anti-lock braking systems (ABS).

Transmit pulses (50–90 per second at 58 kHz)

Transmitter

Tag

Radiated Signal

Receiver

Figure 2.50  Magnetostrictive equipment

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2.8  Machine principles A direct-current (d.c.) machine is one that either produces or consumes electricity as direct current, acting therefore as an energy converter. The same d.c. machine can be either a motor or a generator, although the design is generally optimised as one or the other—when electricity is applied to the machine, it can function as a motor and convert electrical energy to mechanical energy, causing the machine to rotate. When the same machine is driven by mechanical energy so that it rotates, it generates electrical power. In fact, to fully understand how a d.c. machine operates, it is best to remember that even when the machine is acting as a motor, it also generates power, in a form known as ‘back EMF’; also, when operating as a generator, the d.c. Figure 2.51  A typical d.c. machine machine acts as a motor, opposing the mechanical force that drives it. This is known as the ‘reactionary force’. A typical small d.c. machine is shown in Figure 2.51. This machine is rated at 0.25 kW.

2.8.1  Basic operating principle of a generator

Motion

A basic generator converts mechanical energy to electrical energy, and to generate a voltage there needs to be a magnetic flux, conductors and movement. The d.c. machine achieves this effectively and efficiently. When a conductor passes through a magnetic field, a voltage is induced into the moving conductor. This can be determined by the equation e = Blv. This is done in a generator by spinning the conductor through a magnetic field. This spinning conductor is placed into what is known as the ‘armature’. Field

2.8.2  Applying Fleming’s right-hand rule for generators

ent

Curr

The direction in which the induced voltage in a conductor moves can be determined by using Fleming’s right-hand rule (see Figure 2.52). The rule works as follows:

Figure 2.52  Fleming’s right-hand rule

Douglas Morrison Doug M/Wikipedia/CC BY SA 3.0.

a

N

S b

Rotation

Figure 2.53  Generator rotation

  1. Arrange the thumb, first and centre fingers of the left hand at right angles to each other.   2. Point the first finger in the direction in which the lines of force (flux) are acting.   3. Point the thumb in the direction in which the conductor is moving.   4. The centre finger will indicate the direction in which the current is flowing. Conductor ‘a’ in Figure 2.53 will be forced past the north pole and, using the right-hand rule for generators, it can be determined that the current in conductor ‘a’ will be flowing towards the viewer. Conductor ‘b’ will be forced past the south pole, so the current will be flowing away from the viewer.

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2.8.3  Basic operating principle of a motor Motors and generators have the same basic construction and a standard machine can be used in both capacities. For a motor to be useful, it must develop torque or a turning effect. When electrical energy is applied to a d.c. machine, current flows in the armature conductors and produces a magnetic field that interacts with the main magnetic field to cause a rotational torque to be developed (see Figure 2.54). When the two magnetic fields interact, an attractive (axial) force is created on one side of the conductors and a repulsive (radial) force is created on the other side. The resulting magnetic field produces a force that acts on the conductors as indicated in Figure 2.54.

Rotation

N

S

Force Weakened magnetic field

Figure 2.54  Motor effect produced by an electric current Direction of motion or force

Direction of lines of force

2.8.4  Applying Fleming’s lefthand rule for motors The direction in which the force acts can be determined by using Fleming’s left-hand rule (see Figure  2.55). This is done in a similar way to the right-hand rule for obtaining the direction of an induced voltage in a conductor. The rule works as follows:

Strengthened magnetic field

Force

Left hand

Direction of conventional current flow

1. Arrange the thumb, first and centre fingers of Figure 2.55  Fleming’s left-hand rule the left hand at right angles to each other. 2. Point the first finger in the direction in which the lines of force (flux) are acting. 3. Point the centre finger in the direction in which the current is flowing. 4. The thumb will then point in the direction in which the force is acting on the conductor.

The left-hand conductor in Figure 2.54 has a tendency to be forced upwards and the right-hand conductor downwards. As these are normally embedded in an armature core at a fixed distance from the centre of rotation, the effect is to create a turning movement, or torque. In a practical d.c. motor, there is a large number of conductors and the torque produced is sufficient to drive the load connected to the motor, unless the motor is severely overloaded.

2.8.5  Calculation of force and torque developed by a motor The magnitude of the thrust exerted on a conductor carrying a current when located in a magnetic field is given by the equation: ​F = B l I​ where: F = force on conductor in newtons B = flux density of main field in teslas (Wb/m2) l = length of conductor in the field in metres I = current in the conductor in amperes 157

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In a practical case, where an armature has many conductors and also may have several paths, the equation becomes: B l I Z  ​F  = ​ _____    ​​   a where: I = total armature current Z = number of armature conductors a = number of parallel paths in the armature Since T = Fr where r is the radius of rotation of the armature conductors, the equation becomes: B l I Z r  ​T  = ​ ______    ​​   a where: T = torque in newton metres The formula can be further developed to: p ΦI Z  ​T  = ​ ______ ​    ​  2π a where: T = torque in newton metres p = number of poles Φ = flux per pole in webers I = total armature current Z = number of armature conductors a  =  number of parallel paths in the armature

2.9 Rotating machine construction, testing and maintenance 2.9.1  Components of a d.c. machine The main parts of a typical d.c. machine, motor or generator are:

∙ ∙ ∙ ∙ ∙ ∙

field frame or yoke end-shields and bearings field poles field coils armature and commutator brush gear and brushes.

The major components of a d.c. machine are shown in the exploded view in Figure 2.56.

Field frame or yoke In a d.c. machine, the field frame, or yoke, holds the field poles and also provides a magnetic path between them. Since a material of high magnetic permeability is required to provide the magnetic path, cast iron or steel is often used. The yoke has high mechanical strength and brings the advantage of retaining residual magnetism, a factor that will be required for generating a voltage. 158

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Field pole (laminated)

Frame Armature

Field coil

Field pole bolt

Figure 2.56  Major components of a d.c. machine

Figure 2.57  Dismantled d.c. machine

End-shields and bearings The purpose of end-shields is to support the bearings in which the armature rotates. Additionally, one of the endshields usually has provision for mounting the brush gear for electrical connection to the rotating armature. Designs of the end-shields and bearings vary according to the desired use of the machine. They might be waterproof for one situation or completely open for another. The end-shields and bearing can be seen in the dismantled view of a d.c. machine shown in Figure  2.57. The bearings are attached to the armature shaft.

Field poles The field poles provide the magnetic field inside the d.c. machine that is required to either induce an EMF or to be used to create a force to move and spin the conductors placed in the armature. The field poles can be thought of as magnets—either permanent magnets or temporary electromagnets. Their high permeability provides a high concentration of magnetic flux at a particular position in the d.c. machine. To place these field poles (magnets) into the machine, one can be separated from its field coil, as in Figure 2.56. The outer surface of the poles is shaped to fit tightly against the inner surface of the field frame, while the inner surface of the pole is curved to closely follow the shape of the armature. The pole tips have been extended to contain the magnetic fringe. This shaping permits a greater area in the flux path close to the armature and reduces the magnetic reluctance of the air gap. An incidental advantage is that the tips can be used to hold the field coils in position when the pole piece is bolted into place in the yoke.

Field coils To create an electromagnet, field coils are wound with insulated copper wire. The field coils can be connected to the conductors placed in the armature in a number of combinations. The way they are connected determines the type of machine—that is, series, shunt (parallel) or a combination of both. If the field coils are connected in series with the armature conductors, they are called ‘series coils’. These are made of thick wire or even copper bar. If the field coils are connected in parallel with the armature conductors, they are called ‘shunt’ coils and are usually wound with much thinner wire. The actual construction of the coil will vary accordingly. Series coils must carry the high armature current, so they are wound with heavier conductors than shunt coils. Typical shunt and series field coils are shown in Figures 2.58(a) and (b) respectively. The conductor sizes and comparative number of turns on the field coils can be shown in circuit diagrams as three turns for series coils and four or five turns for shunt coils. Some fields are magnetically excited. This means that the field poles become magnetised from the field coils or windings by a field coil consisting of two windings—one a series winding, the other a shunt winding. These are called ‘compound’ (combined) windings (see Figure 2.58(c)). 159

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The magnetomotive force created must be great enough to produce the required magnetic flux through the yoke, field poles, air gaps and armature in a series-parallel magnetic circuit (see Figure 2.59).

Armature The armature is the part of the machine that holds the conductors which are used to induce a voltage. It spins around inside the machine. The armature core is assembled from a number of electrical steel laminations which reduce eddy currents. Figure 2.60(a) illustrates a typically shaped lamination. Equally spaced slots are stamped around the circumference to hold the armature conductors. Their shape influences the winding method used for any particular armature. Laminations for larger armatures also have punched ventilating holes. An unwound armature is shown in Figure 2.60(b).

(a) Shunt field coil

Commutator

(b) Series field coil

(c) Compound field coil

Figure 2.58  Field coil construction

Magnetic circuit Armature

Yoke Air gap

Field pole

As the armature spins past the magnetised field poles, an induced voltage will be produced in the armature conductors. This voltage will actually be an alternating value (a.c.), due to the commutator; without it, the machine will only produce an alternating current. The commutator is placed on the shaft of the armature and the individual segments are insulated from each other, and also from the armature shaft and the retaining rings, by mica insulation (see Figure 2.61(a)). When assembled, the segments lie parallel to one another to form a cylinder. A sectional view of a commutator is illustrated in Figure 2.61(b). In very small commutators, the fixing of segments is achieved by clamping under pressure and rolling over or crimping the edges of the clamping rings. The commutator may be pressed directly onto the shaft or bolted to the armature spider.

Action of the commutator

Mounting feet

Figure 2.59  Magnetic circuit in a four-pole d.c. machine

As in the a.c. generator, a d.c. generator produces an alternating voltage. However, instead of the ends of the loop being connected to slip-rings, they are connected to a two-segment commutator, then through the brushes to the external circuit. The brushes remain stationary, making contact with the segments of the commutator as they turn with the loop. The commutator acts as an automatic switch, reversing the current flow to the external circuit by

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exchanging the connections between the loop and the brushes. The commutator is designed to produce a d.c. voltage output.

Brush gear and brushes The brushes are used to transport the current into or out of the armature conductors, depending on whether it is a motor or a generator. Graphite or carbon brushes, sometimes mixed with copper dust, are used to provide a lowresistance electrical connection between the armature windings and the external circuit. The brush makes a sliding contact with the commutator. Figure 2.62 illustrates the brush gear for a fourpole machine. The carbon brushes must be able to move freely within the brush holder to ride up and down over any irregularities on the commutator surface, and to adjust for wear. The brush is usually connected to the brush holder with a flexible lead called a ‘pigtail’ and held down by a spring. The same connection terminal is used to connect to the external circuit. The brushes must maintain contact with the spinning commutator. The brush gear must be suitably insulated from the frame, and in many cases the position of the brush around the commutator must also be adjustable. Figure 2.62 shows the brush mounting on an adjustable ring, which permits positioning of the brush gear.

2.9.2  Difference between a generator and a motor in terms of energy conversion

(a)

Slots

Commutator (b)

Laminations

(c)

Figure 2.60  Typical lamination and armature before being wound Riser

Mica sheets between bars Micanite vee rings Clamping ring

Clamping ring

Copper

Copper segments Taper of segment (a)

(b)

Figure 2.61  Commutator construction

As a d.c. machine can be used as either a motor or a generator, the construction of each is identical. A d.c. machine operating as a generator will convert mechanical energy to electrical energy; a d.c. machine operating as a motor will convert electrical energy to mechanical energy.

2.9.3  Machine nameplates Figure  2.63 shows a typical nameplate for a d.c. machine. It provides the manufacturer, year of manufacture, serial number, output power rating, rated speed, field excitation voltage, rated armature current and mass.

Figure 2.62  Brush gear assembly of a d.c. machine

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Electrical Principles

06-1995

Sep.

Motor

Type DMP 112–4L 12.5

No

300

Exc. IP 23S Cat. No.

r/min

Ins. Class

495

Arm.

1124 01659 1500

kW

Duty S1

IEC 34-1-1969

IC

V

Arm.

V

Exc.

06

IM

FR 159 101-1A

MADE IN FRANCE

F 29.9

2.18

A

1001 123.5

FABRIQUE EN FRANCE

Figure 2.63  d.c. machine nameplate

A

kg

2.9.4  Using electrical equipment to make electrical measurements and comparison of readings with nameplate ratings It is important to be able to quickly and safely measure voltage current and resistance of a d.c. machine when trying to identify operational issues. The nameplate in Figure 2.63 shows that the armature has a voltage of 495 V and a current of 29.9 A. An ohmmeter would be expected to measure approximately 16.5 Ω across the armature. The excitation field has 300 V and 2.18 A, which would give a reading of 137 Ω. It should be possible to identify the armature and field windings and to measure the voltages across each. Current can be measured using a d.c. ammeter.

2.9.5  Identification of faults in a machine from electrical measurements There are several tests for identifying a fault in a d.c. machine. First, ensure that the machine is safe to touch. The casing should be tested for voltage using a voltmeter from the frame to a known earth, then a resistance test should be carried out from the frame to the known earth to ensure that the frame is earthed correctly. The meter should be tested on a known live source after testing for voltage. The case should be opened and checked for voltage (A-N, A-E). If there is voltage at the terminals and the machine is not working, the machine will have to be investigated. If there is no voltage, the issue is between the machine and the switchboard. The supply should be correctly isolated and tagged, and the resistance of the field windings and the armature checked. The nameplate (see Figure 2.63) shows that the armature has a voltage of 495 V and a current of 29.9 A. An approximate reading of 16.5 Ω would be expected. The excitation field has 300 V and 2.18 A, which would give a reading of 137 Ω. An infinite reading would mean an open circuit; a smaller reading (perhaps 30 Ω) on the excitation field would indicate that there is a short circuit in the windings. Other possible issues could include worn brushes not making contact with the commutator.

2.9.6  Care and maintenance processes for rotating machines It is important to create a preventative maintenance program for rotating machines. The type of program and regularity of the maintenance will be determined by the time of use and general environment that the machines are operating in. Some of the tasks carried out during these maintenance checks would be as follows:

∙ ∙ ∙ ∙ ∙

visual inspection for condition, safety and fitness for purpose general clean of machine body, vents and screens check commutator and brushes test field coils and armature windings lubricate bearings.

2.9.7  Safety risks associated with using rotating machinery Plant is a major cause of workplace death and injury. Risks associated with its unsafe use include:

∙ limbs amputated by unguarded moving parts of machines ∙ being crushed by mobile plant

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∙ fractures from falls while accessing, operating or maintaining plant ∙ electric shock from plant that is not adequately protected or isolated ∙ burns or scalds due to contact with hot surfaces or exposure to flames or hot fluids.

Other risks include hearing loss due to noise and musculoskeletal disorders caused by manually handling or operating plant that is poorly designed. Safe Work Australia has released a code of practice for managing the risks of plant in the workplace. It is available on www.safework.nsw.gov.au. The information in the code of practice covers plant installation, commissioning and use through to decommissioning and dismantling.

2.10   Generators 2.10.1  Calculation of generated and terminal voltage of a d.c. shunt generator The value of the voltage generated in an armature winding depends on the following three factors: 1. strength of field flux 2. number of effective armature conductors connected in series (influenced by the number of coils and the turns in each) 3. relative speed between conductors and magnetic field. The generated voltage for a d.c. machine is found from: pΦnZ ​​V​  g​​  = ​ _____    ​​   a where: vg = generated voltage p = number of poles in the machine Φ = magnetic flux per pole in webers n = revolutions per second (r/s) Z  =  number of effective armature conductors a = number of parallel paths in the armature A lap-wound armature has as many parallel paths as there are poles. A wave-wound armature always has two parallel paths. The above formula is often expressed with the speed given in revolutions per minute: pΦnZ ​​V​  g​​  = ​ _____ ​​     60a where: n = rpm 163

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Voltage regulation Regulation for a d.c. machine covers speed regulation for a motor and voltage regulation for a generator. As a standard, regulation is the difference between the no-load and full-load values, compared with the full-load value as a percentage. That is: ​V​  nl​​  − ​V​  fl​​ ​Voltage regulation ​ _________      ​ × 100%​ ​V​  fl​​ where: vnl = voltage at no load vfl = voltage at full load

2.10.2  Prime movers, energy sources and energy flow used to generate electricity In order to generate a d.c. supply, the generator needs to be mechanically driven. There are many ways to provide the mechanical input. A prime mover (motor) connected to the shaft of a generator can be fuelled by diesel, gas or electricity. More sustainable methods are being developed to provide the drive for generators, with many smaller installations successfully using hydro, geothermal, tidal and wind technologies as a fuel source.

2.10.3  Types of d.c. generators and their applications There are two main methods of voltage control for d.c. generators. 1. Field flux control The general concept is of resistance in series or parallel with field: a. permanent magnet—shunt of soft iron to bypass flux b. separately excited—resistance in series with field to limit current c. shunt excited—resistance in series with field to limit current d. series excited—resistance in parallel with field to bypass field e. compound excited—resistance in shunt field to limit current. 2. Speed control Use is limited mostly to special cases, the concept being to adjust the speed of the prime mover.

Uses

1. separately excited: a. permanent magnet—instruments b. wound field—process control, rotary amplifiers 2. shunt excited—small, cheap generators 3. series excited—almost nil 4. compound excited—all general-purpose work.

Excitation

1. separately excited—permanent magnet or power from outside source 2. shunt, series and compound—builds up own field; self-excited

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Type

Field winding

Permanent magnet

Circuit diagram

Voltage / speed

Volts

—

Voltage / load

Load

Load

1. Volts directly proportional to speed 2. Output drops slightly on load

Control field current

Load

1. Voltage is not linear with speed 2. Voltage drops more than permanent magnet on load

Control field current

d.c. supply Separately excited

Many turns fine wire

Volts

Volts Speed

Shunt generator

Many turns fine wire

Volts

Volts Speed

Series generator

Few turns heavy wire

Volts

Volts Load

Series assists shunt

Volts

Volts

Differential compounding

Series demagnetises shunt

Volts

flat Load

Speed

Voltage characteristic can be made flat or increase with load, depending on compounding

Control shunt field

Voltage drops quickly on load

Volts Speed

d.c. supply

Diverter over

Cumulative compounding

Use magnetic shunts on field system

Rising voltage characteristics

Speed

with a set load

Voltage control

1. Volts directly proportional to speed 2. Output drops slightly on load

Volts Speed

Characteristics

Load

Control shunt field

Figure 2.64  Summary of the main points for all types of d.c. generators

The factors affecting self-excitation of shunt-, series- and compound-generators are:

1. 2. 3. 4. 5.

residual magnetism needed resultant field flux to assist residual magnetism machine connected correctly machine electrically in good order direction of rotation.

Figure 2.64 gives a summary of the main points relating to d.c. generators.

2.10.4  Methods of excitation used for d.c. generators The term ‘separately excited generator’ indicates that the field windings have current passing through them from an external source; the current is not supplied by the generator itself. The field windings can have a few turns with a comparatively high current flowing, or many turns with a much lower value of current, depending on the external source used. The connection diagram is shown in Figure 2.65, Rheostat and the characteristics in Figure  2.66. As with the permanent-magnet generator, the terminal voltageto-speed characteristic of the separately excited generator is linear. The usual method of voltage control is by series DC Output Field G resistance to regulate the current flowing through supply the field. A stronger field gives a higher voltage output at the same generator speed. The excitation curve showing the variation in generated voltage for varying values of field current is illustrated in Figure 2.65  Separately excited generator connections 165

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Electrical Principles

Full load

Voltage

Voltage

Full load

Voltage

Voltage

Figure 2.66(a). At zero field current, there may be a small generated voltage due to residual magnetism (iii) Vg in the field pole, in region (i). In region (ii), the (ii) curve is effectively linear, showing a steady increase V ° in output voltage as the field current is increased. Once the saturation region (iii) is reached, large (i) changes in field current are needed to produce Field current Load current small changes in voltage. This indicates that there (a) Excitation curve (b) Voltage/load curve is not enough iron in the generator for this level of Figure 2.66  Separately excited wound field generator characteristics excitation. The generator may be designed to work in either region (ii) or region (iii), according to the application. Rheostat In a shunt generator, the armature voltage is applied to the generator field that is connected in parallel with the armature. The connection is shown in Figure  2.67. The machine is said to be ‘selfexcited’ because, when running, it does not rely on Output Field G an external power source for field excitation. The shunt generator does, however, require a field from some source in order to start generating. The series generator, being a self-excited machine, also requires certain conditions to be fulfilled Figure 2.67  Shunt generator connections before it can generate a satisfactory output voltage. These conditions are identical to those of the shunt generator in that there must be residual magnetism Saturation present, and the magnetism produced by the fields region must assist the residual magnetism. As with the shunt machine, any loss of residual magnetism can be rectified by the application of a direct current to the fields for a short time. A compound generator has both shunt and series Field current Load current (a) Excitation (b) Voltage field windings. It begins to generate by residual magnetism as with both series and shunt generators. Figure 2.68  Characteristic curves for a shunt generator The field flux is generated in the voltage-driven shunt windings and in the current-driven series windings. In the no-load condition, the primary operational field is the shunt field, and because of that the machine excitation curve is the same as that for any shunt machine (see Figure 2.68(a)). The series field, however, only becomes operational as the load increases. Therefore, the series field is useful for adding to the excitation as load is applied. The circuit for the compound generator is shown in Figure 2.69 (a).

2.10.5  Equivalent circuit for a d.c. generator Figure 2.64 shows a summary of the main points for all types of d.c. generators, including the equivalent circuits for each of the generator types. The circuits are identified by the excitation used by the machine.

2.10.6  Importance of residual magnetism for a self-excited generator Self-excited generators rely on a magnetic field supplied by the magnetism that remains in the iron field poles from the last time the generator was operated. It is a result of the hysteresis of iron and is known as ‘residual magnetism’. 166

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Overcompounded Long-shunt compound Levelcompounded

Series field Rheostat

Shunt field

Voltage

Short-shunt compound

G

Output

Undercompounded Differentialcompounded

Load current (a) Circuit

(b) Characteristic curves

Figure 2.69  Compound generator connections and load characteristic

When the generator armature conductors start to cut this residual flux, a small voltage is generated, causing a current to flow in the field windings. If the residual magnetic field has the same polarity as the field generated by the field poles, the amount of magnetism increases, thus increasing the field—and so on as the generator comes up to full speed and full excitation. If the residual magnetism opposes the field flux, the two will cancel and no energy will be generated. If the two magnetic components oppose each other, the machine cannot build up a voltage. Self-excitation therefore only occurs when:

1. a residual field exists 2. the residual field acts in the same magnetic polarity as the wound field 3. the generator is rotated in the correct direction for the excitation to generate a supporting field.

If any of these three factors are missing or are of incorrect polarity, the machine will not generate a voltage. If these three factors are correct, the small current circulating in the field winding provides a strengthening of the magnetic flux. This leads to an increased generated voltage, more field current, more magnetic flux and so on until the field current is high enough to provide a magnetic flux great enough to send the field poles into saturation. When this is achieved, the generated voltage stabilises at some design value. Control of output voltage is achieved by a field resistance, as with the separately excited machine.

2.10.7  Open circuit characteristics of d.c. generators Open circuit characteristic (OCC) shows the relationship between generated EMF at no load and the field current at a given fixed speed. The OCC curve mimics the magnetisation curve and it is similar for all type of generators. OCC curve data is obtained by operating the generator at no load and keeping a constant speed. It is also known as magnetic characteristic or no-load saturation characteristic. The open circuit characteristics for a separately excited d.c. generator can be seen in Figure 2.66. The open circuit characteristics for a series d.c. generator can be seen in Figure 2.70. The open circuit characteristics for a shunt d.c. generator can be seen in Figure 2.68. 167

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2.10.8  Load characteristics of a d.c. generator

Full load

Voltage

Figure 2.64 shows a summary of the main points for all types of d.c. generators, including the load characteristic for each machine type. Figure 2.68(a) shows the relationship between field current and generated voltage for a shunt generator. In the curve shown in Figure 2.68(b), the decreasing voltage characteristic that is typical of the separately excited machine can still be seen, although in the shunt machine the voltage drop is more pronounced at full load. This is because the load is also in parallel with the field and a decreasing output voltage means a decreasing field current, which further decreases the output voltage. If the generator is loaded to the point where the armature is short-circuited, then the field is also short-circuited because it is in parallel with the armature. The only magnetic flux left in the machine is that due to residual magnetism, and the result is a small generated voltage, which causes a circulating current to flow between the armature and the short-circuit. This is shown in Figure 2.68(b) as a value of current when there is no apparent voltage being generated. The shunt generator can be safely run under short-circuit conditions, but it is the only type of generator that can. Under the usual operating conditions, terminal voltage control is by means of a rheostat connected in series in the field circuit (see Figure 2.67). The practical range of voltage control is limited; the upper voltage limit is governed by field pole saturation while the lower voltage is determined by residual magnetism. Voltage control can also be achieved by speed control, but the method has limitations. These include maximum design speed, physical size and the need for a variable-speed drive source. The uses for a shunt generator are generally limited to smaller, less costly machines or cases where the load and speed are practically constant. The shunt generator is very seldom used for larger machines. In the series generator, the full load current also flows through the field winding. Consequently, a series field winding must have a low resistance so as not to restrict the load current or cause excessive terminal voltage drop. In the no-load condition, no current flows through the field; the only generated voltage is that due to the existence of residual magnetism. As load is applied to the series generator, the field current and the magnetism in the field poles gradually increase. The increasing field strength gives rise to a generator voltage/load current characteristic that is also an excitation characteristic for the field magnetic circuit (see Figure 2.70(b)). It has the same typical shape as the excitation curves for separately excited and shunt machines (see Figures 2.66(a) and 2.68(a)). Once the fields have saturated, any increase in load results in decreasing output voltage because the field flux remains almost constant, while losses in the machine continue to increase. Output voltage control can be achieved by speed variations within certain limits, but the most usual method is by connecting a resistor in parallel with the field to divert current around the field. When used in this manner, the resistor is called a ‘diverter resistor’. If the shunt field is connected across the armature as shown, the generator is then called a ‘short-shunt compound machine’; if connected across the output terminals, the generator is called a ‘long-shunt compound machine’. From a theoretical viewpoint, there are minor differences in losses and voltages—but in practice there is almost no difference in performance, whether as a motor or a generator, and either connection can be used. In the compound d.c. generator, the rising voltage Field characteristic of the series field is used to compensate for the falling voltage characteristic of the shunt field. When the series field overcompensates for the falling Output G voltage characteristic of the shunt field, the terminal voltage rises as load is applied and the generator is said Load current to be ‘over-compounded’ or ‘overcompensated’, as (a) Circuit (b) Voltage / load current curve shown by the appropriate curve in Figure 2.69(b). An (also excitation curve) overcompensated generator is often used on long feeder lines, where line losses due to voltage drop result in Figure 2.70  Series generator connections and load characteristics 168

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a low terminal voltage at the load end at full load. The generator would be adjusted so the terminal voltage at the load end of the feeder lines is approximately constant from no load to full load. The final adjustment is by means of a diverter resistance adjusted to the level required on the actual installation. As with the shunt machine, initial voltage adjustment is with a series field resistor. It is sometimes combined with a measure of speed control. The under-compounded generator is seldom used because the prime function of a generator is to supply varying loads at a constant voltage. The level-compounded generator, sometimes called the ‘critically compounded’ generator, is often used as a power source for installations where the machines it supplies are close to the generator, thereby eliminating voltage-drop problems. Examples are shipboard installations, machinery where a high degree of control is necessary (as with rolling mills), large automated planers and multiple-lift installations where a converter is needed. A series field that opposes a shunt field can be used to create a differentially compounded machine. The characteristic of the differentially compounded generator is to drop terminal voltage dramatically under load. Figure 2.69(b) shows the characteristics for a differentially compounded machine. The differentially compounded connection is seldom used but often occurs when one of the field windings is mistakenly connected in reverse after repairs. Differentially compounded generators have been used in the past as electric welding machines (with varying degrees of success).

2.10.9  Reversing the polarity of a d.c. generator To reverse the polarity of a generator, reverse either the field or armature leads, but not both.

2.10.10  Connecting and testing a d.c. generator on no load and load d.c. generators should be tested using the open circuit test and the load test to ensure proper operation. The open circuit test determines the OCC or magnetising characteristics by giving the MMF and thus the excitation or field current necessary to produce the required voltage on no load at a fixed speed. The OCC curve shows the variation of induced EMF as a function of field current at constant speed and zero load current. The load test should be carried out to establish the rating of a d.c. generator. Some energy is lost while running a machine, converting into heat; if too much heat is produced it can affect the operation of the machine and eventually lead to it breaking down. The load must be tested to ensure it can operate safely within the temperature limit.

2.10.11  Identifying safety risks associated with using generators As mentioned in Section 2.9.7, Safe Work Australia has released a code of practice for managing risks of plant in the workplace. It is important to be familiar with this document prior to working on rotating d.c. machines.

2.11   Motors 2.11.1  Operation of a motor and its energy flow A direct current machine is one that either produces or consumes electricity as direct current. The machine therefore acts as an energy converter. The same d.c. machine can be either a motor or a generator although the design is generally optimised as one or the other—when electricity is applied to the machine, it can function as a motor and convert electrical energy to mechanical energy, causing the machine to rotate. A d.c. motor converts electrical energy to mechanical energy. 169

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2.11.2  Effect of back EMF in d.c. motors When the armature of a d.c. motor rotates under the influence of the driving torque, the armature conductors move through the magnetic field and EMF is induced in them, just as in a generator. According to Lenz’s Law, the induced EMF acts in the opposite direction to the applied voltage (V) and is known as back or counter EMF. It is always smaller than the applied voltage.

2.11.3  Torque as the product of the force on the conductors and the radius of the armature/rotor The magnitude of the thrust exerted on a conductor carrying a current when located in a magnetic field is given by the equation: ​F = B l I​ where: F = force on conductor in newtons B = flux density of main field in teslas (Wb/m2) l = length of conductor in the field in metres I = current in the conductor in amperes In a practical case, where an armature has many conductors and also may have several paths, the equation becomes: B l I Z  ​F  = ​ ______    ​​   a where: I = total armature current Z = number of armature conductors a = number of parallel paths in the armature Since T = Fr where r is the radius of rotation of the armature conductors, the equation becomes: B l I Z r  ​T  = ​ _______    ​​   a where: ​T = torque in newton metres​ The formula can be further developed to: p FI Z  ​T  = ​ ______ ​​     2p a where: T = torque in newton metres p = number of poles F = flux per pole in webers I = total armature current Z = number of armature conductors a = number of parallel paths in the armature 170

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2.11.4  Types of d.c. motors and their applications

Printed circuit motors

Full load

Speed

Figure 2.71  View of the alnico magnets of a permanentmagnet motor

Load current (a)

Torque

The most common d.c. motor of any type is the permanent-magnet electric motor. In this motor, the field has no winding but consists of a permanent magnet. Everyday use for the permanent-magnet motor is in small applications such as the vibrating motor in mobile phones, cordless tools, toys, radio-controlled aeroplanes and boats. This category of both motors and generators was once reserved for smaller machines, but the present stage of development in permanent magnets allows the construction of much larger motors with permanentmagnet fields. As they have no wound field, there is a growing tendency towards a reduced unit cost and an increase in efficiency. Motors up to approximately 7.5 kW use ceramic magnets. While highly resistant to demagnetising, they have a relatively low flux level and are therefore limited in application and size. For larger motors, alnico magnets are used and the motor is easily adaptable to extreme applications such as steel mill service (furnace electrode drives and live table drives, for example). Normally, the magnet is moulded and set in the motor frame and used for low-speed applications (such as machine tools). The magnets can be seen in Figure 2.71. These magnets have been fixed in position by a hightemperature bonding agent. Speed control is traditionally achieved by electronically varying the voltage applied to the armature. This makes for a very effective and efficient method of speed control. Torque is comparatively linear throughout the normal load range. Figure 2.72 shows characteristic curves for a permanent-magnet motor.

Load current (b)

Printed circuit motors are a variation in construction of the permanent-magnet motor. The armature itself has no Figure 2.72  Characteristics for a permanent-magnet motor iron in its construction and is consequently an air-cored armature. Figure 2.73 shows the construction of the motor in its simplest form. Several circular magnets are fastened to a casting that forms the basis of field support and motor end-shield in one piece. The motor end has provisions to mount a bearing so that the armature can be maintained in its correct position within the air gap. The second end-shield consists of magnetic material to concentrate the magnetic paths within the motor and provides brush and bearing mounting facilities. For increased torque, motors may have a set of magnets each side of the armature, and the material used in end-shield construction may be non-magnetic. The armature coils are created by an etching process on a non-conducting substrate. Often of Bakelite or fibreglass, the base material is initially coated with a film of pure copper deposited on it by an electroplating process and may be single- or double-sided. Where an armature coil might need to consist of more than one turn, 171

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Permanent magnet poles

Magnetic flux return ring

End-shield

double-sided material may be used. The conductor shapes are outlined on the copper and the material in between is removed by photo-etching. Printed circuit motors are light-weight, with a short shaft length, and run at low speed and low voltage. Output torque is limited because of armature construction using no iron and efficiency is low. Commutation problems are never encountered because of low coil inductance.

Separately excited motors The wound-field separately excited motor has no limitations in size, like the permanent-magnet variety. Printed circuit Like the separately excited generator, the motor is Bearing armature disc used mainly in process control work. This type of field connection is adaptable to a wide range of speed control, and the torque is also linear with respect to Figure 2.73  General construction features of a printed circuit the applied load. Figure  2.74 shows the circuit of motor the wound-field type and can be compared with the generator circuit shown in Figure 2.67. As the machine has similar characteristics to the permanent-magnet motor, its uses are also similar. It has the advantage of being used in other circuits, Field such as Ward-Leonard control systems, gun-platform d.c. supply supply levelling and rotary amplifiers, where a small change in field current can be made to cause a large change in speed. A special construction of the separately excited wound-field motor makes it suitable for positioning work, as in long-distance readings of anemometers Figure 2.74  Circuit for a separately excited wound-field motor and engine speed governors. The normal or rated speed of a separately excited d.c. motor is obtained with rated voltage applied to both the field and the armature. This speed is termed the ‘base speed’ of the motor. If the voltage applied to the armature is reduced, the motor will slow down. So, for speeds below base speed, armature voltage control is used. If the voltage applied to the field is reduced, with rated voltage on the armature, the motor speed will increase. This method is called ‘field weakening’ and is used to give speeds above base speed. Under normal circumstances, the field-current control method is preferred, owing to lower currents in the control device, giving less electrical power wastage. However, modern electronic methods of armature voltage control are very efficient. When a motor armature rotates in its magnetic field, a voltage is generated that opposes the applied voltage. The current flowing in the armature is, based on Ohm’s Law, proportional to the difference in these two voltages divided by the armature resistance. If a rheostat is connected in series with the field, any reduction in resistance results in an increase in field current and, in turn, an increased field strength. At a constant armature speed, an increase in field strength leads to an increased generated voltage (back EMF), which tends to reduce the armature current, and the motor therefore produces less torque. As a consequence, the motor slows down as the armature current increases and the motor stabilises at a lower speed. Conversely, a decrease in field current leads to an increase in speed. Therefore, precautions must be taken to ensure that the field current does not decrease below a certain level that permits excess armature currents and dangerous speeds to result. Brushes

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Shunt-field motors Under normal operating conditions, the speed of the motor is set with the field rheostat. Decreasing the resistance value increases the field current and causes the same sequence of events with speed adjustment for the separately excited machine. Below normal speed operating ranges, the voltage to the armature is varied with a series armature resistor to give speed variations. In a similar fashion to the separate-field motor, precautions must be taken to ensure that the field current is never reduced below a certain value in order to prevent excessive armature speeds and current. Reversal of rotation is by the same method as the separate-field machine in that either the armature or the field current flow is reversed—but not both.

Series-excited motors With larger-sized series motors, speeds can be attained under no-load conditions that are sufficiently high to cause damage to the motor. A normal precaution is to have a minimum load permanently connected by direct coupling or similar means to prevent the possibility of removing all of the mechanical load. The torque characteristic of a series motor is non-linear because, as the load applied to the motor increases and the motor slows down, both armature and field current increase together. Torque has been stated to be: pΦIZ  ​T  = ​ _____ ​​   2πα For any one machine, the number of poles p, the number of conductors Z, the number of parallel paths α and the value of 2π will remain constant—so the formula can be written in the form T ∝ ΦI. Since Φ, the field flux, is proportional to the armature (field) current, T ∝ I2 for a series motor. Inspection of the characteristic curves shows that an armature current increase is associated with a decrease in speed and an increase in torque. These factors show the big advantage and common use of the series motor: starting against heavy loads. Typical uses are traction motors in electric trains, cranes, anchor winches, lifts and—the most common application—as the starter motors for motor vehicles. To reverse the direction of rotation, reverse either the field or armature leads—but not both. Speed control methods are not really applicable to series motors because of their inherent wide range of speeds, but at any one load and voltage the speed can be increased with the use of a diverter resistance to bypass some of the armature current around the field.

Compound motors The compound motor is the general workhorse among d.c. motors. It is especially suitable to loads that require a reasonably high degree of starting torque but do not require a series motor. The shunt winding allows the motor to run at very light loads, a factor that gives it an advantage over the series motor. Applications include punches, shears, rolling mills and drive motors for machines subject to sudden or shock loads and reversals such as large metal planing machines. Characteristics of the compound motor are shown in Figure 2.75. With large traction loads, such as diesel electric drives in ships, and particularly diesel electric locomotives with multiple bogie drives, the basic drive motor is referred to as a ‘series motor’. (In fact, it is probably a compound motor with the shunt field open-circuited during starting.) Several series motors may also be connected in series with one another. As the load becomes mobile, it is normal practice to reconnect the series motors in parallel, and then to convert the series motor connection to a shunt or a cumulative compound type. While a series motor (or a shunt motor) is applicable to certain particular jobs, the motor can be electrically reconnected while still rotating to suit conditions that have changed since the particular job started. Similarly, a d.c. motor in motion can be reconnected to behave as a generator supplying a resistive load and to form part of a braking sequence to reduce wear on brake shoes (e.g. in an electric train travelling downhill). 173

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Shunt field

M

Torque

Full load

DC supply

Speed

Series field

Load current

Load current

Figure 2.75  Compound motor characteristics

One form of emergency braking for electric trains is to reverse the electric motors and apply full voltage. When reversing the cumulatively-compounded motor, it must be remembered that there are two field windings. As is often the case, the machine might have interpoles as well and the reversing has to be handled more carefully. Both the shunt and series windings have to be reversed together—but not the armature or the interpoles. Reversing either the shunt or series windings on their own merely changes the machine’s connection from cumulative to differential compounding. Figure 2.76 summarises the characteristics of d.c. motors.

2.11.5  Circuit diagrams for the types of d.c. motors Figure 2.76 shows a summary of the main points for all types of d.c. motors, including the circuit diagrams for each of the motor types. The circuits are identified by the excitation used by the machine.

Figure 2.76  Summary of the characteristics of d.c. motors

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2.11.6  Equivalent circuit for the types of d.c. motors Figure 2.76 shows a summary of the main points for all types of d.c. motors, including the equivalent circuits for each of the motor types. The circuits are identified by the excitation used by the machine.

2.11.7  Calculation of power output of a motor The output power of a motor is based on the machine’s mechanical performance. It can be calculated using: 2 πnT  ​P  = ​ _____    ​​   60 where: P = output power n = speed in RPM T = torque

2.11.8  Characteristics of the different types of d.c. motors In series-field motors, the field and armature are in series with the supply in a circuit similar to the series generator. The circuit and characteristics are shown in Figure 2.77. The series motor is subject to wide changes in speed as its load is varied, because of the changing field current. With a series motor on full load, both the armature and field current are at comparatively high values. As has been explained, increasing the field current of a motor reduces its speed and, conversely, decreasing the field current increases its speed. Thus, with full load (and field) current, the speed of a series motor is low; and, as the mechanical load is removed from the motor, the armature current (also the field current) is reduced. When the magnetic field becomes weaker, the motor speeds up. The shunt-field connection is commonly used in the smaller size range of motor. In larger-sized motors, the shunt connection is found less frequently, but is still used because of its fairly constant speed characteristic. Of the several types of motor connections, the shunt-excited motor has the best speed regulation throughout the normal speed range. Like the shunt generator, the shunt-field of the motor is connected in parallel with the armature and the motor speed can be controlled by a series resistor, regulating the current flow through the field. The basic motor circuit is shown in Figure 2.78, together with the characteristic curves for speed and torque. In the cumulatively-compounded connection, the series and shunt windings assist one another, thereby increasing magnetic field strength. This is the connection normally used. As with compound generators, compounding can be

Diverter resistor connection

Torque

Speed

d.c. supply

T ∝ I2

M

Load current

Load current

Figure 2.77  Series motor characteristics

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Torque

Power source

Field

Full load

Speed

Speed adjustment

Load current

Load current

Figure 2.78  Shunt motor characteristics

under-compounded, level-compounded, over-compounded or differentially compounded. Differential compounding is possible but has little practical use. If a differentially compounded motor is loaded beyond a certain point, its current increases rapidly and the motor abruptly changes its direction of rotation. This can create a dangerous situation as, depending on size and torque of the motor, a sudden reversal can cause damage to couplings and gearboxes or even twist off a motor shaft. The cumulatively-compounded motor combines the characteristics of both the series and shunt motors. Its speed regulation is not as good as in the shunt motor, but is superior to that of the series motor. While the torque of the shunt motor is approximately linear, the torque of the compound motor increases more rapidly, but at the cost of some loss in speed. Its torque, however, is less than that of the series motor. Figure 2.76 shows a summary of the characteristics of d.c. motors.

2.11.9  Connecting and testing a d.c. shunt motor on no load and load The connection and testing of a d.c. motor on load or no load is conducted in the same manner as described in 2.10.10.

2.11.10  Reversing the direction of rotation of a d.c. motor Motor reversal is achieved by altering the polarity of the supply to either the field or the armature. The basic principle of reversal of rotation for a d.c. motor requires that the direction of current flow through either the field or the armature windings be reversed—but not both. Reversing the polarity of both supplies results in no change in rotation, as the direction of current flow in both the armature and field windings is reversed. Figure  2.79 illustrates one method of reversal of rotation. In both diagrams, the field polarity is unchanged, while the direction of current flow through the armature is changed (see Figure 2.79(b)). The torque created is equal in both cases, but the resultant direction of rotation has changed. F

F

S

N

S

N

F

F (a)

Figure 2.79  Reversal of rotation of a d.c. motor

(b)

2.11.11  Safety risks associated with using motors It is important to be familiar with Safe Work Australia’s code of practice relating to managing risks of plant in the workplace prior to working on rotating d.c. machines.

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2.12   Machine efficiency 2.12.1  Losses that occur in a d.c. machine Losses in machines include friction, windage and electrical losses. Friction is present in all rotating machinery. Windage is present because of air resistance to rotating components, and in fans added to ensure forced circulation of air for cooling purposes. In electrical machines, the term ‘other losses’ comprises copper losses, iron losses, magnetic leakage and other, lesser losses. Together, the losses are wasted energy which should be reduced as much as possible, often by simple good maintenance. Copper power losses are due to the resistance of electrical windings, while iron power losses are due to hysteresis and eddy currents in the iron core of the armature. While the iron loss is almost constant from no load to full load, the copper loss varies considerably due to load current. These two are the main electrical losses in a motor and are added to obtain the total electric power loss. The power loss in copper conductors varies as the square of the current flowing (P = I2R). At light loads, the small current flow means the copper loss is at a minimum. If the armature current is doubled, the copper loss becomes four times as great, and four times as much heat is generated; this heat has to be removed, usually by air circulation, which adds a further loss to the system.

2.12.2  Methods used to determine the losses in a d.c. machine For the purpose of analysis, it is usual to assume that all the armature resistance is concentrated into one component and not distributed throughout the windings. Figure  2.80 shows a shunt-connected generator separated into its various conceptualised component parts, while the broken lines indicate actual components.

2.12.3  Calculation of losses and efficiency of a d.c. machine If the designed generated voltage of the generator in Figure 2.80 is 200 V, and the armature has a resistance of 0.5 Ω, for every ampere of current being supplied by the armature there is an internal voltage drop of 0.5 V due to the armature resistance. For every 2 A of load current, 1 V will be lost internally; and if 200 V is required at the generator terminals, the generating section will have to generate a higher voltage in the windings. That is, for a 10 A load, the generated voltage will have to be 205 V to give a terminal voltage of 200 V between points A and B. The armature current Ia will also include the field current If as well as the load current Iload; that is: ​​I​  a​​  = ​I​  f​​  + ​I​  load​​​ The voltage drop due to internal resistance is equal to IaRa (V = IR) and the generated voltage Vg is equal to the terminal voltage V plus the IaRa voltage drop. That is for a generator:

I load

A Ia Rf

Ra

IaRa

With a series field winding, the resistance of the field must be added to the armature resistance. The theoretical approach to the efficiency of a motor is similar to the generator method. Armature resistance is considered as one component and the winding as another. This is shown in Figure 2.81, and the similarity to Figure 2.80 can easily be seen.

Armature

​V  = ​V​  g​​ + ​I​  a​​ ​R​  a​​​

Field

+ Load

G

V −

Vg

B

Figure 2.80  Equivalent circuit of a shunt generator

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I load Ia +

Ra

IaRa

​V = Vg + IaRa​

Armature

Field

Rf

The back EMF generated is subject to the armature voltage drop (IaRa) and is equal to the difference between the supply voltage and the IaRa voltage drop. That is, for a motor:

d.c. supply

M

Vg −

Figure 2.81  Equivalent circuit of a shunt motor

The only variation from the formula for generators is the polarity of the armature voltage drop (IaRa). This is illustrated in Figure  2.81, with arrows indicating the directions of the applied and generated voltages, and showing them opposing each other. The result is that the effective voltage causing a current to flow through the armature circuit is smaller than the applied voltage. That is: V  − ​V​  g​​    ​​I​  a​​  = ​ _______  ​​   ​R​  a​​

Electrical power in

d.c. motor

Losses

Figure 2.82  Losses in a d.c. motor

Mechanical power out Windage Other Field Ia2 Ra Iron Friction

The overall efficiency of a motor can be found in a similar manner to that of a generator, that is: power input = power output + losses. Whereas the input to a generator was mechanical power and the output electrical power, the input to a motor is electrical power and the output mechanical power. The losses are shown in Figure 2.82.

2.12.4  Efficiency characteristics of a d.c. machine and the conditions for maximum efficiency The efficiency of a d.c. machine will change with a change of load and will always be at a maximum when the load current is such that the variable losses equal the constant losses.

2.12.5  Application of Minimum Energy Performance Standards (MEPS) Minimum Energy Performance Standards (MEPS) are used for all machines over 0.75 kW. This standard is used to specify the minimum level of energy performance that appliances, lighting and electrical equipment (products) must meet or exceed before they can be offered for sale or used for commercial purposes.

2.12.6  Methods used to maintain high efficiency Machine efficiency is affected by several losses. In order to improve or maintain the efficiency of a d.c. machine, it is important to understand what the losses are and their impact on the machine. Heat plays a role in poor efficiency. The frame is designed to assist in the transference of heat via forced movement of air. The fan design will affect the cooling of the machine. Ensuring that the vents are not blocked or up against a barrier will allow the air to move freely. Copper losses in the form of electrical resistance will contribute up to 60% of the losses in a machine. The design of the stator and sizing of stator windings needs to take into consideration the impact that I2R losses have on the overall efficiency of the machine. Approximately 20% of the losses are iron (magnetic) losses. Hysteresis and eddy current losses can be reduced by using high-grade iron and steel containing small amounts of silicon to be used in laminations. Mechanical losses can be minimised by preventative maintenance. Check bearings and brushes regularly and ensure that the machines are free of grit and dirt. 178

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Summary ∙ A magnetic field acts outwards at the north pole and inwards at the south pole. ∙ A magnetic field tends to expand to fill the available space, to produce a field of flux that will extend to infinity in a vacuum. ∙ Like poles repel. ∙ Unlike poles attract. ∙ Lines of force existing outside the desired magnetic path are called leakage flux. ∙ Induction is a process whereby magnets induce a magnetic field in other magnetic materials. ∙ The permeability of a magnetic material indicates the ease with which magnetic induction can occur. ∙ Paramagnetic materials have low permeability and are termed non-magnetic materials. ∙ Ferromagnetic materials have high permeability and are termed magnetic materials. ∙ Materials that are used for permanent magnets are called hard materials. ∙ Materials that can easily be induced to exhibit magnetic properties but lose the induced magnetic field when the magnet is removed are called soft materials, and are useful in electromagnetism. ∙ Magnetism apparent in a material after the magnetising force has been removed is called residual magnetism. ∙ Magnetic fields can be shielded by highly permeable materials such as Mu-metal. ∙ The right-hand-grip rule for magnetism can be used for a straight conductor or for a solenoid. ∙ The force created by conductors in a magnetic field is proportional to the flux density, the length of the conductor and the current in the conductor, and can be found from the formula: F = BIl. ∙ Magnetomotive force (MMF) creates a magnetic field: Fm = IN (ampere-turns). ∙ Magnetising force: H = ​IN/l​ (ampere-turns/metre). ∙ Flux density is the flux per unit of area: B = Φ/A (webers/m2). ∙ Permeability of free space: μ0 = 4 × 10−7π (or 4π × 10−7). ∙ Permeability (actual): μ = μr × μ0 (for air, μ = 1) = ​B/H​. ∙ Relative permeability is the permeability of a material relative to free space: μr = μ /μ0. 1 ∙ Reluctance of a magnetic circuit: Rm = ​​ _____    ​​  . μoμrA ∙ The reluctance in a magnetic circuit is related to the MMF and the flux in much the same way as resistance is related IN to voltage and current. Therefore, reluctance can be found by the formula: Rm = ​​ ___ ​​ . Φ ∙ The magnetisation curve for a non-magnetic material is a straight line. ∙ The magnetisation curve for magnetic materials is a curve with a pronounced ‘knee’ at saturation. ∙ Magnetic hysteresis is the difference between the increasing and decreasing magnetisation curves resulting from residual magnetism and the coercive force required to remove it. ∙ The area within a hysteresis curve is proportional to the losses in a magnetic material. ∙ Permeability can be found using the straight portion of the B/H curve and the formula: μ = B/H ∙ Magnetic leakage is a magnetic flux that passes outside the intended magnetic circuit. ∙ Magnetic fringing is a magnetic flux that expands over a wider area than intended when passing through an air gap in a magnetic circuit. ∙ Electromagnetic relays have a fixed magnetic part called a stator, a moving magnetic part called an armature, a coil and a set of contacts that switch on. 179

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Electrical Principles ∙ An inductor is a component that generates a magnetic field when current passes through it, and that magnetic field in turn causes a current to be generated in the inductor while the magnetic field is changing. ∙ The inductance of an inductor is determined by: – the material in the core – the number of turns of wire in the coil – the cross-sectional area of the coil – the length of the coil. ∙ The core of an inductor is usually air, solid iron, laminated iron or iron-powder. ∙ The unit of inductance is the henry (H). A henry is the inductance of a closed circuit in which an EMF of 1 volt is produced when the electric current flowing in the circuit varies uniformly at the rate of 1 ampere per second. ∙ When a conductor cuts through a magnetic flux, a voltage is induced that is proportional to the number of turns, the strength of the flux and the inverse of the time taken to cut across the flux (i.e. the induced voltage is proportional to NΔΦ the velocity of the conductor). Induced voltage is therefore found by the formula: E = ​​ _____  ​​.    Δt ∙ The voltage induced into an inductor can be calculated using: e = Blv Sinθ. ∙ Lenz’s Law states the induced current will appear in such a direction that it opposes the change that produced it.

Questions Exercises 2.1 How would you determine whether a piece of iron was magnetised? 2.2 What is meant by the term ‘magnetic field’? Describe a magnetic field. 2.3 Show how a sensitive instrument may be protected against an external magnetic field. 2.4 Draw the general arrangement of an electromagnetic relay switch, labelling all parts. 2.5 What effect do electromagnetic forces have on magnetic materials and non-magnetic materials? 2.6 Draw a single wire bent into a coil with 20 turns. One end is attached to a battery positive terminal and the other to a battery negative terminal. (Do not try this, as the current would be very high.) Draw the current flow in the wire and show the expected magnetic field around the wire. 2.7 Draw a solenoid. Show a direction of current flow, and the magnetic polarity of the solenoid (N and S). 2.8 In street lighting, two wires carry the current up the street and back again. Will the current cause the wires to be attracted or repelled? (Use a diagram to help visualise this.) 2.9 How can the force of a solenoid be calculated? What values must be known? 2.10 What is the important difference between the permeability of a ferromagnetic material and that of air? 2.11 Sketch a typical B/H curve for a magnetic core made from silicon steel. Label the axes with the correct units. Mark the estimated saturation region on the curve. What is the significance of this saturation region? 2.12 What is the value of the permeability of free space? 2.13 Briefly explain what is meant by the terms ‘magnetic leakage’ and ‘magnetic fringing’. 2.14 State Lenz’s Law in your own words and explain what it describes. 2.15 What is electromagnetic force? Describe it in your own words. 2.16 When and where does magnetic leakage occur? 2.17 Where does magnetic fringing occur? 2.18 State typical applications of electromagnets. 180

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Solve problems in electromagnetic circuits  Chapter 2 2.19 What is an electromagnetic relay? Why is it used? 2.20 What is a contactor? How is it different from a relay? 2.21 Name the unit of inductance and define the unit. 2.22 What is meant by the terms ‘primary coil’ and ‘secondary coil’? 2.23 What is a time constant? What symbol is used to represent it? 2.24 What is the value of current and voltage after one time constant? 2.25 What happens when a highly inductive circuit is quickly opened? What adverse effect could result from this? 2.26 List types of inductors and their common uses. 2.27 Explain the function of the commutator in a d.c. machine. 2.28 List the physical differences in construction between series- and shunt-field windings. 2.29 Why is a shunt generator the only type of connection that can be run on a short-circuit?

Calculations 2.30 Two conductors placed 10 mm apart carry a current of 35 A to and from a d.c. motor 50 m away. What force acts between the conductors per metre length? Are they attracting or repelling? 2.31 What magnetomotive force (MMF) is generated by an electromagnet with 150 turns when a current of 12 A flows in the coil? 2.32 Determine the MMF necessary to create a flux of 0.2 Wb in a magnetic core which has a reluctance of 2000 At/Wb. 2.33 A magnetic circuit has a reluctance of 750 At/Wb. The coil, having 800 turns, carries 0.5 A. Find the total flux produced. 2.34 The mean length of a magnetic path is 600 mm. The cross-sectional area is 800 mm2. The relative permeability is 600. Determine the reluctance of the magnetic path. 2.35 The magnetising force in an iron ring is 1500 At/m. It creates a flux density of 0.95 T. Find the relative permeability for these conditions. 2.36 A long solenoid of 0.8 m has a current of 2 A flowing through a coil of 2000 turns. What is the magnetising force? 2.37 Calculate the voltage that would appear across the terminals of a 10 H inductor if the current of 5 A is reduced to zero in 0.2 seconds. 2.38 What is the inductance of an inductor that has a d.c. resistance of 35 Ω and takes 0.8 s to charge to 63.2% of full current? 2.39 A 0.8 H inductor has an internal resistance of 10 Ω. What is the maximum current it will take when supplied from a 12 V battery? 2.40 What is the current rating of a 25 kW 400 V d.c. generator at full load? What current will flow at half load? 2.41 The terminal voltage of a 15 kW shunt-connected generator is 600 V on full load. If the field resistance is 200 Ω and the armature resistance is 0.1 Ω, what is the actual value of generated voltage? 2.42 A 25 kW shunt-connected generator operates with a terminal voltage of 250 V. The armature has an effective resistance of 0.18 Ω and the shunt field has a resistance of 110 Ω. Calculate: (a) the full load current (b) the field current (c) the total armature current (d) the induced armature voltage (e) the voltage regulation. 2.43 Find the power output of a d.c. motor that develops a torque of 98 Nm when rotating at 1440 rpm. 181

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Electrical Principles 2.44 A 200 V d.c. motor draws a current of 15 A. Given an armature resistance of 0.4 Ω, calculate the value of the generated back EMF. 2.45 Calculate the generated back EMF of a 600 V d.c. motor if it has an armature resistance of 0.37 Ω and is drawing an armature current of 12 A. 2.46 Find the resistance of a 25 A shunt if the voltage across it at full load is 0.05 V. 2.47 A permanent-magnet moving-coil meter has an internal resistance of 100 Ω and a full-scale deflection current of 1 mA. Calculate: (a) the value of shunt resistor necessary to extend the range to 500 mA (b) the value of the multiplying resistor required to extend the range to 250 V.

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3

CHAPTER OBJECTIVES • understand environmentally sustainable work practices, including: – the notion of sustainable work practices – the effects of neglecting sustainable work practices – the greenhouse effect—causes and consequences – international and national greenhouse imperatives – the role of regulators and similar bodies, and legislative requirements – the economic benefits of sustainable initiatives • understand techniques for reducing carbon-produced energy and hence greenhouse gases, including:

– domestic, commercial and industrial strategies – trade-related technologies and methods – energy-efficient retrofits – renewable energy technologies

3.0  Introduction The term ‘sustainability’ means the ability to maintain something at a certain level. For example, if the generation of power from a solar panel installation is sufficient to keep a battery bank charged at a useable level, taking into account the current drawn from those batteries, it can be said to have sustainability. As another example, if the amount of water consumption of a particular household is low enough for rainfall to be able to keep the supply tanks from emptying, this is a water supply system that has sustainability. In the global environmental context, ‘sustainability’ refers to the ability of the earth to continue to provide human beings with an environment that will allow our quality of life—and way of life—to be maintained. One way of gauging this kind of global sustainability would be to ask, for example, whether the recycling of finite metals such as copper and gold is sufficient to allow us to continue to produce the cables and electronic components that use them. 183

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We might also ask what strategy we will adopt when the copper and gold resources are depleted. How will we continue to provide the function of a copper cable when there is no copper left to mine or recycle? How will we continue to produce electronic components such as microprocessors when there is no gold left to plate their electrical contacts? Answers to these questions range from using alternative materials to adopting strategies that avoid their use. For example, a wireless transmission medium can be used in place of copper cabling, and alternative materials can be used to replace the gold coatings on the contacts of many electronic components. But such alternative materials are not always ideal: for example, aluminium can be used in place of copper, but it does have a lower conductivity and it too is a finite resource; materials such as silver and tin can be used in place of gold but they tend to corrode more easily. The broad concept of sustainability requires an acknowledgement of the detrimental effects on our planet that resource usage has. It is not only important to conserve the earth’s resources but also to use them in such a way that the planet does not become uninhabitable to human beings. This consideration raises questions such as how we can reduce greenhouse gas emissions to a level that will avoid the earth’s temperature rising so high as to make living difficult. Environmental sustainability is a required state for human existence. However, when population growth along a never-ending timeline is factored in, it looks unachievable over the long term: at some stage, there will simply not be enough to go around. This is why strategies aimed at environmental sustainability usually involve the ‘minimisation’ of harm and/or resource usage. This, it is hoped, will buy the human race enough time to come up with alternatives such as renewable energy. Sustainable work practices are minimisation and replacement strategies to reduce the impact of resource usage on the earth and its inhabitants and make our current environment more sustainable. The production of energy through the use of gas, coal and petroleum and the extraction of metals such as copper and gold illustrate that the electrotechnology industry must implement sustainable work practices. They are all resources which affect sustainability because they are limited and because their use and/or manufacture creates greenhouse gases (GHGs) that contribute to global warming, a phenomenon that could make life on earth unsustainable. Refrigerants and other chemicals are also relevant to sustainability and the electrotechnology industry. Aside from their effects on global warming, they are pollutants that damage the earth and its atmosphere. For example, chemicals leak into waterways and damage plants and animals, while man-made refrigerants, which are used for refrigeration and air conditioning, affect the ozone layer, allowing harmful ultraviolet radiation from the sun through to the earth.

3.1   Sustainable work practices The practical application of sustainable work practices should occur right across the electrotechnology industry, from the utilisation of renewable power sources and low-emission fuel sources to the minimisation of waste materials and energy used on the job. Companies often implement policies requiring employees to minimise their negative environmental impact. Examples include directives for managers to consider sustainability issues as part of the planning process, to promote environmental awareness and to ensure that employees are aware of their environmental responsibilities. At an individual level, each person should follow the maxim ‘reduce, reuse, recycle, repair’, the particular aspects of which are examined in the following sections.

3.1.1 Reduce Job sites are places where the consumption of resources is above average. This is due to both construction and maintenance activities being labour and material intensive. One very effective way of reducing this consumption is simply to turn machinery and apparatus off when it is not in use, examples of which include:

∙ turning off vehicle engines rather than letting them idle ∙ turning off taps or hoses rather than letting them flow into drains ∙ turning off electric motors when they are not in use.

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3.1.2 Reuse In the process of upgrading, replacing or changing infrastructure or equipment, materials can often become surplus to requirements. This is an opportunity to reuse the surplus materials rather than consigning them to the tip. Materials that can be reused include (but are not limited to) cabling, cable tray, ducting and even saddles. PVC conduit can also be reused, and it is important to do so where possible as PVC is not a product that is easily recycled. Although it is predominantly plastic, it contains additives such as lead, cadmium, tin, barium and zinc that cannot be easily separated from it. As with all plastics, its manufacture requires oil.

3.1.3 Recycle Most materials used in the electrotechnology industry are recyclable. Metals like copper and aluminium can be sold to scrap metal yards, while paper, glass and plastic can be delivered to recycling plants. The resource cost offset by recycling rather than producing new materials is significant. Batteries can be recycled. When they are dumped into landfill, the chemicals they contain can leak and contaminate groundwater, posing a health hazard to humans and animals. Not only do batteries contain hazardous waste, but they also often contain recyclable materials such as lead, so delivering them to a recycling plant is worth the trip. The Australian Battery Recycling Initiative (ABRI) was created to promote the responsible disposal of batteries. Online resources from the ABRI—available at http://www.batteryrecycling.org.au/—explain the issue in detail and show where batteries can be recycled.

3.1.4 Repair As many products are cheap and labour is expensive, it is often seen as a better option to simply throw an item out rather than repair it. That might well be the case in terms of saving time and money, but not repairing items may not be the best option in terms of environmental responsibility.

3.2  Effects of neglecting sustainable work practices 3.2.1  Consequences of neglecting sustainable work practices The most catastrophic long-term consequence of neglecting sustainable work practices would be that the earth’s resources are consumed at a faster rate than they can be replaced. A lack of resources could combine with damage to the environment to cause widespread famine and disease. A medium-term consequence could be the loss of habitats for animals, which could result in certain species becoming extinct and food sources becoming scarce. The more immediate consequences of failing to practice sustainability are considerably less speculative and include:

∙ ∙ ∙ ∙

increasing air pollution, causing a decrease in air quality and an increase in respiratory problems and illness increasing water pollution, causing a decrease in water quality, potentially making it unsuitable for drinking an increase in contaminated land, causing a reduction in usable land and potential sickness an increase in global warming, making life on earth increasingly difficult to sustain.

The sources and causes of pollution as a result of neglecting sustainable work practices include (but are not limited to) the following:

∙ ∙ ∙ ∙ ∙ ∙

chemical and oil spills generation and inappropriate disposal of waste asbestos (handling and removal) air emissions (toxic and greenhouse gases) noise and vibration dust generation 185

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∙ PCB (polychlorinated biphenyls) management ∙ radiation (electric and magnetic fields, or EMF) ∙ greenhouse gas emissions.

Neglecting sustainable work practices may not have catastrophic consequences, but collectively it will exact a toll on future generations. The excess waste of one person is not enough to doom humanity; but as each resource is squandered, the cost to the environment is increased. The resources that we currently take for granted may not be available in five or 50 years’ time. The environment we live in today is unlikely to remain as healthy as it is now if the demand for raw materials increases. If sustainable practices are not followed, future generations may well have a reduced quality of life. They may need to adapt to an inhospitable environment, with fewer resources available and more health issues emerging.

3.3  The greenhouse effect—causes and consequences 3.3.1  The greenhouse effect—definition A greenhouse is a plastic or glass house in which plants are grown. Its purpose is to counteract the effects of cold weather. Greenhouses stay warm because heat from the sunlight which shines through the transparent glass or plastic is partly trapped inside and cannot easily escape. The term ‘greenhouse effect’ is often used in connection with the earth and sustainability. A natural greenhouse effect is created by water vapour and greenhouse gases such as carbon dioxide in the atmosphere reflecting back to earth some of the sunlight that rebounds from it (see Fig. 3.1). The water vapour and greenhouse gases have a similar effect to the plastic or glass of a greenhouse.

Figure 3.1  The greenhouse effect Shutterstock/Designua

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3.3.2 Causes The greenhouse effect occurs naturally, but some of humanity’s activities increase it. Burning fossil fuels (coal, oil and gas) to generate electricity and power vehicles and making concrete for construction produces large amounts of carbon dioxide (CO2), increasing the greenhouse effect. Other chemicals created by humans and the effects of pollution and land clearing increase the warming effect. The main ‘greenhouse’ gases are carbon dioxide, methane, nitrous oxide and ozone. There are various ‘feedback loop’ mechanisms which also increase the greenhouse effect. An example of such a loop mechanism would be:

1. 2. 3. 4.

Burning fossil fuels creates more CO2 in the atmosphere. More CO2 in the atmosphere prevents heat from escaping, further warming the earth. The earth becomes hotter, melting the ice at the polar caps. White ice reflects sunlight/heat away from the earth, and as the ice melts, less sunlight/heat is reflected and is instead absorbed by the earth. Consequently, the earth heats up even further, melting more ice and continuing the feedback loop.

The main feedback loop that contributes to the greenhouse effect involves water vapour. As the earth warms, more water vapour is produced, which traps more heat and heats the earth further, thereby creating even more water vapour. This traps more heat and the earth becomes still warmer—and the cycle continues. Feedback loops such as these may lead to very sudden ‘avalanche’ effects rather than the gradual changes which have been noticed since the beginning of the Industrial Revolution in the late 1700s.

3.3.3 Consequences The consequence of the greenhouse effect on the earth is an increase in the global temperature. Although a certain amount of global warmth is required for the earth and its inhabitants to thrive, too much causes the following:

∙ ∙ ∙ ∙ ∙ ∙ ∙

an increase in the earth’s temperature changed patterns and amounts of precipitation reduced ice and snow raised water levels increased ocean acidity increased frequency, intensity and/or duration of extreme weather events shifting characteristics of ecosystems.

These issues increase health risks for humans and animals, as well as the need to migrate to maintain acceptable nutritional, climatic and other living conditions.

3.4  International and national greenhouse imperatives Australia has been proactive in limiting greenhouse gas emissions since 1988, when the Government adopted a reduced CO2 emissions target in response to the World Conference on the Changing Atmosphere in Toronto. Since then, Australia has continued to be a part of a worldwide commitment to climate change, participating in various national and international initiatives such as the Kyoto Protocol (1992) and the Paris Agreement (2015). Australia has implemented policies relating to climate change, and provides tools and programs to help reduce it. Among many examples is the National Landcare Program, which is aimed at creating a more sustainable and productive agriculture industry. The Asia-Pacific Rainforest Partnership was formed to reduce greenhouse gas emissions from deforestation, and the International Partnership for Blue Carbon targets the restoration of coastal ecosystems. Some of the major current initiatives are discussed in the following sections.

3.4.1  The Renewable Energy Target (RET) The Renewable Energy Target is a Government scheme introduced in 2011 to lead to the production of a higher level of renewable energy—specifically, to have 23.5% (33 000 gigawatt hours) of Australia’s electricity coming from 187

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renewable energy by 2020. The RET offers incentives for small- and large-scale renewable energy installations. Examples of large-scale systems are power stations such as wind and solar farms, while smaller systems include solar water heaters and small-scale wind farms. To achieve the RET, the number of large-scale installations will need to double. The initiative for small-scale installations is well under way, with over 2.5 million households already using solar systems. Australia has the world’s highest penetration rate of solar PV (photovoltaic) panels on household roofs (15%).

3.4.2  The Emissions Reduction Fund (ERF) The Emissions Reduction Fund provides businesses, land owners, government departments, community groups and individuals with incentives to reduce emissions via new technologies and practices. It aims to reduce 2020 emissions to 5% below 2000 levels and 2030 emissions by 26%–28%. To benefit from the ERF, a business needs to create a project that reduces emissions beyond its current activities. Once that is done, an administrative body called the Clean Energy Regulator will issue one Australian Carbon Credit Unit (ACCU) for each tonne of reduced emissions. These ACCUs can then be sold to the Government or to private-sector purchasers who can offset their emissions with them. A system called the national registry of emissions units tracks the location and ownership of ACCUs.

3.4.3  The Clean Energy Innovation Fund The Clean Energy Innovation Fund supports the growth of emerging technologies and businesses that target clean energy, renewable energy, energy efficiency and low emissions. Suitable initiatives might include large-scale solar with storage, off-shore energy, biofuels and smart grids.

3.4.4  National Greenhouse and Energy Reporting (NGER) The National Greenhouse and Energy Reporting scheme is a framework for the reporting and dissemination of company information about greenhouse gas emissions, energy production and energy consumption. The information is used to inform policy and meet international reporting requirements.

3.4.5  Other national initiatives Other Australian schemes and initiatives include: ∙ The Carbon Neutral Program—certifies an organisation as having met certain carbon offset standards ∙ Hydrofluorocarbon (HFC) management—controls manufacturing, importing and exporting of ozonedepleting substances and synthetic greenhouse gases ∙ taxation measures—luxury cars that are not fuel efficient incur higher tax penalties than those that are ∙ 20 Million Trees—a scheme to plant 20 million trees by 2020 to help reduce greenhouse gas emissions by creating a carbon sink ∙ The Solar Communities program—provides funding for community groups in some regions to install rooftop solar PV, solar hot water and solar-connected battery systems ∙ Energy Efficiency Measures—a scheme to provide practical information on saving energy and cutting power bills ∙ The Carbon Farming Initiative—a scheme where storing carbon or reducing greenhouse gas emissions enables farmers to earn Carbon Credits that can be sold to businesses who want to offset their emissions ∙ Minimum Energy Performance Standards (MEPS)—an initiative introduced to ensure that electrical products meet a minimum performance level before they can be supplied or sold in Australia ∙ Energy Rating Labels—a scheme ensuring that electrical appliances have an energy rating label attached, enabling consumers to make informed decisions on purchases. Appliances covered by the scheme include washing machines, fridges, freezers and air conditioners (see Fig. 3.2). 188

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Australia’s various initiatives fulfil binding international requirements set out by The United Nations Framework Convention on Climate Change (UNFCCC). Compared with many other countries, Australia is a relatively small contributor to overall global emissions. However, its per-capita emissions relative to the rest of the world are high.

3.4.6  The United Nations Framework Convention on Climate Change (UNFCCC) In 1992, Australia, along with 153 other nations, signed The United Nations Framework Convention on Climate Change (UNFCCC). The aim of the framework was to ensure the protection of the atmosphere. All of the signatory nations recognised that the continual production of harmful greenhouse Figure 3.2  Sample 3.5 Star Energy Rating icon gases (GHGs) was contributing to climate change © Energy Rating,Commonwealth of Australia 2016 and therefore that the activities of human beings are contributing to global warming. The UNFCCC created a formal agreement to ensure that participating countries took steps to limit the amount of GHGs and to allow ecosystems to adapt to the ever-changing climate. Two major initiatives have come from the UNFCCC—the Kyoto Protocol and the Paris Agreement.

3.4.7  The Kyoto Protocol The Kyoto Protocol is an international agreement created under the UNFCCC in Kyoto, Japan, in 1997. It aimed to reduce the world’s collective greenhouse gas emissions by binding developed countries to emission reduction targets but left developing countries to join on a voluntary basis. The latter category included China and India, both of which had significant emissions due to their large populations, despite being relatively under-developed. The developed/ under-developed issue led some large-emissions countries to drop out of the agreement, including the USA and Canada. In 2015, the Kyoto Protocol was effectively replaced by the Paris Agreement.

Figure 3.3  How Australia tracks against the Kyoto Protocol target (2008–2012)

DoE (Australian Government Department of the Environment) (2014a). National inventory report 2012, DoE, Canberra, www.environment.gov.au/climate-change/greenhouse-gas-measurement/publications/national-inventory-report-2012 © Commonwealth of Australia 2017

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3.4.8  The Paris Agreement The Paris Agreement aims to reduce climate change. But, unlike the Kyoto Protocol, it binds both developed and developing countries to it, which has led to more countries signing up to it. The aim of the Paris Agreement is to ensure that the earth’s ‘pre-industrial’ temperature is not exceeded by more than 2° Celsius this century, and to endeavour to limit the actual temperature increase to no more than 1.5° Celsius. To put this into perspective: as of 2018, the world is at about 1° Celsius above pre-industrial temperatures and, predictions suggest, if emissions are allowed to continue unabated, the temperature could rise to about 4° Celsius above pre-industrial temperatures by the year 2100. It is important to note that this refers to the mean global temperature. The temperature in some areas could rise well above that, and in other areas it could fall below that. The consequences of a 4° Celsius mean global temperature increase would be catastrophic.

3.5  The role of regulators and similar bodies There are various regulators nationally and internationally that regulate policies, legislation and changes relevant to emissions and the climate.

3.5.1  Climate Change Authority (CCA) The Climate Change Authority provides expert advice about Australia’s climate change policies. It has a particular role in reviewing and making recommendations on the Carbon Farming Initiative and the National Greenhouse and Energy Reporting system.

3.5.2  Clean Energy Regulator The Clean Energy Regulator’s role is to administer Australian Government schemes for measuring, managing, reducing or offsetting the country’s carbon emissions. The regulator is responsible for the National Greenhouse and Energy Reporting scheme, the Emissions Reduction Fund, the Renewable Energy Target and the Australian National Registry of Emissions Units.

3.5.3  The Environment Protection Authority (EPA) Each state and territory in Australia has an EPA. Their purpose is to protect the environment and human beings by taking action on pollution and waste.

3.5.4  Department of the Environment and Energy The Department is responsible for the protection of the environment, water and heritage. It implements policies and procedures relevant to climate change action and reliable and affordable energy.

3.5.5  International bodies The peak world body for climate change information is the Intergovernmental Panel on Climate Change (IPCC). Formed in 1988, it regularly releases reports that assess the impacts of climate change. The IPCC coordinates thousands of experts from around the world to bring together information to help understand climate science, including meeting the challenges posed by climate change. 190

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3.6  Legislative requirements Legislation relevant to sustainability comes from acts, regulations and policies. There are examples relating to climate change, air pollution, water, chemicals and ozone protection, as well as renewable energy. The key pieces of legislation are dealt with in the following sections.

3.6.1  Climate Change Act 2017 All Australian states and territories have created acts of parliament, regulations and policies relevant to climate change. For example, Victoria’s Climate Change Act 2017 is consistent with the Paris Agreement and is designed to manage climate change risks.

3.6.2  Ozone Protection and Synthetic Greenhouse Gas Management Act 1989 The Ozone Protection and Synthetic Greenhouse Gas Management Act 1989 was introduced to control the manufacture, import and export of all ozone-depleting substances (ODSs) and synthetic greenhouse gases (SGGs). Licensing controls have been introduced in Australia to guide the use of synthetic refrigerants and to ensure that only licensed persons can work with them.

3.6.3  Environment Protection and Biodiversity Consideration Act 1999 The Environment Protection and Biodiversity Consideration Act 1999 is the major single piece of legislation relating to the environment and it applies to all states and territories of Australia. It provides a legal framework to protect and manage heritage areas, wetlands, threatened species and marine areas.

3.6.4  What the acts, regulations and policies mean Each state and territory’s acts, regulations and policies are administered by its Environment and Protection Authority (EPA). When businesses, government departments and land owners lodge an application for works, the EPA must consider the potential impacts of those works in light of the requirements set out in all legislation. If it is established that the works will either not meet or will be in contravention of legislative requirements, they are not allowed to proceed.

3.7   Economic benefits of sustainable initiatives The electrical industry in Australia contributes significantly to both the national economy and to the production of greenhouse gases. Incorporating sustainable work practices in the electrical industry can bring significant benefits, not simply in terms of the longevity and wellbeing of the environment but also in terms of the economic welfare of electrical businesses and their customers. Various economic initiatives provide direct economic benefits and incentivise businesses, land owners, state and local governments, community organisations and individuals to adopt new practices and technologies which reduce emissions. These include:

∙ The Emissions Reduction Fund—participating individuals and organisations can earn Australian Carbon Credit Units. One ACCU is earned for each tonne of carbon dioxide equivalent (CO2-e) stored or avoided by a project. ∙ Renewable Energy Target—its two core components, the Large-scale Renewable Energy Target and the Small-scale Renewable Energy Scheme, provide financial incentives for investment in renewable energy. 191

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Electrical Principles Table 3.1   Australia’s greenhouse gas emissions by economic sector (2015) Emissions (Mt CO2-e)

Share of total emissions

All Sectors

538.2

100.0%

Primary Industries

160.1

29.7%

Sector

  Agriculture, Forestry and Fishing

85.1

15.8%

 Mining

74.5

13.8%

Manufacturing

62.4

11.6%

194.4

36.1%

Services, Construction and Transport

61.9

11.5%

Residential

59.5

11.1%

Electricity, Gas and Water

National Inventory by Economic Sector 2015, Commonwealth of Australia 2017

Carrying out practices to reduce waste results in more efficient spending and higher profits. If practices to reduce carbon emissions are adopted, businesses or individuals may be eligible to seek monetary compensation. For example, a person or business who invests in small-scale renewable power systems can access credits as part of the Small-scale Renewable Energy Scheme.

3.7.1  HFC Refrigerant Levy As part of the Clean Energy Future Plan (2012), synthetic greenhouse gas refrigerants attract a levy. The size of the levy is proportional to the gas’s Global Warming Potential (GWP). Although it is the refrigerant importers who pay the levy, the costs are passed down the supply chain, ending up with the customer. The HFC refrigerant levy aims to bring the following benefits:

∙ ∙ ∙ ∙

Reduced refrigerant leakage through improved system design. Reduced emissions through improved maintenance. Systems that use a smaller charge of refrigerant are preferred for future use. Lower GWP refrigerants and systems are more likely to be implemented.

The electrical industry is under continual pressure to move towards the use of work practices and procedures that minimise the use of electrical energy and synthetic greenhouse gases.

3.8 Techniques for reducing carbon-produced energy and greenhouse gases Burning fossil fuels such as natural gas, coal and oil causes the level of carbon dioxide in the atmosphere to rise, which is a major contributor to the greenhouse effect and global warming. Individuals can take action by using energy wisely and thus reducing the demand for fossil fuels. Table 3.2 shows methods of reducing greenhouse gas emissions. 192

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Apply environmentally and sustainable procedures in the energy sector  Chapter 3 Table 3.2  Methods of reducing greenhouse gas emissions Reduce, reuse, recycle, repair

Buying products with minimal packaging helps to reduce waste. Over 1000 kilograms of CO2 can be saved annually if each person recycles half of their household waste.

Use less heat and air conditioning

Adding insulation to walls and installing doubleglazed windows can lower heating costs by more than 25% by reducing the amount of energy needed to heat and cool a home. Heating can be turned down while people are sleeping at night or are out during the day. Temperatures should be kept moderate at all times, and set no higher than 19°C in winter and no lower than 25°C in summer. By doing this, Australian businesses could save $100 million and 300 000 tonnes of carbon every year.

Replace light bulbs

Traditional, inefficient incandescent light bulbs are being phased out in Australia. There are other more efficient types of lighting available, including lightemitting diodes (LEDs) and compact fluorescent lamps (CFLs). It is estimated that the phasing out of incandescent light bulbs is saving the average household 300 kilowatt hours and $75 per annum.

Drive less and drive wisely

Less driving means fewer emissions. People could use public transport or consider carpooling to work. If people decide to drive, they could make sure that their cars are running efficiently—having tyres over- or under-inflated by 1 bar or 15 psi from the recommended inflation pressure could lead to a 5% difference in rolling resistance, which may result in a significant fuel cost increase. A reduction of 10% of rolling resistance on a complete vehicle results in approximately 3% reduced fuel consumption. Every litre of petrol saved keeps 10 kilograms of CO2 out of the atmosphere.

Buy energy-efficient products

Home appliances come in a range of energyefficient models. Compact fluorescent bulbs, along with LED lamps, use far less energy than standard light bulbs.

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Use less hot water

An average household can use around 25% of its total energy on heating water. Using a more efficient hot water system reduces energy costs.

Remember to switch lights and appliances off

People can switch off lights when they leave a room, and use only as much light as they need. It is also important to turn off televisions and computers that are not in use.

Plant a tree

One tree will absorb approximately one tonne of carbon dioxide during its lifetime.

Request an energy audit from utility companies

Many utility companies provide free home energy assessments to help consumers identify areas in their homes that may not be energy efficient. Utility companies may also offer rebates to help pay for the cost of energy-efficient upgrades.

Encourage others to conserve energy

People can share information about recycling and energy conservation with friends, neighbours and colleagues, and take opportunities to encourage public officials to establish programs and policies that are good for the environment.

Source: Adapted from ‘Ten Ways to Reduce Greenhouse Gases’. Town of East Gwillumbury. http://www.eastgwillimbury.ca/Services/Environment/Ten_Ways_to_Reduce_ Greenhouse_Gases.htm

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3.9  Domestic, commercial and industrial strategies In order to reduce greenhouse gas emissions and fossil fuel use (and to conduct business legally), the electrotechnology industry as a whole could adopt sustainable work practices. The three main areas where changes could be made involve copper, electricity, and oil and gas.

3.9.1 Copper The electrotechnology industry uses large amounts of copper. With copper reserves being limited, it is imperative that changes are made to reduce its use and to recycle it. Recycling is beneficial as copper can be recycled over and over again with no loss in quality. In fact, a process of electrolysis can be refined to upgrade it. Recycling copper means there is less of it in landfill and less of it being mined (it is cheaper to recycle copper than to mine it). This in turn means there is less environmental damage, due to a reduction in the waste gases produced when mining and refining copper. Further benefit from recycling copper comes from a reduction in the use of resources used to manufacture it: oil, gas and coal are used as fuel sources in its production; not having to use them is good for the environment. Reducing the use of copper is not as easily achieved. However, reductions can be made in LAN cabling and required cable diameters. Wireless communication technology is increasing data throughput speeds, and is often sufficient without needing a hard-wired copper-cabled network (particularly for small installations)—so wireless installations should be preferred over hard-wired networks when possible. This could include an entire network, but may also apply to a single run only. For example, rather than a single run of copper cabling to an outside IP camera, perhaps a wireless IP camera would suffice. This is also more economical for the customer. The diameter of copper cable used is important and is indeed mandatory in relation to safety, functionality and reliability. Australian Standards mandate that cabling of a minimum specific diameter is used in various situations. However, it is not uncommon for larger diameters to be used, just to make sure that all bases are covered. However, as copper is a finite resource it is important that this practice is curbed within the limits of safety, reliability and functionality. The overall benefits of recycling copper and reducing its use include:

∙ ∙ ∙ ∙

minimised environmental damage reduction in landfill copper resource conservation financial savings.

3.9.2 Electricity Electricity costs are rising constantly and its production is affecting the environment. The following are strategies for reducing its consumption:



∙ Minimising the use of fossil fuel. Although significant change has been made in moving towards renewable energy through hydropower, wind, rooftop solar and bioenergy, approximately 86% of Australia’s electricity still comes from burning fossil fuels. Therefore, minimising the use of fossil fuel-driven electricity is a major consideration. The various ways of doing this include turning off appliances at the wall when not in use rather than putting them on standby. ∙ Replacing standard devices and lights with more efficient or lower-consumption versions. Examples include replacing fluorescent lights with LEDs and replacing desktops with laptops or tablets. ∙ Turning off lights when they are not required or installing motion detectors to control lighting in infrequently used rooms. ∙ Installing blinds and shutters on windows to block out direct sun, reducing the need for air conditioning in the summer and allowing sun and light in during winter. 195

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∙ Choosing green energy plans from energy providers. ∙ Keeping doors closed to minimise the need for air conditioning and setting the temperature to avoid overheating or over-cooling (19°C during winter and 25°C during summer). ∙ Turning air conditioning off for the last hour or so of the day. ∙ Cleaning air conditioning filters and condenser coils regularly. ∙ Installing a solar power system. ∙ Using signs, posters and stickers to keep the idea of saving energy in people’s minds. ∙ Incorporating building improvements that maximise natural heating and cooling systems. ∙ Hiring an energy efficiency expert to analyse work areas and develop an energy savings plan.

3.9.3  Oil and gas The use of fossil fuels such as oil and gas is one of the major contributors to the production of greenhouse gases. Oil is distilled to create petrol and diesel and, along with gas, is used to fuel vehicles. Gas in a different form is also used for heating. Sustainable work practices to minimise oil and gas use include the following: ∙ Gas heating is similar to electricity. Certain points that apply to electricity, such as making building improvements, keeping doors closed and not setting the temperature too high, also apply to gas. ∙ Using energy-efficient vehicles that consume less fuel. This includes hybrid electrical/fuel vehicles as well as vehicles that use less petroleum-based fuel. ∙ Minimising the purchase of plastic products (crude oil is used in the production of plastic). ∙ Using non-synthetic work clothes and boots where safe to do so, rather than those made from oil-based nylon and polyester plastics. ∙ Switching to soy-based printing inks rather than the standard petroleum types. ∙ Using natural cleaners rather than oil-based cleaners. ∙ Choosing plastic products that are made from recycled material and that can be recycled themselves. ∙ Using tap water rather than bottled water to reduce the use of petroleum-based plastic bottles. ∙ Purchasing products made locally rather than overseas to reduce long-distance transportation. From the items in this list, the greatest beneficial impact would come from reducing vehicle fuel use and the use of plastics.

3.10   Trade-related technologies and methods There are various technologies and methods in the electrotechnology industry that can be used to reduce energy consumption.

3.10.1 Technologies Greater energy efficiency can be achieved by using the following technologies:

∙ ∙ ∙ ∙ ∙ ∙

programmable time clocks—switch appliances on and off at preferred times and off during holiday periods motion sensors—enable ventilation systems to operate during holiday periods if regular motion is detected LED lighting—is more energy efficient and cost effective than standard lighting building design and position—can maximise weather conditions such as sunlight solar energy systems energy monitoring systems—can be used to assess the energy efficiency of an installation

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∙ building management systems (BMS)—can control plant and equipment. For example, a BMS can be set to use air from outside rather than conditioned air ∙ C-Bus microprocessor systems—capable of controlling lighting, security, air conditioning and other residential and commercial functions.

3.10.2 Methods Methods to reduce energy consumption include:

∙ switching devices and machines off when not in use, including through the use of automation such as sensors and timers ∙ matching generators to the load ∙ replacing ageing, low-efficiency equipment with newer, more efficient versions ∙ using blinds and window shutters ∙ wearing clothing to keep warm rather than using air conditioning ∙ adjusting the thermostat for air conditioning 1 degree warmer in summer and 1 degree cooler in winter ∙ using induction cooktops rather than gas ∙ using renewable power sources and batteries rather than diesel generators ∙ installing variable speed drives (VSD).

In addition to using technology and other ways of reducing electricity consumption, the regular servicing of plant and equipment is necessary to keep all systems working as efficiently as possible. Work practices and methods that contribute to sustainability include: ∙ conducting a site survey of the plant equipment and air-conditioning equipment and measuring power consumption, with the aim of reducing the electricity bill ∙ ensuring that any visible faults such as leaks and damaged switches are repaired or replaced ∙ replacing worn or damaged cables, seals, etc. ∙ selecting the most efficient electrical appliances for each installation ∙ fitting electronic timers to systems to ensure they are not accidentally left running in an empty building or office ∙ testing the installation before leaving the site.

3.11   Trade-related retrofits In the context of sustainability, retrofitting is the process of replacing old technologies with newer ones to improve energy efficiency. The many examples of these technologies include:

∙ solar photovoltaic systems and battery storage systems—these respectively generate and store power so that fossil fuel-based power does not need to be used ∙ electric vehicles—reduce the use of fossil fuel-based vehicles, reducing fossil fuel use and greenhouse gas emissions ∙ variable speed drives that match working conditions—can cut energy use by up to 50% in comparison with constant speed drives (this includes applications in pumping, fans and HVAC systems) ∙ low-power LEDs—can replace compact fluorescent lighting ∙ programmable controllers—enable the efficient use of resources by activating equipment only when needed, based on factors such as time and temperature ∙ electric water heaters and induction cook tops—these are energy-efficient replacements for standard electric appliances 197

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∙ improving power quality—reduces electromagnetic disturbance from inferior equipment such as lighting systems and electric motors and decreases power and energy losses ∙ replacing synthetic refrigerants with natural refrigerants such as ammonia (R717), carbon dioxide (R744) and hydrocarbons (R290 and R600). There are dangers associated with these natural refrigerants so manufacturers’ advice should be sought.

3.12   Renewable energy technologies 3.12.1  What is renewable energy? Renewable energy is any form of energy that can be used over again and/or is self-replenishing and/or is generated by a near-limitless source like the sun. Renewable energy technologies, sometimes referred to as ‘green’ energy technologies, use natural resources that can be continually replaced to create energy. Renewable energy technologies include solar, wind, hydro, bioenergy, geothermal, ocean and hybrid technologies.

3.12.2  Solar energy Photovoltaic panels convert sunlight into electricity, and concentrated solar thermal collectors use energy from the sun to heat up water or oil that then can be used to heat water to make steam. This can be used to drive a turbine attached to a generator. Photovoltaic panels are found in both small-scale roof-top installations and on large-scale utility-sized installations. According to the Clean Energy Council, ‘small-scale solar was responsible for 16.0 per cent of Australia’s clean energy generation and produced 2.8 per cent of the country’s total electricity’ in 2016 (Clean Energy Council, 2016, Solar PV, https://www. cleanenergycouncil.org.au/technologies/solar-pv.html). The Council reports that, by the end of 2016, ‘Australia had 12 solar projects larger than 5 MW in size. With the exception of one solar thermal plant, the solar farms used photovoltaic technology, and together they provided 319 MW of generation Figure 3.4  Small-scale solar installation capacity’ (Clean Energy Council, 2016, Large-scale solar PV, https://www.cleanenergycouncil.org.au/ technologies/large-scale-solar-PV.html).

3.12.3  Wind energy

Figure 3.5  Large-scale solar installation

Wind power is currently the cheapest source of largescale renewable energy. Turbines capture energy as the wind moves past the blades, causing them to turn, the blades being coupled to a generator. According to the Clean Energy Council, ‘Australia’s wind farms produced 30.8 per cent of the country’s clean energy and supplied 5.3 per cent of Australia’s overall electricity during the year’ in 2016 (Clean Energy Council, 2016, Wind energy, https://www.clean­ energycouncil.org.au/technologies/wind-energy.html).

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Very few small-scale wind turbines exist as they are not cost effective.

3.12.4  Hydro energy The movement of water causes a turbine to spin, and the turbine is connected to a generator that produces electrical power from the mechanical power of the water. On large-scale systems, the water often flows from a high level (a dam) to a lower level (a river). In some cases, other intermittent renewable sources pump water from low areas into higher points to allow the hydrosystem to act as a large renewable battery. This system has been proposed as part of the Snowy Mountains Hydro Scheme 2.0 and will potentially increase its energy-producing capacity by 50%.

Figure 3.6  Wind power

3.12.5  Geothermal energy Geothermal energy uses naturally occurring heat from deep underground to create steam that is used to drive turbines. Iceland and the Philippines generate 25% and 17% respectively of their energy via geothermal means. Even though Australia does not have any significant volcanic activity, geothermal is a potentially viable renewable energy source (Clean Energy Council, 2014, Geothermal, https://www.cleanenergycouncil. org.au/technologies/geothermal.html).

3.12.6  Ocean energy

Figure 3.7  Guthega Dam, a part of the Snowy Mountains Hydro Scheme Shutterstock/Phillip Minnis

Ocean energy refers to the movement of ocean water to generate electricity. The two main types are tidal and wave energy.

Tidal energy Tides cause movements in ocean waters, and constrained topology near coastlines can accelerate these movements. Tidal energy generates electricity using the regular local flows of the tidal cycle. The Kimberley and Pilbara coasts of northern Western Australia see the largest tides in Australia. Other potential sources of tidal power are the Torres Strait off the coast of Darwin, Broad Sound in Queensland and Bass Strait in Tasmania.

Figure 3.8  Geothermal energy station

Wave energy Waves are created by wind passing over the surface of the ocean. Wave power plants can harvest the energy in the up-and-down motion of waves and convert it into electricity. According to the Clean Energy Council, ‘wave energy is strongest where there are trade winds and ocean swells. In Australia, our wave energy resources are greatest along the southern coastline’ (Clean Energy Council, 2014, Marine energy, https://www.cleanenergycouncil.org.au/technologies/marine-energy.html). 199

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3.12.7 Bioenergy Bioenergy uses biomass to create energy. (Biomass is the name given to all plants and animals—including human beings—on earth.) ‘Energy from biomass’ refers to ways of using plants and animals as energy sources. Typically, the energy is extracted via either burning of the biomass using the heat given off to create steam and drive a turbine or by anaerobic or aerobic digestion. Newer technologies can convert the biomass directly to petrol and diesels. Common sources of bioenergy are:

Figure 3.9  Tidal power Shutterstock/Alex Mit

∙ sugar cane residues (also known as ‘bagasse’) ∙ landfill gas (the methane produced by landfills) ∙ agricultural crop and livestock waste ∙ household garbage ∙ sewage gas ∙ wood waste ∙ black liquor (a by-product of the papermaking process).

In Australia, the bioenergy sector currently generates approximately 3600 gigawatt hours of energy per annum. This equates to 1.5% of total electricity generation and 8.6% of total clean energy generation (Clean Energy Council, 2014, Bioenergy, https://www. cleanenergycouncil.org.au/technologies/bioenergy.html). An overview of the different capacities for electrical generation by the main sources is given in Table 3.3. Figure 3.10  Bio-fuel production As well as the individual renewable energies, there are also hybrid schemes (hybrid energy combines renewable energies, examples being biomass and wind, and solar and wind). Hybrid energy schemes may also include a traditional power source such as, for example, solar combined with a diesel generator.

Table 3.3  Summary of renewable energy capacity and generation in 2015 Technology

Installed capacity (megawatts)

Generation (gigawatt hours)

Hydro

7800

14 046 (mostly pre-baseline)

Wind

4187

11 802

Large-scale solar

224

303

Bioenergy

990

3200

9.3

27

Marine

0.24

0.5

Geothermal

0.12

0.50

Solar thermal

© Clean Energy Council, www.cleanenergycouncil.org.au

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Summary ∙ Human beings need to reduce their consumption of the earth’s resources. ∙ To ensure the survival of the species, resources must be managed so that future generations can also use them. This is called ‘being sustainable’. ∙ Sustainable development has been defined by the United Nations as development which meets the needs of the present without compromising the ability of future generations to meet their own needs. ∙ Methods of being sustainable include reducing waste, reusing materials and recycling materials. ∙ Not adopting sustainable practices causes harm to the environment and can lead to death and disease. ∙ The greenhouse effect is where the heat from the sun is trapped within the earth’s atmosphere. ∙ Greenhouse gasses (including water vapour) are causing more heat than is normal to be trapped, thereby heating the planet up. ∙ Increases in temperature cause damage to the environment. ∙ Agreements have been reached in Kyoto and Paris between countries to lower the amount of greenhouse gasses being released into the atmosphere. ∙ To ensure that Australia meets its obligations to the international community, several government bodies are responsible for making sure that individuals and companies follow the Environment Protection and Biodiversity Conservation Act 1999. ∙ Reducing greenhouse gas emissions also reduces the cost of materials and energy. ∙ The most significant way of reducing emissions is to turn off energy-consuming devices, appliances or tools when they are not in use. ∙ The use of renewable energy sources reduces emissions. ∙ Types of renewable energy sources include: – hydro – wind – solar (PV) – solar thermal – biomass – wave – tidal – geothermal.

Questions Exercises 3.1. Explain the term sustainability. 3.2. Give an example of two uses of copper in the electrical industry. 3.3. Name two pollutants used in the electrotechnology industry. 3.4. Give an example of a sustainable work practice. 3.5 Give three examples of reducing the consumption of electricity. 3.6 Give an example of where we can reuse surplus materials in industry. 201

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Electrical Principles 3.7 Give two examples of materials in industry that can be recycled. 3.8 What does the abbreviation ABRI stand for? 3.9 What is a disadvantage with regards to not repairing some relatively cheap products? 3.10 Name three consequences of neglecting sustainable work practices. 3.11 Name four causes of pollution as a result of neglecting sustainable work practices. 3.12 What effect will neglecting sustainable work practice have on our future generations? 3.13 Define ‘The Greenhouse Effect’. 3.14 Give one cause of the greenhouse effect caused by humans. 3.15 Give two examples of ‘feedback loop’ mechanisms that can increase the greenhouse effect. 3.16 What is the primary greenhouse gas that contributes to the greenhouse effect? 3.17 Name five consequences of the greenhouse effect. 3.18 Give the names of two international initiatives brought about to limit greenhouse gas emissions. 3.19 What is Australia’s Renewable Energy Target for 2020? 3.20 Which country has the highest penetration rate of solar panels on household roofs? 3.21 There are numerous national initiatives in place to reduce carbon gas emissions. Name seven of them. 3.22 What was the aim of the ‘Kyoto Protocol’? 3.23 What is the aim of the Paris agreement? 3.24 Name four regulatory bodies aimed at cleaning up emissions and our climate. 3.25 Name eight methods of reducing greenhouse gas emissions. 3.26 What are the three main areas the electrotechnology industry can affect, which will result in a reduction in greenhouse gas emissions? 3.27 How can we protect our reserves of copper? 3.28 How can we reduce the consumption of electricity? 3.29 How can we reduce the consumption of oil and gas? 3.30 Name five technologies that can be utilised to reduce energy consumption. 3.31 Name five methods to reduce energy. 3.32 What is renewable energy? 3.33 Explain how solar energy works. 3.34 Explain how wind energy works. 3.35 Explain how hydro energy works. 3.36 Explain how geothermal energy works. 3.37 Explain how ocean energy works. 3.38 Explain how bioenergy works.

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4

CHAPTER OBJECTIVES This chapter deals with alternating-current (a.c.) circuits in the electrotechnology industry. After examining various facets of their operation, we examine how to tackle the problems that can affect them. The chapter also covers hazards associated with alternating-current circuits and ways of lowering the consequent risks. • • • • • • • • • • • • • • • • • • • • • • • • •

understand sine waves understand generation of an a.c. EMF list factors affecting a generated EMF recognise causes of loss in generating an EMF list factors affecting sine wave shape understand sine wave terminology compare maximum, average, RMS, peak and peak-to-peak values define period and frequency of a waveform use phasor diagrams to aid calculations including addition and subtraction understand harmonic frequency relationships understand resistance, reactance and impedance in a.c. circuits understand effects of connecting components in series and parallel in a.c. circuits understand and use phasor diagrams in solving a.c. circuit problems perform calculations involving voltage, current, resistance, reactance, impedance, power, phase angle and frequency in a.c. circuits understand and perform calculations involving power factor and power factor correction in a.c. circuits understand and recognise the issues and dangers of resonance in a.c. circuits understand that three-phase power is more efficient than single-phase and that three-phase systems are the more economical option describe two-phase systems describe how three-phase power is generated describe the advantages of three-phase systems construct three-phase sine waves in sequence and timing describe three-phase star and delta connections relate phase and line values for star and delta describe the infinite grid concept describe typical transmission voltages

(continued) 203

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• • • • • • • •

describe an SWER system differentiate between balanced and unbalanced loads calculate line values from phase values and phase values from line values calculate neutral current in an unbalanced load calculate power in three-phase systems describe methods of power measurement in three-phase loads understand and comply with the requirements of AS/NZS 3000:2018 and AS/NZS 3008.1:2017 for single- and three-phase voltage drop understand and comply with the requirements of AS/NZS 3000:2018 and AS/NZS 3008.1:2017 for fault loop impedance.

4.1   Alternating current 4.1.1 Introduction Alternating current (a.c.) is generated when a loop conductor, or coil, is rotated within a uniform magnetic field. Alternating current is used in preference to direct current for power transmission, transformers and effects that require self- or mutual inductance. A coil of wire rotating within a magnetic field produces a waveform with a positive voltage for one halfrevolution and a negative voltage for a second half-revolution. The waveform has a constant rate of change, so there are no sharp corners. Such a perfect waveform is called a ‘sine wave’ (see Figure 4.1). The sine wave is the output generated by an alternator that is perfect in theory. Real-world alternators have to be carefully designed and manufactured to generate perfect sine waves. Sinusoidal-shaped voltages are what the laws of physics naturally produce. The maths of a.c. electricity is based on sinusoidal waveforms.

4.1.2  Sinusoidal waveforms When doing calculations about circuits and components, it is easiest to work with pure d.c. and pure sinusoidal a.c., as shown in Figure 4.1. The term ‘sinusoidal’ means that its form follows the strict mathematical function of the sine (this is discussed in the Appendix). When tables of sine values are plotted as a graph, the resulting characteristic curve is a sine wave; it is sinusoidal in shape. The first half of the curve is a mirror image of the second half and is always positive; the second half is always negative. The advantages of the sine wave are:

Figure 4.1  Sine wave

1.   It is an easy shape to reproduce because it is a naturally occurring waveform based on the trigonometry of a circle. 2.  It is pure, having only one frequency. Other waveforms may have many frequencies mixed together.

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3. It is the only waveform that produces a current flow with the same waveform as the voltage. 4. Its shape allows the maximum permissible power per unit size of machine. 5. As the sine wave has an alternating voltage, current and magnetic flux, it can operate any equipment that relies on mutual induction, such as transformers.

4.1.3  Other waveforms In the electrical power industry, any waveform other than sinusoidal is considered to be distorted. There are other waveforms in use, though. These are generated for specific purposes but not for the transmission of electrical energy. Figure 4.2 shows the more common waveforms. Figure 4.2(a) shows the straight line of a d.c. voltage. It attains a steady value and remains constant at that value. Although the voltage value may change over time, it does not change periodically like the other waveforms. Figure 4.2(b) shows the sinusoidal waveform. A pure sine wave is continually changing at a constant rate. Its shape is symmetrical around the zero line. It is not, as some may think, a series of semicircles. The next waveform is the sawtooth wave in Figure 4.2(c). It is immediately above the triangular wave in Figure 4.2(d), and the two are often confused. Both rise symmetrically but, while one decreases at the same rate as it increases, the other changes abruptly to its most negative value. Both are used in timing circuits because the voltage changes proportional to time.

+v 0v −v +v

(a) Direct current (d.c.)

0v −v +v

(b) Sinusoidal wave

0v −v +v

(c) Sawtooth wave

0v −v +v

(d) Triangular wave ON

ON

ON

0v OFF

−v +v

ON

OFF (e) Square wave (symmetric) ON ON

OFF

0v −v

OFF

OFF (f) Square wave (asymmetric)

OFF

Figure 4.2  Examples of waveforms

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Figure 4.2(e) shows the square waveform. When the positive or ‘on’ time period is equal to the zero or ‘off’ time period, it is considered square or symmetric. This switches a voltage from positive to zero (or negative) at a steady rate: there is a positive voltage for a period, and then a zero (or negative) value. The transition from positive to zero (or negative) is abrupt and seems to be instantaneous. But in real waveforms, this must take a definite period of time. When the ‘on’ period is not equal to the ‘off’ period, the waveform is described as ‘asymmetric’ or ‘rectangular’. To ensure that an electronic circuit is switched off completely, it is sometimes necessary to make sure there is a negative voltage. The square waveform is also used in logic circuits and variable frequency motor drives. Electronic components sometimes use it in comparison-type circuits to indicate that an event has occurred; for example, that one voltage has exceeded another voltage. The waveform in Figure 4.2(f) is a variation of the square wave used to control power circuits. There are two ways of varying the amount of power, and each provides power only when the square wave is positive. One way is to vary the ratio between the time period when the voltage is on and the time period when it is off. This means that the frequency of the power pulses does not change. The other method simply varies the amount of time the power is off, changing the frequency of the power pulses. In both methods, the ratio of on-time to off-time is known as the ‘mark/space’ ratio.

Representing values The custom when calculating and representing values of voltage and current is to use capital letters for DC values and lower-case letters for a.c. values. However, as RMS values (discussed in section 4.45) are equivalent to DC values, they are also given in capital letters. Therefore, lower-case letters in this book usually refer to instantaneous values. Another custom is to always use RMS a.c. values unless otherwise specified. Modern a.c. instruments are calibrated to read RMS values, while some are what is known as ‘true RMS’ instruments, which means that they read RMS even if the waveform is not a true sine wave.

4.1.4  Sine, cosine and tangent ratios of a right angle triangle The output generated from an alternator is a sine wave. We can use a circle to help calculate values along it because points on the sine wave correspond to points on the circle. Step 1. Draw a horizontal line from the centre of the circle to its perimeter. Step 2. Then draw another line from the centre of the circle to the perimeter at an angle of 40° (see Figure 4.3). Step 3. Now draw a (downward) line between the point at which the angled line radiating from the centre meets the perimeter of the circle and the first horizontal line. The third line will always join the first line at a right angle. This is extremely useful in calculating corresponding points on the sine wave as, because of the mathematical nature of a right angle triangle, trigonometry can be used to calculate values. Take the triangle in Figure 4.23. The side going from the centre of the circle to the perimeter is the radius. The magnitude of this line equals the peak value of the sine wave. It is consistent all the way around the circle. This side is called the Hypotenuse. The point that corresponds with 40° when extended perpendicular to the horizontal line forms a right angle triangle in the centre of the circle. Here it has a 40° angle. The line on the triangle from this point to the horizontal line is equivalent to the instantaneous magnitude of the sine wave at 40° (‘instantaneous magnitude’ meaning here the distance between zero and the point that corresponds with 40°). This side is called the Opposite—it is the side opposite to the 40° angle. The remaining side is called the Adjacent as it is adjacent to the 40° angle.

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90°

180°

0° 360°

270°

0°

90°

180°

270° 360°

Figure 4.3  Sine wave construction We can use trigonometry to calculate these values consistently when the magnitude of the maximum value and the desired angular point is known. The main equation operators are known as Sine (SIN), Cosine (COS) and Tangent (TAN) and these relate to the ratios of the sides. (Equation operators are mathematical tools that aid calculations and are always the same for each angle.) The Sine of the angle—in this example SIN 40°—is determined by the Opposite divided by the Hypotenuse. This ratio will always be the same, regardless of the size of the triangle, as long as the angle remains the same. Opposite   ​Sine = ___________ ​       ​​ Hypotenuse The Cosine of the same angle (in this example COS 40°) is determined by the Adjacent divided by the Hypotenuse. Again, this will always be the same as long as the angle remains the same. Adjacent ​Cosine = ___________ ​       ​​ Hypotenuse The Tangent of the angle, TAN 40° is determined by the Opposite divided by the Adjacent. Opposite ​Tangent = _________ ​     ​​ Adjacent A simple way of remembering these ratios is SOH CAH TOA: Opp ∙ SOH  − Sin = _____ ​​   ​​  Hyp Adj ∙ CAH − Cos = _____ ​​    ​​  Hyp Opp ∙ TOA − Tan = _____ ​​    Adj

 ​​4.1.5  Applying Pythagoras’ theorem to a right angle triangle Pythagoras’ theorem is a useful tool that is associated with right angle triangles. It shows how, if the lengths of two of the triangle’s sides are known, the third side can be determined. The theorem states that the sum of the Opposite squared and the Adjacent squared equals the Hypotenuse squared. ​Hypotenuse​​  2​= O ​ pposite​​  2​ + ​Adjacent​​  2​ We can make the Hypotenuse the subject of the equation by taking the square root of each side of the equals sign: ____________

_____________________

√ ​​   ​H    ypotenuse​​  2​ ​ = ​ √ (​    Opposite​​  2​ + ​Adjacent​​  2​) ​ 207

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5

4 U 25 s nit

Q°

te po

Hy

5

se nu

Adjacent

16 Units

4

Opposite 9 Units

3

3

Figure 4.4  Applying Pythagoras’ theorem to a right angle triangle

Since the square root of the Hypotenuse squared is just the Hypotenuse, the equation can also be expressed as: _____________________ ​Hypotenuse  =  √  ​     (​Opposite​​  2​ + ​Adjacent​​  2​) ​ To determine the Opposite or the Adjacent, the first formula is transposed: ​Opposite​​  2​= ​Hypotenuse​​  2​ − ​Adjacent​​  2​ or ​Adjacent​​  2​= ​Hypotenuse​​  2​ − ​Opposite​​  2​ Again, these can be simplified in the same way: _________

________________________

_________

________________________

√  ​​  ​Opposite​​  2​ ​   = ​ √     (​Hypotenuse​​  2​ − ​Adjacent​​  2​ ) ​ or ​ √ ​Adjacent​​  2​ ​   = ​ √ (​     Hypotenuse​​  2​ − ​Opposite​​  2​) ​​ And: ________________________ ________________________ ​Opposite  =  √  ​      (​Hypotenuse​​  2​ − ​Adjacent​​  2​ ) ​ or Adjacent = ​ √     (​Hypotenuse​​  2​ − ​Opposite​​  2​ ) ​​

4.2 Use of the oscilloscope to measure d.c. and a.c. voltage levels 4.2.1 Oscilloscope An oscilloscope shows an electronic signal as a picture or graph on a screen. It is used to demonstrate how a voltage changes over a small amount of time. If you need to examine any electrical signal, simply change it into a voltage and you can look at it on the screen for as long as you wish. Oscilloscopes only seem complicated because they are so versatile. Oscilloscopes are used in most electronic laboratories. They are essential in automotive repair workshops for diagnosing engine faults and tuning fuel injection and engine management systems. They are also used widely in 208

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the medical field and in interpreting signals from television stations. Oscilloscopes are essential for maintaining any industrial servicing set-up that has any appreciable amount of electronic equipment. Modern oscilloscopes have LED screens and are computerised. This means they can self-calibrate input signals and retain settings, functions and readings in their memory. Some can even send their stored information to other machines and the internet. Older style oscilloscopes called ‘Cathode Ray Oscilloscopes’ (CROs) may still be used to measure a.c. waveforms, and knowing how they work may help to understand the information they display.

4.2.2  Cathode-ray tube (CRT) The cathode-ray tube (CRT) is vital to the operation of the CRO. It consists of an elongated glass tube with a glass faceplate at the viewing end. This is internally coated with a phosphor compound. This coating glows when bombarded by an electron beam. When the electron beam is removed, the glowing spot remains briefly then gradually fades, in the same way that the human eye briefly retains its most recent image. The length of this period indicates the retentivity (or persistence) of the screen. At the other end of the glass tube is an electron gun. This produces the electron stream and directs it towards the screen or faceplate. The gun section consists of a heater inside a metal tube called a cathode. The filament heats the cathode, causing it to emit electrons. The electrons form a beam and are accelerated by electrostatic forces from the application of voltages to the metal grids. This beam is directed at the phosphor-coated end of the tube. Where it hits the face, it shows as a small glowing dot. Surrounding the cathode and on top of it are circular wire-wound metal grids. Between these and the face of the tube are two sets of paired metal deflection plates. These control the electron stream. Controls on the front of the CRO allow fine adjustment or focus of the beam to make the dot as small as possible. (Figure 4.5 shows the layout of a standard CRO.)

4.2.3  The deflection plates As has been seen, this small glowing dot is moved around the screen via electrostatic force. As an electron stream has a negative charge, applying voltages to the plates means it can be bent in any direction through attraction and repulsion. This is illustrated in Figure 4.6. In Figure 4.6(a) no voltage has been applied to either set of plates, so the electron stream dot stays centred on the screen. In Figure 4.6(b) a voltage has been applied to one pair of plates, attracting the beam horizontally to the right. This is helped by the electrostatic repulsion created by the left-hand plate, and the beam is said to have been ‘swept horizontally’. Consequently, these plates are called ‘horizontal deflection plates’. In Figure 4.6(c) the polarity has been reversed and the beam has been swept in the opposite direction. The distance the spot moves depends on the value of voltage applied to the deflection plates. For example, if 100 V sweeps the spot 2 cm to the right, 200 V will sweep it 4 cm to the right, meaning that the deflection capability is 50 V/cm. Figures 4.6(d) and (e) show a similar situation. The beam can be swept vertically up or down when a voltage is applied to the other set of plates. These are called the ‘vertical deflection plates’. Applying voltages to both sets of plates at the same time produces simultaneous vertical and horizontal deflection. This is shown in Figure 4.6(f), where a positive polarity has been applied to the top vertical plate and the right-hand horizontal plate. The beam is swept to the upper right-hand corner of the screen. Gun assembly Filament

Grids Phosphorcoated faceplate Cathode

Deflection plates

Figure 4.5  Cathode-ray tube

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(a)

If the voltages applied to the plates are allowed to vary, the glowing spot will move around accordingly. If the voltages change fast enough, the spots on the CRT will continue to glow even though the actual spot has moved. This leads to the screen appearing to show continuous lines. If the applied voltage is changed slowly, the image will be of a dot moving around on the screen. If the voltage change is rapid, the persistence of both the screen and the human eye makes a line seem to appear on the screen.

(b)

− + V

(c)

(d)

4.2.4 Block diagram of an oscilloscope + V − +

V

−

A block diagram of a CRO is shown in Figure  4.7. It illustrates the essential components of all CROs.

4.2.5  Vertical amplifiers

(e)

(f)

− +

+ V −

V

− + V

Figure 4.6  Horizontal and vertical plates deflect the electron stream

Vertical deflection amplifier

Vertical preamp.

Deflection plates (CRT)

Sweep circuits Horizontal deflection amplifier

Figure 4.7  Simplified block diagram showing basic electronic blocks of all oscilloscopes

The CRO input is often attenuated (meaning limiting its signal) to protect the instrument and isolate the CRO from the circuit under test. The vertical scale is also set in V/cm as a form of calibration. The size of the signal can be adjusted to take up as much or as little of the screen as required. When the oscilloscope is isolated from the circuit, it cannot load the circuit and give potentially false readings. Circuit isolation or buffering can mean that the incoming signal might have to be amplified again. That is why there is a preamplifier before the vertical deflection amplifier. Vertical deflection amplifiers are voltage amplifiers. They boost the incoming voltage signal so that sufficient deflection of the beam can occur. The amplification of the signal must be equal at all frequencies that the instrument is expected to operate over. A positive incoming signal causes the beam to deflect upwards from the centre line of the screen. A negative signal causes it to deflect downwards. The vertical display is always calibrated as a voltage. If the centre line of the screen is not needed, a vertical position control is usually added. This sets the centre line of the display up or down as required. (See Figure 4.8, where the display centre is shown centre, up and then down.)

4.2.6  Horizontal amplifiers

The horizontal deflection amplifier drives the horizontal deflection plates. Similar in action to the vertical amplifier, it is used to produce sufficient voltage to ensure adequate horizontal deflection of the electron beam. Again like the vertical amplifier, it deflects the beam according to the voltages imposed on the plates. The horizontal display can also be adjusted so that it can be shifted to the left or right. For most oscilloscope work, the horizontal deflection circuit is driven by a sweep generator, not by an applied external signal. (An external signal is only applied in special cases, and these are discussed in section 4.2.13.) The 210

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sweep circuit unit generates a sawtooth wave (whose name is derived from its shape on a CRO—see Figures 4.9 and 4.2(c)), which moves the electron beam from left to right across the screen. The horizontal display is always calibrated in seconds or parts of a second, depending on the speed selected.

Vert. pos.

Vert. pos.

Vert. pos.

4.2.7  The sweep circuit The sweep circuit generates sawtooth waves at designated frequencies. The electron beam is swept from left to right by the voltage of the sawtooth wave at the selected frequency. Figure 4.9 illustrates the basic sweep signal. Since frequency is time related, the sweep is expressed in seconds per centimetre (s/cm). Consequently, it is called a ‘time base’. Initially, the voltage polarity of the sawtooth wave is negative (T0 in Figure 4.9), meaning that the value of its initial voltage is below zero (see also Figure 4.2(c)). This starts the beam on the left-hand side of the screen. As the voltage goes more positive, the beam moves at constant speed across the screen to the right until it reaches the end of its ‘travel’ (T2). The beam must then be returned quickly to its starting point— the wave is shaped so that it drops to its negative value as quickly as possible to position T3 and starts its next travel.

Figure 4.8  Vertical position control

Sweep

Right

Retrace

Centre

Left

T0

T1

T2

T3

At time T 0 the trace is at the left of the CRT. At time T 1 the trace is at the middle of the CRT. At time T 2 the trace is at the right of the CRT. At time T 3 the trace is returned to the left of the CRT

Figure 4.9  Basic sweep signal

4.2.8  Vertical input attenuator A vertical input attenuator is a network of resistors connected in a circuit so they can be selected with a rotary switch. Figure 4.10(a) is a representation of the layout and connections. Figure 4.10(b) shows a typical front-panel view of the switch. At its extreme left-hand position, each vertical centimetre on the face of the oscilloscope represents 50 V. At its extreme right-hand, each centimetre represents 10 mV/cm. In both diagrams, the 10 V/cm switch position has been selected. The usual input impedance of most oscilloscopes is around 1 MΩ shunted by an input capacitance in the range 20–50 pF. These values are an industry standard and accessories are made to match them. A value of 1 MΩ does not cause any appreciable loading effect on many circuits. The capacitors connected across the resistors network stabilise the input.

Vertical attenuator input Volts ——— cm 500

10 mV 100 mV Vertical preamp. 1V

V —— div.

1

200 100

2

10 V

mV —— div.

50

5 100 V

20

10 20 (a) Schematic diagram

50

10

(b) Front-panel control

Figure 4.10  Vertical attenuator

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4.2.9  Horizontal time base

Time/cm

To improve the performance of an oscilloscope, the time taken for the electron beam to travel across the screen has to be 20 2 µs ms —— —— known exactly. This time period is known as the ‘horizontal div. 5 10 div. time base’. The unit of time is controlled by an oscillator in 5 10 the sweep circuit module (see Figure  4.7) with a sawtooth 2 20 waveform (see Figure 4.9). 1 50 The time base control on the front panel selects period of time for each complete cycle. The time can be shortened or 100 .5 .2 200 lengthened by rotating the panel switch. 500 .1 Figure  4.11 shows a front-panel layout for a time base switch. Here, the slowest sweep time is 500 ms/cm. This means that the beam travels from left to right at a rate of one Figure 4.11  Horizontal time base control half-second for each centimetre of travel (2 cm/s). The fastest sweep time is 0.1 μs/cm. An external sweep signal can also be inserted into the oscilloscope circuit in measurements that require synchronising with another signal. 500

200

100

50

1

.

Ext

4.2.10  Triggering the time base The vertical movement of the electron beam is controlled by a voltage input to the vertical attenuator. Its horizontal movement is controlled by a purpose-built oscillator. These two entirely separate circuits produce a graph on the face of the oscilloscope. When an oscilloscope is used to check the waveform of an alternating voltage supply, the cycles of a.c. keep repeating themselves as long as there is an input. Each time a cycle occurs, it draws a trace on the screen. Unless the sweep is controlled, it might draw the input voltage later or earlier in the cycle, resulting in a meaningless jumble of lines. To enable an oscilloscope to draw a graph that makes sense, a trigger circuit is provided. Trigger circuits allow the oscilloscope to synchronise the beam movements, ensuring that the horizontal sweep always starts when the vertical input reaches a specific voltage. For example, where there is only one part of a cycle when the voltage is not only going positive but is also positive in value, a trigger circuit can sense this. It sends a pulse to the sweep circuit so that it starts its horizontal travel. The level of positive voltage required can also be selected—going positive and +1 V, for example. The result is that only one line is swept or repeated continuously on the screen. It is not the same cycle but is the same waveform traced over and over. The trace appears to remain stationary and can be examined.

4.2.11  Interpreting an oscilloscope display Most oscilloscope screens have a transparent cover with a graticule (or grid) inscribed on it in centimetre squares. (The screen is usually 8 cm high by 10 cm wide.) If the instrument is calibrated correctly, measurements taken by the graticule can be translated into values. Figure 4.12 shows two cycles of a sinusoidal waveform as they would appear on an oscilloscope screen. The sinusoidal waveform can be evaluated using horizontal and vertical reference values. As an example, use the values set on the vertical attenuator from Figure 4.10(b) and the horizontal time base from Figure 4.11. This gives the oscilloscope screen values of 10 V/cm vertically and 20 ms/cm horizontally. The peak-to-peak value of the voltage wave is 6 cm. Since each centimetre vertically represents 10 V, this can be translated as 6 × 10 = 60 VP−P or 30 Vmax from the centre line to either peak. This can then be converted to an effective value of 30 × 0.707 = 21.2 V; that is, the waveform shown on the oscilloscope has a value of 21 V. Two cycles of alternating current take up a horizontal distance of 9 cm. That is equivalent to 4.5 cm per cycle. Since the time base is set at 20 ms/cm, this represents a time of 4.5 × 20 = 90 ms. So, one cycle takes up a period of 90 ms, or 0.09 s. Taking the reciprocal of this figure gives the frequency in cycles per second. Here, the frequency is 11.1 Hz. 212

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Voltage

Solve problems in a.c. circuits  Chapter 4

Time in µs/cm

Figure 4.12  Sinusoidal waveform

Frequency is the inverse of the time in seconds. Expressed as a formula it is: 1 ​f = __ ​   ​​   t

EXAMPLE 4.1 Find the peak-to-peak voltage and frequency of the sinusoidal waveform in Figure 4.12 if the vertical attenuator is set on 50 V/cm and the time base is set on 5 ms/cm. Two cycles take 9 cm horizontally. This is equivalent to 4.5 cm/cycle. ∴ the horizontal time for 1 cycle = 4.5 × 5 ms = 22.5 ms = 0.0225 s 1 ∴ Frequency = ______ ​​     ​​  = 44.4 Hz 0.0225 The peak-to-peak value of the wave is 6 cm. ∴ Voltage = 6 × 50 = 300 V

Of course, not all waves are sinusoidal. Figure 4.13 shows one version of a square wave. The same wave appears in each of the diagrams but with different time bases. The apparent frequency differs considerably, but when the horizontal calibrations are taken into account, all are still the same—the voltage is constant in each. In Figure 4.13 the time base is set at 1 μs/cm. One complete cycle takes 10 cm or 10 μs. The voltage is high for 2.5 μs and low for 7.5 μs. This translates to a frequency of 100 kHz. In Figure 4.13(b), given a time base of 2 μs/cm, one complete cycle takes 5 cm or 5 × 2 = 10 μs as before. Although the wave looks different, it is the same wave at the same frequency. It is still high for 2.5 μs and low for 7.5 μs. In Figure 4.13(c) the time base has been altered to 10 μs/cm. Each cycle is completed in 1 cm and still gives a cycle time of 10 μs and a frequency of 100 kHz. However, this time it is more difficult to determine the high and low periods of each cycle. Altering the timing of the horizontal time base from one value to another does two things—it gives an overall picture of events and/or enlarges a cycle for analysis. 213

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(a) Time 1 µs/cm

(b) Time 2 µs/cm

(c) Time 10 µs/cm

Figure 4.13  Effect of altering the sweep frequency

4.2.12  Dual trace oscilloscopes Sometimes it is necessary to compare waveforms. For example, the input waveform to an electronic circuit might need to be compared with the output waveform. a.c. waveforms that are being manipulated may become displaced in time from each other. But if both can be shown on the screen at the same time, their relationship can be compared. With a normal oscilloscope, each waveform can be shown in turn. However, this does not allow a direct comparison between the two, nor does it show any relationship between them. There are two ways of creating a situation where a Vertical comparison can be made. One is by making a cathodedeflection amplifier ray tube with two electron guns and connecting each Electronic switch Vertical wave shape to its own input. (Cathode-ray tubes in TV preamp A sets have three guns for the three primary colours.) The other, more common, method uses a high-speed Horizontal electronic switch which allows portions of each wave deflection Vertical amplifier to be displayed in turn. The relevant circuit is shown in preamp B block form in Figure 4.14. Trigger and There are two vertical inputs but still only one time sweep base circuit. Samples of each input signal are shown on the oscilloscope screen in turn against the same time Figure 4.14  Simplified block diagram of a dual trace oscilloscope interval. 214

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The persistence of vision of the human eye and the persistence of the oscilloscope screen cause the trace to appear to remain on the screen until the next piece of information arrives. The result is that two traces appear on the screen against a common time base. A meaningful comparison between them can then be made. Theoretically, there is no limit to the number of traces that can be shown at the one time. But in practical terms, four appears to be a reasonable limit for most oscilloscopes. Even then, the upper operational frequency limit is reduced by the conflict between the number of traces, the number of samples, the speed of the electronic switch and the screen persistence.

0°

30°

60°

4.2.13  Other oscilloscope measurements Sections 4.2.4 and 4.2.9 covered the application of an external signal to the horizontal time base. If a sinusoidal waveform is applied to both the horizontal and vertical deflection plates simultaneously, specific patterns can be displayed on the oscilloscope screen. The type of pattern that emerges depends on the relative amplitudes, frequencies and phases of the two voltages. Stationary patterns appear if the ratios of these values are kept constant.

4.2.14  Phase displacements

90°

120°

150°

If the same voltage and frequency are applied to both sets of plates, the resulting pattern will be a straight line inclined upwards to the right at 45°. If a circle appears, the two voltages are at 90° to each other. Some of these patterns are shown in Figure 4.15.

180°

Figure 4.15  CRO patterns for various phase displacements

EXAMPLE 4.2 Find the phase displacement between two voltages if the display gives measurements of 11.8 mm and 13.6 mm (see Figure 4.16).



11.8 sin θ = ____ ​   ​  ​​ ​  ​  13.6 ​  ​​ ​ = 0.867 that is, θ = 60°

y = 11.8

Y = 13.6

Figure 4.16  Sketch for Example 4.2

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Electrical Principles

Patterns

Freq.ratio 1:1

2:1

Actual phase differences between two voltages can be found quite accurately. This is done by measuring parts of the curve against the graticule. The ratio between two of the measurements is related to the angle of phase displacement, as: y sin θ = __ ​​    ​​  Y where: θ = phase angle y = first measurement Y = second measurement

3:1

3:2

4.2.15  Frequency comparisons

When two different frequencies are applied to the deflection plates, more complex patterns appear on the oscilloscope screen. These are called ‘Lissajous figures’. Figure 4.17 shows some common examples. A frequency ratio is obtained by counting the number of loops touching any two Figure 4.17  Lissajous figures adjacent edges of an imaginary frame enclosing the figure. For example, in the third figure from the top, there are three loops touching one horizontal edge—only one loop touches the adjacent vertical edge. The ratio of one frequency to the other is 3:1. So, if a 50 Hz input voltage causes only one loop to touch the imaginary vertical frame, then the frequency of the other input is 150 Hz. The equation is: 4:3

frequency on horiz. plates loops touching horiz. edge ______________________________     ​​      ​ = ​ ___________________________________         ​​ frequency on vert. plates loops touching vert. edge

4.2.16  Oscilloscope applications Cathode-ray oscilloscopes have the following uses:

Electrical

1.  observing waveforms in electrical circuits 2.  measuring quantities such as voltage, current, power and phase angles 3.  comparing known and unknown frequencies 4.  measuring short time intervals 5.  examining the characteristics of magnetic materials 6.  examining the harmonic content of a.c. wave shapes.

Electronic

1.  2.  3.  4. 

aligning tuned circuits for audio and radio frequencies television modulating measurement in transmitters testing radio components.

Digital storage oscilloscopes with liquid crystal displays have made oscilloscopes far more portable and compact. Consequently, Figure 4.18  Fluke 435 Series II Power Quality they are suitable for field work (the heavy 230 V-operated CROs and Energy Analyser © Fluke Australia, www.fluke.com.au were restricted to the workshop). Handheld oscilloscopes are becoming much more widely available. They have a multitude of functions, much like a multimeter but with a far higher level of sophistication. A handheld power analyser is becoming a vital part of an electrotechnology worker’s testing equipment. 216

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4.3 Sinusoidal voltage generated by a single-turn coil rotated in uniform magnetic fields 4.3.1 Alternators A machine producing a voltage with an alternating waveform at its terminals is called an ‘alternator’, or, occasionally, an ‘alternating-current (a.c.) generator’. Both terms are correct, although ‘generator’ is usually reserved for d.c. machines. The modern generator or alternator consists of two sets of electromagnetic coils, one set of which rotates to produce an EMF at the terminals. These coils may be connected in either series or parallel to produce a desired voltage.

4.3.2  Loop rotating in a magnetic field Figure 4.19 shows a single-loop generator in which the loop may be rotated in the field between two fixed, permanent magnets. As this happens, an EMF will be generated within the loop. Two metallic rings are connected to the loop ends to connect the loop to an external circuit, and carbon brushes running over these ‘slip-rings’ complete the connection.

4.3.3  Direction of an induced EMF The direction of a generated voltage depends on the direction of relative movement between a magnetic flux and the conductors that link with it. Fleming’s right-hand rule (see Figure 4.19) finds the direction of an induced EMF if the direction of flux and relative direction of motion are known.

4.3.4  Magnitude of a generated EMF The value of an induced EMF depends on three factors—the magnetic field density, the number of conductors in series (i.e. the total length of conductor in the magnetic field) and the relative rate of motion between the first two factors. It is easy to determine the rate of rotation of machines and then factor in the comparative direction of the conductors in relation to the magnetic field. By combining these two factors, the relative rate of motion can be found from the expression: v sin (θ). By combining all these factors, an equation can be developed. The generated voltage can be found from: ​e = Blv sin θ​ where: e = value of induced voltage B = flux density in webers l = length of conductor in metres v = velocity in metres per second. This agrees with Fleming’s right-hand rule, where the movement of the conductor is at right angles to the magnetic flux. It also takes into account the fact that a conductor might not always be travelling at right angles to the magnetic flux—it could be travelling at some other angle.

4.3.5  Effect on EMF as the loop rotates The position of the loop shown in Figure 4.19(a) means that the initial movement of its sides is parallel to the magnetic flux. No cutting across the flux will occur, and no EMF will be generated. 217

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When the loop begins rotating, it starts to cut across the flux at an acute angle. This generates a small EMF in each loop side. Further rotation causes a corresponding increase in the angle between the flux and the path of the conductors. This increases the value of generated EMF. In the position shown in Figure 4.19(b), the loop sides cut across the flux at 90º, resulting in the generation of maximum EMF at this position. The direction of the generated EMF is shown by the arrows. It can be confirmed by Fleming’s right-hand rule (see Figure 4.19). Further rotation of the loop causes a gradual decrease in EMF. The angle of cutting becomes increasingly acute until, at the position shown in Figure 4.19(c), the EMF will fall to zero again. As the loop rotates from position (c) towards position (d), the relative direction of motion of the coil sides reverses. Since the field direction remains fixed, the direction of the generated EMF must reverse. This is indicated by the arrows in Figure 4.19(d). In Figure 4.19(d), the EMF will again reach a maximum, but in a direction opposite to that of the previous maximum. Further rotation will cause a gradual decrease in EMF until it again becomes zero, when the loop completes one revolution and returns to its original position. This is shown in Figure 4.19(e).

0

0 +

−

+

Load

N

S

Current

Load

N

Cross-section view from front 0 (a) Loop vertical; begin to rotate clockwise; 0° rotation 0 0 − +

S

0 (b) Conductors cutting flux; 90° rotation 0 −

0

+

Load

N

S

Current

Load

N

0 (c) Loop vertical; not cutting flux; 180° rotation

S

0 (d) Conductors cutting flux; 270° rotation

0 0

−

Current

−

0

+

Current

0

First finger flux

Thumb motion

Load

N

S

Current

Middle finger current

0 (e) Return to starting point; 360° = 0° rotation

Figure 4.19  EMF in a loop and Fleming’s right-hand rule

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4.3.6  Alternative alternator construction The basic construction of an alternator is a loop rotating in a magnetic field, as in Figure 4.20(a). The alternating voltage produced when the ends of the loop are connected to sliprings causes current to flow in alternate directions. This result can also be achieved by keeping the loop stationary and rotating the magnetic field to produce the relative motion. It is often easier to have the generating coils on the outside of the magnetic field, as shown in Figure 4.20(b). This is especially true when there are three phases instead of one. There are several advantages to this type of construction: ∙ Slip-rings are not necessary for connection, so solid connections can be made. ∙ With small alternators, the rotating magnetic field can be obtained from a permanent magnet. ∙ With large alternators, the field can be driven by a smaller excitation generator (in a similar fashion to a separately excited d.c. motor). This avoids the need for brushes but still allows adjustment of the excitation.

−

0

+

Load

(a) Fixed magnetic field—rotating coil 0

−

+

Load



In machines, the solid connections allow higher voltages and currents to be handled and connected safely to the external circuit. Sliding connections via slip-rings, brush gear and brushes are removed using permanent magnets (or separate excitation). This reduces friction, wear and other maintenance and safety problems. Voltage may be increased by adding turns to coils or simply adding more coils (see Figure 4.21).

(b) Fixed coil—rotating magnetic field

Figure 4.20  Rotating coil versus rotating field

0

−

Multiple-turn coil +

Load

Figure 4.21  Multi-turn coil

4.4  Sinusoidal waveform 4.4.1  Instantaneous values Figure 4.23 shows the sine wave of EMF generated as an alternator coil is rotated through 360°E (electrical degrees). In this example, the maximum voltage generated occurs when θ = 90°. This is usually indicated by the symbol Vmax or Vm. At this instant, the coil cuts the flux at 90°. The instantaneous voltage v can be found from v = Vmax × sin θ. Since Vmax occurs when θ = 90°, Vmax corresponds to a sine ratio of 1. The sine curve, however, varies between 0 and 1, as θ varies between 0° and 90°. The instantaneous voltage v must also vary between 0 and a maximum value: ​v = ​V​  max​​  sin θ​ where:

v = instantaneous voltage

Vmax = maximum voltage

θ = angle of rotation 219

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In general, if an alternating voltage is applied to a load, the current that flows is also alternating. So the formula above is still applicable—that is: ​i = ​I​  max​​  sin   θ​ where: i = instantaneous current Imax = maximum current ​θ​ = angle of rotation Sine values can be derived from a scientific calculator.

EXAMPLE 4.3 The maximum EMF generated in an alternator coil is 200 V. Calculate the instantaneous voltage v for the following angles of rotation: (a) (b) (c) (d) (e)

θ = 30° θ = 75° θ = 150° θ = 240° θ = 310° ​va​  ​​ = ​Vmax ​  ​​  Sin θ

​​(​​1)​ ​​​

​ = 200 × Sin (30)

​​(​​2)​ ​​​

​ = 200 × 0.5 ​ = 100 V​ 

​​(​​3)​ ​​​ (​​ ​​4)​ ​​​

​vb​  ​​ = ​Vmax ​  ​​  Sin θ

(​​ ​​5)​ ​​​

​ = 200 × Sin (75)

(​​ ​​6)​ ​​​

​ = 200 × 0.9659 ​ = 193 V 

(​​ ​​7)​ ​​​

​  ​​  Sin θ ​vc​  ​​ = ​Vmax

​​(​​8​)​​​ ​​(​​9)​ ​​​

(​​ ​​10​)​​​ ​ = 200 × Sin (150) ​​         ​     ​  ​  ​  ​  ​  ​  ​  ​  ​  ​​​ (​​ ​​11​)​​​ ​ = 200 × 0.5 (​​ ​​12​)​​​ ​ = 100 V

​vd​  ​​ = ​Vmax ​  ​​  Sin θ

​​(​​13​)​​​

​ = 200 × Sin (240)

​​(​​14​)​​​

​ = 200 × − 0.87 ​ = − 173 V

​​(​​15​)​​​ ​​(​​16​)​​​

​ve​  ​​ = ​Vmax ​  ​​  Sin θ

​​(​​17​)​​​

​ = 200 × Sin (310)

​​(​​18​)​​​

​ = 200 × − 0.76 ​ = − 153 V

(​​ ​​20​)​​​

​​(​​19​)​​​

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4.4.2 Voltage and current cycles

90°

S

The term ‘cycle’ means a recurrent order of events. For example, the seasons of the year follow a definite cycle: summer, autumn, winter, spring. The output of an alternator follows a definite cycle. 180° 360° Figure 4.22(a) shows the output EMF of a two-pole 0° One complete revolution of the alternator — 360°M (Mechanical) alternator for one of these cycles or one complete revolution. During this time, the EMF starts from 0°, rising to a maximum positive voltage as the conductors N S pass the magnetic north pole. It then reduces to zero. 2-Pole Alternator 270° In the second half of the cycle, the voltage increases (a) One complete sine wave cycle — 360°E (Electrical) to maximum negative voltage, finally returning to zero 90° 450° voltage back at 0°. During the period of one revolution, the value of EMF has made one complete electrical cycle. Rotation of the coil through further revolutions causes the same cycle for each. Consider the effect of four poles being used 180° 360° 540° 720° in the alternator, as in Figure 4.22(b). During one 0° One complete revolution of the alternator — 360°M (Mechanical) revolution, a particular side of the coil will rotate from 0° through a north pole to a south pole, then to the next north pole and on to the next south pole. N Finally, it returns to the original position. During this time, the output EMF rises to a maximum in each 630° 270° 4-Pole Alternator direction. It does the same again before returning (b) Two complete sine wave cycles — 720°E (Electrical) to 0° of the mechanical rotation. The rotor therefore Figure 4.22  Electrical versus mechanical degrees completes two electrical cycles in one mechanical cycle, as shown in the waveform of Figure 4.22(b). So, the number of completed cycles of EMF in a given time depends on the number of poles that a rotor passes in that time, and not only on the number of mechanical revolutions that it rotates through in the same time. In the majority of cases, electrical motors and generators require two poles per cycle: one north pole and one south pole. These relationships are shown in the following example.

N

S

nP  ​f = ____ ​    ​​   120

EXAMPLE 4.4 Two alternators are available to generate the required 50 Hz. Alternator A has two poles and alternator B has four poles. At what speed (in RPM) must each be driven to generate this frequency? The frequency of the generated voltage depends on the speed of the machine and the number of pairs of poles. (North and south are a pole pair.) Also, the frequency is in cycles per second, but the speed of the mechanical drive is in revolutions per minute (RPM). So the RPM must be divided by 60 to find the revolutions per second (n). Number of Poles _____ RPM f = ______________    ​   ​   × ​   ​    (1) 2 60      ​​  ​  ​  ​  ​  ​​​ nP ____ ∴ f = ​    ​  (2) 120 (continued) 221

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Electrical Principles

Now to calculate the speed in RPM, the formula must be transposed: 120f ∴ n = ____ ​   ​     P

(3)

120 × 50 ​nA​  ​​ = ________ ​   ​     (4) 2 ​​          ​ ​    ​  ​  ​  =​  3000 RPM (5)​​​ 120 × 50 &​  n​ B​​ = ________ ​   ​     4 ​ = 1500 RPM

(6) (7)

4.4.3  Electrical frequency The number of cycles in a given time is a function of mechanical rotation and the number of poles in the machine. Thus it is necessary to define one electrical cycle as 360°E. Mechanical angles should be referred to as ‘°M’ whenever there could be some confusion. In Australia, the standard a.c. current found in power sockets is 50 Hz. That is, 50 hertz or 50 ‘cycles per second’. There are 50 sine waves in one second, so the ‘frequency’ at which the sine waves are generated is 50 times a second. Another way to look at it is to define how long a waveform is in time. This is known as the ‘period’ of the waveform. From 0°E through to 360°E is one waveform or period. If there are 50 cycles per second, each period must be 1/50 seconds long (or 20 ms). 1  ​f = __ ​    ​​  P or

1  ​P = __ ​   ​​   f ​​

4.4.4  Construction of sinusoidal curves A sinusoidal waveform can be drawn, but the accuracy of the resulting curve naturally depends on the accuracy of construction. The curve is neither simply two semicircles, nor does it have straight lines in any section.

Graphical method Step 1. Draw a circle of some convenient diameter. Its radius represents the maximum instantaneous voltage to some selected scale, e.g. 100 V = 100 mm. Step 2. Draw the x-axis for the graph of the sine wave directly through the centre of the circle, extending it far enough to the right to accommodate the degree axis to some appropriate scale, e.g. 360° = 180 mm. Step 3. Divide up the circle. This is done by swinging an arc of the circle radii each side of the line and then bisecting one or both semicircles to plot a line perpendicular to the x-axis. Swinging two more arcs top and bottom divides the circle into 12 parts. Label each mark accordingly, with 0° starting at the right side of the circle (see Figure 4.3). The horizontal axis is divided into the same number of equal spaces as the angle intervals in the circle. The construction points for drawing the actual curve are located as follows. Step 1. The points on the circumference are projected to the right until they meet the corresponding points on the horizontal axis, projected either upwards or downwards as required. 222

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Step 2. Once the points are located, a curve joining them is drawn in. With only 12 points and some care taken in joining the dots, a rough sine wave will appear.

1.0

Calculated instantaneous values method

0°

Step 1. Axes for a graph are constructed as in the previous method, preferably on graph paper. The vertical (y-) axis is scaled for both positive and negative values of voltage (or current). The horizontal (x-) axis is marked out in degrees of rotation.

90° .8

180°

x

270°

360°

−1.0

Figure 4.23  Computer-drawn sine wave

Step 2. The instantaneous values are then calculated for angles using the formula v = Vmax sin θ. Calculate every 10 degrees from 10° to 80°, remembering that the same values are used for 100° to 170°. Converting these values into negative numbers produces the remaining half of the sine wave. Step 3. The values are then plotted against the corresponding angle, as shown in Figure 4.23. The curve is identical to that produced by the previous method, except for having more plot points. Some computer programs will plot the sine wave directly, given a Vmax value and the formula. These programs include GNUPlot, Grapher.app, Graph.exe and DPlot.

4.4.5  Sinusoidal wave values Here is a summary of some of the terms used so far to describe alternating waveforms: ∙ Periodic function is an alternating wave that repeats itself in a cycle. ∙ Frequency (of a wave) is the number of times a wave repeats itself in one second. (This is expressed in cycles per second or hertz.) ∙ Period is the time taken for one cycle to complete itself. It is equal to the reciprocal of the frequency (1/f seconds). ∙ An instantaneous value of either a voltage or current waveform is a value expressed at only one instant of time. Other values are often used to describe a sinusoidal waveform or to do calculations on sinusoidal values.

Average value As an alternating sinusoidal waveform is continually varying in value, a meaningful standard must apply when describing its value (whether as a voltage or a current). Mathematically, the average value of a sinusoidal function is 2/π or 0.637. Therefore, the average voltage or current can be found from: ​Vav ​  ​​  =  0.637 ​V​ max​​ ​​    ​​​ ​   I​ av​​  =  0.637 ​I​ max​​ These expressions are accurate only for sinusoidal waveforms. The average value applies only for individual half-cycles. As the direction of flow alternates, the average value of the second half-cycle in this example is –0.637. Therefore, the average flow for a complete cycle is zero. Average values are more applicable in circuits involving the conversion of a.c. to d.c. than in the usual a.c. circuits. 223

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Average values are not suitable as a general basis for comparing alternating waveforms with direct current in terms of energy use or power. This makes it essential that there is another value for comparing the real effects of alternating waves.

Root–mean–square values The value of a sinusoidal waveform that produces the same heating effect as d.c. can be obtained mathematically by a process called the ‘root–mean–square’ (RMS) value of that wave. The RMS can be defined as the square root of the arithmetic mean of the squares of a set of values. Calculating this requires an understanding of calculus, but fortunately there is another way of explaining why the calculus can be trusted. If maximum values of voltage and current are used, the power can be shown by experiment or maths to be exactly one half of the power produced by the same d.c. values. That is: ​  ​​  Power (peak) ________ ​Vmax ​  ​​ ​Imax ___________ ​Power (actual) = ​     ​     ​=  ​​  2  2 As the current is proportional to the applied voltage, the RMS factor must be applied to both the voltage and current maximum values. That is: ​V​  ​​  I​ ​  ​​  1 1  1 ​Power = ​ _____ ​  max ​  ​  × ​ ____ ​  max ​  ​ ​ i.e. ​ __  ​  = ​ ___   ​  × ​ ___   ​  ​​ (  √2 ) (  √2 ) ( 2  √2  √2) This results in a value of: 0.707Vmax × 0.707Imax or what we usually write as P = VRMSIRMS. The RMS value is often described as the effective voltage that will create an effective current flow to do the same work as a d.c. voltage: ​  ​​ = 0.707 ​V​ max​​ ​VRMS ​​    ​  ​   ​​​ ​IRMS ​  ​​ = 0.707 ​I​ max​​ These expressions are accurate only for sinusoidal waveforms. Unless specifically stated otherwise, any given a.c. value should always be considered as the RMS value. The normal domestic a.c. supply is referred to as 230 V, but the maximum value is 325 V. Throughout this book, when working with a.c., unless otherwise stated it is the RMS value that is intended. The maximum value of a 230 V RMS supply can be found from the expression: ​VRMS ​  ​​ = 0.707 ​V​ max​​ ​V​  ​​  ​Vmax ​  ​​ = _____ ​  RMS    ​  0.707 ​  ​  ​  ​​​ ​​      230  ​ = ​ _____  ​   0.707 ​ = 325.3 V

4.4.6  Peak-to-peak values The value of a wave from its positive peak to its negative peak can be important. With most alternating waveforms, this is equal to twice the maximum value in either direction. For example, with a 230 V a.c. supply, the maximum value of voltage is found by dividing 230 by 0.707. The same value can be obtained by multiplying 230 by 1.414 (the reciprocal of 0.707 is 1.414, which equals √2). Either method gives 325.3 V as the peak value. The peak-to-peak value is twice this, or 650.6 V. This is useful when measuring the values of alternating waveforms on a cathode-ray oscilloscope as there is no zero-voltage line on the trace. 224

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4.5  Phasor diagrams 4.5.1  The purpose of phasor diagrams ‘Phasor’ describes the rotating vectors which appear in electrical calculations. A vector is a line that, by its length and direction, represents the magnitude and angle of application of a force or velocity (or other vector quantity). Voltage and current phasors represent the RMS value of the voltage or current by their length and the angle of the phase difference between the phasor and the reference plane.

4.5.2  ‘In-phase’, ‘out-of-phase’, ‘phase angle’, ‘lead’ and ‘lag’

−90° Voltage Phasor leads Current reference Mag.Flux

ILead

Angle of rotation (θ)

180° Origin

Phasor lags reference

Phasors (i.e. time) rotate counterclockwise (CCW)

0° Vref

ILag

90°

Figure 4.24  Phasor diagram

Note: Both sine waves start at the same time, Alternating currents and voltages, and their phase and are therefore in phase. Vref relation, can be represented by sine waves, as in The phasors are scaled to the RMS value of each sine wave and both phasors are drawn at 0° or Figures  4.25(a), 4.26(a) and 4.27(a). However, this on the horizontal axis as there is no angle method is inconvenient; it is simpler to use phasors difference to the reference. IPhase in a phasor diagram, as in Figures  4.25(b), 4.26(b) and 4.27(b). Because the RMS values of a.c. are IPhase Vref important, phasor diagrams are nearly always scaled to represent them. Unless otherwise stated, that is the case in this book. Looking at Figure 4.24, the reference phasor is always drawn horizontally and to the right. All phase angles must be measured from it. When choosing the (b) Phasors (V & I) in phase (a) Sinewaves in phase reference phasor, it is usual to select a quantity that has Figure 4.25  In-phase phasors the same value in all parts of the circuit. For a series circuit, the current is used as the reference phasor. This is because the current is common to all parts of the circuit. For a parallel circuit, the voltage is used as the reference phasor. This is because the voltage is common to all parts of the circuit. It will be explained later that transformers have a magnetic flux which is common to both their input and output. Therefore the flux becomes the reference phasor. When the current and voltage curves pass through the zero position at the same time and increase to their maximum values in the same direction, the waveforms are in phase with each other. This is shown in Figure 4.25(a). The phasor diagram for the in-phase condition is shown in Figure 4.25(b). This book distinguishes between voltage and current phasors by showing the voltage phasor in red and the current phasor in blue. In some circuits, the current and voltage curves do not reach their zero and maximum values simultaneously. In such cases, they are said to be ‘out of phase’, and the angle of lead or lag (see Figures 4.26(a) and (b) and 4.27(a) and (b)) is called the ‘phase angle’ (symbol φ). This symbol is conventionally used to indicate an angle between two phasors and is not interchangeable with the ‘theta’ (θ) symbol that indicates an angle of rotation. A second convention is that all phasors are assumed to rotate in an anticlockwise direction, starting at the positive x-axis.

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Electrical Principles Note: The current sine wave starts at 60° after the voltage sine wave, and is therefore lagging. The current phasor is drawn at 60° after (lagging) the voltage reference.

Vref

IPhase 60°

Vref

60° IPhase

Figure 4.26(a) shows the current lagging the voltage by 60° and Figure 4.26(b) shows the same condition using phasors. Figure 4.27(a) shows the current leading the voltage by 60° and Figure 4.27(b) shows the same condition using phasors.

4.5.3 Phasor addition by graphical method

If two a.c. voltages are connected in series, they might not be in phase with each other. Alternating values (a) Sine wave lagging reference (b) Phasor lagging reference of current or voltage cannot be added arithmetically Figure 4.26  Lagging phasor unless they are in phase. One way of adding phasors is to draw them to scale and angle, using RMS values, and then add them together using the parallelogram method, as shown in Example 4.5 and Figure 4.29.

EXAMPLE 4.5 Two voltages A and B are connected in series. Voltage A is 150 V and leads the current by 45°; voltage B is 100 V and lags the current by 30°. Find the total EMF and phase angle. Since the two voltages are in series, the current is used as the reference phasor. To construct the phasor diagram, follow these steps (Figure 4.29): Step 1. Draw the current phasor horizontally to the right as the reference phasor. Step 2. Draw the phasors for VA and VB to scale, measuring the phase angles from the reference phasor using a protractor. Step 3. Construct the phasor parallelogram. Step 4. Draw the resultant and determine the total EMF by scale and measure the phase angle. Total voltage    = 201 V Phase angle φ = 17° leading

Vref

Note: The current sine wave starts at 60° before the voltage, and is therefore leading. That’s the same as lagging by 300° when both sine waves are continuous! IPhase

IPhase −60° = 300°

(a) Sine wave leading reference

Figure 4.27  Leading phasor

−60° = 300°

Vref The current phasor is drawn at 60° before (leading) the voltage reference.

(b) Phasor leading reference

A variation on the parallelogram method is to construct the diagram using a compass and a protractor. Step 1. Draw the current phasor horizontally to the right as the reference phasor. Step 2. Draw the phasors for VA and VB to scale, measuring the phase angles from the reference phasor with a protractor. Step 3. Open the compass to the scaled measurement for VA and then place the compass at the END of VB. Draw an arc between the two phasors. (Figures 4.30 and 4.31.) Step 4. Open the compass to the scaled measurement for VB and then place the compass at the END of VA. Draw  a second arc between the two phasors. (Figures 4.32 and 4.33.)

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VA Peak

VA RMS VA Peak

VA

VB

VB RMS I Peak

I

I RMS 45° Lead

30° lag

30° 60° 90° 120° 150° 180° 270° 248° 270° 300° 330° 360° 30° 60° 90°

I RMS I Peak

VB RMS

VB Peak VA RMS

VA Peak

Figure 4.28  Graphical representation of the current and two voltage waveforms

Step 5. Draw a line representing the resultant phasor VTOTAL from the point where all the phasors originate to the intersection of the two arcs. (Figure 4.34.)

VLead Step 3 Step 2

Step 6. Measure the length of VTOTAL and apply the scale to obtain the magnitude of the voltage. In this case it is 201 V. (Figures 4.35 and 4.36.) Step 7. Measure the angle between the reference phasor (I) and the resultant phasor (VTOTAL) to obtain the phase relationship between the current (I) and the resultant supply voltage (VTOTAL). In this case φ = 17° leading.

5°

–4

V@

0

15

10

Step 1

0V

Step 2

Step 4 ltant Resu

Step 3 Reference

Iref

@3

0° VLag

This is a variation of the ‘tip to tail’ method for diagrammatically finding the resultant of two phasors. Figure 4.29  Parallelogram method Tip to tail is a method of drawing phasor addition but first plotting the first phasor horizontally and then starting to draw the next phasor’s tail where the tip (arrow-head end) of the first phasor finishes. The second phasor must not only have a scaled magnitude in common with the first but also a relative direction. Another quick way of using the tip to tail method for simple phasors with one phasor in phase (at an angle of 0°) and the second angle at 90° (leading or lagging) is to draw the phasor as a right angle triangle and use trigonometry and/or Pythagoras’ theorem to determine the resultant phasor and angle.

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VA

VTOTAL

45°

17°

I

−30°

VB

Figure 4.30  Step 3(a)

VA

VTOTAL

45°

17°

I

−30°

VB

Figure 4.31  Step 3(b)

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VA

VTOTAL

45°

17°

I

−30°

VB

Figure 4.32  Step 4(a)

VA

VTOTAL

45°

17°

I

−30°

VB

Figure 4.33  Step 4(b)

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VA

VTOTAL

45°

17°

I

−30°

VB

Figure 4.34  Step 5

VA

70

80

90

100

110

12

0

13

0

VTOTAL

14

0

40

50

60

0

30

15

20

160

10

17° deg°

−30°

I

180

0

170

45°

VB

Figure 4.35  Step 6(a)

VA

VTOTAL

45°

17°

I

−30°

VB

Figure 4.36  Step 6(b)

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EXAMPLE 4.6 Two voltages A and B are connected in series. Voltage A is 200 V and is phase with the current; voltage B is 113.58 V and leads the current by 90°. Find the total EMF and phase angle. Since the two voltages are in series, the current is used as the reference phasor. VTOTAL VB (VB) If the phasor for VB is instead drawn with the ‘tail’ on the ‘tip’ of VA, or moved to the right-hand side of the drawing, a right angle triangle is produced. As the resultant VTOTAL is the hypotenuse of the triangle, the magnitude of VTOTAL can be determined using either trigonometry or 29.59° Pythagoras’ theorem: I VA Trigonometry method: Figure 4.37  Determining the VTOTAL

OPP  ​  Tan θ = ____ ​  ADJ V ​ = ___ ​  B ​   VA    ​​  ​    ​  ​  ______ ​  ​  ​   ​​ ​  ​ 113.58 ​ = ​   ​     200 ​ = 0.5679 Therefore θ = ​Tan​​  −1​  (0.5679) ​ = 29.59°

By using Cos (or Sin) of 29.59° and the corresponding side, VTOTAL can be determined. ADJ Cos θ = _____ ​     ​ HYP ​​ ​  ​  ​  ​​ VA _______ ​ = ​    ​   ​VTOTAL ​  ​​ Therefore V ​VTOTAL ​  ​​ = __________ ​  A   ​  Cos θ ​    ​  200 ​  ​ ​ = ____ ​   ​  (29.59° ) Cos ​​

​​

​ = 230 V leading at 29.59° While this method takes quite a few steps, it does give an accurate answer for both the magnitude of VTOTAL and the angle. A quicker method to find just the magnitude is by using Pythagoras’ theorem: ​​HYP​​  2​ = ​ADJ​​  2​  + ​OPP​​  2​​ Or ​​​V​  TOTAL2​​​​  ​ = ​VA2​​  ​  + ​VB2​​  ​​ (continued) 231

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Therefore

__________ ​VTOTAL ​  ​​ = √ ​   (​VA​​  2​  + ​VB​​  2​  ) ​  ______________ 2 2 ​​    =​  √ ​   (​   200​​  ​​ ​  + ​113.58​​  ​  ) ​​ ​​       ​​ _________ ​= √ ​  52,900.42 ​     ​ = 230 V

4.6  Single-element a.c. circuits 4.6.1 Introduction Due to the effects of inductors and capacitors on alternating current, a.c. circuits require different treatment from d.c. circuits. Ohm’s Law still works for instantaneous values but, when time and frequency come into effect, the maths of electric circuits requires a knowledge and understanding of the concepts of phase angle and lead and lag. Power, which every electrician needs to understand thoroughly, is dependent on the phase angle. Electricians should also understand the disadvantages of having a poor phase angle or power factor. They should be versed in power factor correction and why it is necessary.

4.6.2  a.c. circuits Alternating current using sine waves is the basis of worldwide electricity distribution. Circuits using alternating current are very similar to d.c. circuits, but there are several important differences which must be understood before the electrical worker becomes proficient with electricity.

4.6.3  Resistance in a.c. circuits

V Ohm’s Law works out the current flowing through a pure resistance at any point in time. It is: I = ​​ __ ​​  for any R part of the cycle. When the resistance remains the same, the current is directly proportional to the applied voltage. Therefore, the current waveform for a purely resistive circuit is in phase with the voltage curve and V ​​  RMS  ​​   (see Figure 4.51). IRMS = _____ R

Pure or non-inductive resistance When doing calculations, we can think of resistors on power line frequencies as consisting of ‘pure’ or non-inductive resistance. Examples include incandescent lamps, radiators and electric kettle elements. Real resistors are often made from a coil of resistance wire. Theoretically, this wire will exhibit some inductance, but its value is usually so low that it can be ignored. The same goes for capacitance. At higher frequencies like the ones in modern switch-mode power supplies and motor controllers, inductance can become a problem. It must either be sorted out in the design stage or dealt with by using special non-inductive resistors. The inductive effect can be avoided fairly easily. Half the resistor is wound clockwise on a non-magnetic former, and then the other half is wound on anticlockwise (see Figure 4.38). The magnetic fields produced around the conductors cancel each other out and so prevent self-induced voltages. Capacitive effects cannot be neutralised so directly—they have to be minimised. The main method of doing this on long-distance transmission lines is to keep them as far apart from each other as is economically possible. 232

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EXAMPLE 4.7 A pure resistance of 12 ohms is connected across an a.c. power supply that generates a pure sine wave of 100 volts peak voltage. What current will flow and what power will be taken? ​VRMS ​  ​​ = 0.707  ​Vmax ​  ​​ ​ = 0.707 × 100 ​ = 70.7 V​ ​  V​  ​​ ​IRMS ​  ​​ = ____ ​  RMS  ​     R

​​(​​1)​ ​​​ ​​(​​2)​ ​​​ ( ​ ​ ​​3)​ ​​​ (​​ ​​4)​ ​​​

70.7 ​ = ____ ​   ​    12

​​(​​5​)​​​

​ = 5.89 A​

​​(​​6​)​​​

P = ​VRMS ​  ​​  × ​IRMS ​  ​​

​​(​​7​)​​​

(​​ ​​8)​ ​​​ = ​​     ​         ​ ​    ​  ​  70.7 × 5.89 ​  ​  ​  ​  ​  ​  ​  ​  ​  ​  ​  ​  ​​ ( ​ = 416.4 W ​​ ​​9)​ ​​​

Or . . .​​

Or . . .

​V​  2 ​ ​  P = ____ ​  RMS  ​     R

(10 )

​70.7​​  2​ ​ = _____ ​   ​     12

(11 )

​ = 416.5 W

(12 )

P = I​​  2RMS  ​  ​ R

(​​ ​​13​)​​​

​ = ​5.89​​  2​  × 12 ​ = 416.6 W

​​(​​14​)​​​ (​​ ​​15​)​​​

Resistors in series and parallel As the current in resistors is always in phase with the voltage, Ohm’s Law still applies. So do Kirchhoff’s laws, KVL and KCL. This means that, in a purely resistive circuit, the rules for d.c. circuits continue to work for a.c. This is the case whether it is series, parallel or compound.

4.6.4 Inductors Inductors play a major role in a.c. electrical circuits. This is mainly because Figure 4.38  Non-inductive resistor they can create useful magnetic effects. These include the role they play in electrical machines that can either convert motion to electrical energy or electrical energy to motion. They also include creating mutual induction in transformers and their relay and solenoid applications to either switch circuits or open and close mechanical systems such as valves and air dampeners. However, inductors have a related property which opposes change in current and current flow. This makes inductive circuits useful in limiting current in devices like fluorescent lighting. When they are used for that purpose, they are sometimes referred to as a ‘choke’. They can also be coupled with capacitors to ‘tune’ radio circuits (to frequencies such as AM or FM). This coupling is also used in mobile telecommunications and to oppose undesirable frequencies in power quality management (in line reactors or filters). 233

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4.6.5  Inductance in a.c. circuits A change in current flow in an inductive circuit Vref results in an induced EMF. This, according to Lenz’s V ref IXL Law, will oppose the change of current flow. In d.c. IXL circuits, this inductive effect causes the current to Vref +X+ −X− rise slowly, eventually reaching approximately its +X− +X− 90° maximum value according to the circuit resistance. Power In an inductive a.c. circuit, the current is continually changing in value and direction. This IXL generates an induced EMF that must continually oppose the change of current flow. Figure 4.39 shows the relationship between the current, induced EMF and supply voltage for a purely inductive circuit. Figure 4.39  Inductive a.c. circuit Using the voltage phasor as the reference, the current phasor lags by 90°E. Consequently, it is drawn at right angles to the voltage reference. Remember that at maximum voltage the current will be zero but rising. At zero voltage the current is at maximum. As incongruous as this may sound, the effect is a very important one. On a.c., the change in current flow produces an induced EMF that opposes it. The effect of this current opposition is called ‘inductive reactance’ (symbol XL), and is measured in ohms. Ohm’s Law effectively states that the current is equal to the voltage divided by the opposition to current flow. Inductive reactance is a type of opposition to current flow, so for pure inductance I = V/XL. The value of inductive reactance in a circuit depends on the inductance and the rate of change of current flow, and that depends on the supply frequency. Inductive reactance can be calculated from the formula: ​​XL​  ​​ = 2πfL​ where: XL = inductive reactance f = frequency in hertz L = inductance in henrys Once the inductive reactance is known, Ohm’s Law works just as if reactance and resistance were the same (they are not, as will be explained in due course).

Inductors in series If two inductors are placed in series, each will produce an induced EMF. This means the total induced EMF will be increased, and that in turn means the opposition to current flow is increased. By placing inductors in series, the total inductive reactance increases in the same way that placing resistors in series increases the total resistance: ​​XLtotal ​  ​​ = ​XL1 ​  ​​  + ​X​ L2​​  + ​X​ L3​​ … + ​XLn ​  ​​​ As the total value of induced EMF is increased, the total inductance is increased. Consequently, the total inductance is found in the same way: ​​Ltotal ​  ​​ = ​L1​  ​​  + ​L​ 2​​  + ​L​ 3​​ … + ​Ln​  ​​​ 234

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EXAMPLE 4.8 A coil has an inductance of 0.05 H. What would be the inductive reactance at a frequency of: (a) 25 Hz   (b)  50 Hz   (c)  at what frequency would it have a reactance of 10 Ω? ​XL​  ​​ = 2πfL

       (1)

​ = 2 × 3.142 × 25 × 0.05

(2)

​ = 7.85 Ω

(3)

​XL​  ​​ = 2πfL ​ = 2 × 3.142 × 50 × 0.05

(4) (5)

​​  =​  ​  15.7 Ω (6)​​​ ​​            ​       ​ ​  ​  ​  ​  ​  ​XL​  ​​ = 2πfL (7) X ​ ​  ​​ ∴ f = ____ ​  L  ​  (8) 2πL 10 ​ = ______________ ​       ​ 2 × 3.142 × 0.05 ​ = 31.8 Hz

(9) (10)

EXAMPLE 4.9 A 500 V 50 Hz supply is applied to a coil with an inductance of 0.12 H. Determine the current. ​XL​  ​​ = 2πfL ​ = 2 × 3.142 × 50 × 0.12 ​ = 37.7 Ω

   (1) (2) (3)

V ​      ​  ​​ I     ​  =​  ​  ___ ​    ​ ​ ​  ​  ​  (4)​​​ ​XL​  ​​ 500 ​ = ____ ​     ​  (5) 37.7 ​ = 13.26 A (6)

EXAMPLE 4.10 A 230 V 50 Hz supply is applied to a choke coil of negligible resistance and the current through the coil is 2.5 A. Determine the inductance of the coil. V XL = __ ​   ​       (1) I 230 ​ = ____ ​   ​  (2) 2.5 ​ = 92 Ω (3) ​​      ​      ​  ​  ​  ​ ​  ​  ​  ​​​ ​XL​  ​​ ___ L = ​    ​  (4) 2πf 92 ​ = ____________ ​       ​ (5) 2 × 3.142 × 50 ​ = 293 mH

(6)

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EXAMPLE 4.11 Two inductors, one with an inductive reactance of 11 Ω and the second with an inductive reactance of 12 Ω, are connected in series across a 230 V 50 Hz supply. (a) What is the total inductive reactance? (b) What is the total current? ​XL total ​  ​​ = ​XL1 ​  ​​  + ​XL2 ​  ​​ ​ = 11 + 12 ​ = 23 Ω ​​

(1) (2) (3)

V ​     I    =​  ___ ​    ​ ​  ​  ​  ​  ​  (4)​​​ ​XL​  ​​ 230 ​ = ____ ​   ​  (5) 23 ​ = 10 A (6)

4.7   Capacitors 4.7.1  Applications of capacitive a.c. circuits The most common use for capacitive a.c. circuits is for power factor correction, where a capacitor is placed in parallel with the load and/or supply. This is covered in greater detail later in this chapter. Capacitive a.c. circuits are also used in single-phase motors as the source of phase shift for starting, running and reversing them. This is explained in Chapter 6. As well as ‘tuning’ resonant circuits, capacitive a.c. circuits are used in TV and mobile communication technology and as a method of switching frequency-sensitive relays for off-peak and other loads. These typically require a ‘matched’ inductor. This is an inductor with an inductive reactance equal to the capacitive reactance of the capacitive circuit at the desired frequency. Resonance and harmonics are discussed later in this chapter. The transformerless power supply has enabled a.c. mains-powered electronic devices to become a lot smaller. Specifically designed capacitors are placed in series with the load to substantially drop the applied voltage (for example, from 230 V a.c. to 5 V a.c.) before it is converted to d.c.

Vref

Vapplied

IXC

IXC +X+

+X−

−X−

4.7.2  Capacitors in a.c. circuits

IXC

Vcapacitor

90° +X−

Power

Figure 4.40  Capacitive a.c. circuit

Vref

Figure 4.40 shows a capacitor circuit and illustrates a full cycle of alternating voltage and current within it. Without resistance in the circuit, capacitance changes according to the rate of change of the applied voltage. So, when the voltage is changing most, the current in the capacitor will be the greatest. When the voltage reaches its maximum value, the current will be zero. But then, as the voltage decreases, the current changes direction. As the current is already at maximum positive flow when the voltage sine wave crosses zero (going

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positive), the current seems to come before the voltage. Consequently, it is said that in a capacitive circuit the current ‘leads’ the voltage. For any purely capacitive circuit, the current leads the applied voltage by 90°E, as shown. The phasor diagram in Figure 4.40 shows a current phasor leading the voltage by 90°.

4.7.3  Capacitive reactance When an a.c. voltage is applied to a capacitor, it is continually being charged and discharged. Current flows in and out of the capacitor at a regular rate, dependent on the supply frequency. An a.c. ammeter connected in the circuit would indicate a current apparently flowing through the capacitor; however, the capacitor has an insulating dielectric between the two plates, so the ammeter is actually recording a displacement current. These factors affect the value of this current: the applied voltage, the supply frequency and the capacity of the capacitor. Since a capacitor reacts when connected to a.c., it is said to have a type of reactance called ‘capacitive reactance’. The symbol for this is XC and the unit is the ohm: 1 ​​XC​  ​​ = _____ ​     ​​  2πfC where: XC = capacitive reactance in ohms f = frequency in hertz C = capacitance in Farads

4.7.4  Capacitors in series When two capacitors are placed in series, the effect is as if the distance between the outside plates were increased and the capacity therefore decreased. On an alternating-current supply, this effectively increases the opposition to a current flow in a similar way to that of resistors placed in series: ​that is, ​XCtotal ​  ​​ = ​XC1 ​  ​​  + ​X​ C2​​  + ​X​ C3​​ … + ​XCn ​  ​​​

EXAMPLE 4.12 Find the capacitive reactance of an 8 μF capacitor and the current flowing when it is connected to a 100 V 50 Hz supply. If it is then connected in series with another capacitor of the same capacity, find the new current flowing. 1 ​XC​  ​​ = _____ ​     ​  2πfC 1 ​ = ________________ ​       ​ 2 × π × 50 × 8 × 10−6

(1) (2)

​​      ​ ​     ​  ​  ​    ​  =​ ​  397.9 Ω​ (3)​​​​​​ V I = ___ ​    ​  ​XC​  ​​

(4)

100 ​ = _____ ​    ​  397.9

(5)

(continued) 237

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​ = 251 mA

(6)

V I = ________ ​     ​  (7) ​XC1 ​  ​​  + ​XC2 ​  ​​ ​​     ​     ​  ​  ​  ​  ​  ​​​ 100 ___________ ​ = ​       ​ (8) 397.9 + 397.9 ​ = 125.7 mA

(9)

EXAMPLE 4.13 Calculate the current drawn by a 16 μF capacitor when connected to a 230 V 50 Hz supply. 1 ​XC​  ​​ = _____ ​     ​  2πfC

(1)

1 ​ = _________________ ​        ​ (2 ) 2 × π × 50 × 16 × 10−6 ​ = 198.9 Ω (3 ) ​​      ​      ​  ​  ​  ​  ​  ​  ​​​ V ___ I = ​    ​  (4 ) ​XC​  ​​ 230 ​ = ​ _____  ​  (5 ) 198.9 ​ = 1.156 A (6 )

4.8  RC and RL series a.c. circuits 4.8.1  Series circuits on a.c. current Pure components are theoretically possible but practically impossible. This means that most a.c. circuits will exhibit a combination of the three types of load described earlier. The effects of two of the three are often too small to be considered. As a reminder, the three basic components and their effects are:

1. Resistance: no phase shift between voltage and current 2. Inductance: 90° phase shift; current lagging 3. Capacitance: 90° phase shift; current leading

In other circuits, the load will mostly be two of the three types, say, resistive and inductive. It is therefore necessary to learn how to deal with circuits that contain different types of loads in series and/or parallel. In an a.c. circuit, the combined opposition to a current flow of both resistance and reactance is called the ‘complex impedance’. This is given the symbol Z and is measured in ohms. Ohm’s Law is still applicable: ​V​  ​​  ​Z = _____ ​  RMS ​​   ​IRMS ​  ​​ 238

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4.8.2  Series circuit impedance Each voltage drop can be expressed as a factor of current, i.e. VZ = IZ, VR = IR and VL = IXL. The voltage phasors in Figure 4.41(a) can also be drawn in triangle form, as in Figure 4.41(b). The current is common to each component and is the same in each. Therefore, each resistance, reactance or impedance has a voltage developed across it that is proportional to its opposition to current flow. This means the triangle in Figure 4.41(b) can also represent R, XL and Z (or XC when it_________ is present). Since it is a right angle triangle, Pythagoras’ theorem applies, i.e. Z2 = R2 + XL2 and therefore, Z = √  ​​  (R2 + XL2) ​​  . If it is a series R–L–C circuit, the effective reactance is (XL − XC). In this case, the complete formula is: ______________ ​Z = √  ​     ​R​​  2​  + ​(​X​  L​​  − ​X​  C​​)​​  2​ ​​ where: Z = impedance R = resistance XL = inductive reactance XC = capacitance reactance If XC has a greater value than XL then the value of XL − XC is a negative quantity. However, this has no effect on the value of Z because when a negative number is squared it becomes a positive number. The angle φ between the adjacent sides R and Z has the same value as the angle φ between the voltage phasors VR and V. This is because the two triangular figures are classed as similar triangles. The phase angle can be found using trigonometric ratios from the sides of the triangle: X R X ​θ = ​Tan​​  −1​​ __ ​   ​  ​ = ​Cos​​  −1​​ __ ​   ​  ​ = ​Sin​​  −1​​ __ ​   ​  ​​ (R) (Z) (Z) Capacitive reactance tends to produce a current leading the voltage by 90°. Inductive reactance tends to produce a current lagging the voltage by 90°. When the values of capacitive and inductive reactance are equal, they cancel each other out. This leaves only resistance as an effective circuit component. When this happens, the circuit is said to be ‘resonant’. The circuit then behaves as a purely resistive circuit, at least as far as externally measured. See section 4.13.5 for more information about resonance.

4.8.3  Series R–C circuits When current flows through a series R–C circuit (Figure  4.42), it causes a voltage drop VR (due to the resistance), which is in phase with the  current. It also causes a voltage drop VC (due to the capacitive reactance).This lags the current by 90°. The total voltage V is the  phasor  sum of the two voltage drops VR and  VC.  The current leads the applied voltage by φ.

VZ

VXL

VR

φ

Iref

(a)

R∝VR XL∝VXL

φ

Z∝VZ (b)

Figure 4.41  Parallel R–L circuit φ

VXC

VR

Iref

VZ

Figure 4.42  Series R–C circuit

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Commercially made capacitors are considered as pure capacitance, and the problem of losses (as shown in the series R–L circuits) does not usually occur at line frequency (50 Hz).

4.8.4  AS/NZS 3000 requirements for the installation of capacitors These requirements were established because capacitors provide energy storage and can have high potentials across their terminals when connected in series a.c. circuits. The only exception to these requirements is when capacitors are an integral part of other electrical equipment such as motors and fluorescent lights. Capacitors installed in electrical equipment are deemed to satisfy these requirements as they have been engineered to meet the currentcarrying capacity and other rating requirements. Also, they are designed to provide a discharge path for energised capacitors when the equipment is isolated. The requirements are outlined in AS/NZS 3000 clause 4.15 and include the following points: ∙ Circuit breakers, switches and contactors should be of a type that is suitable for switching the reactive component of the current. A utilisation category of a.c.-6b (specifically for switching capacitors) is an example of an appropriate type. The utilisation category refers to an international standard for categorising the types of load that can be switched by the respective devices. ∙ The provision of a circuit breaker for capacitors (rated individually or in banks of more than 100kvar) not connected  in parallel with individual appliances. For example, power factor correction banks at the point of supply. In this example, the capacitors are specifically connected for power factor correction and are not associated with any particular circuit or equipment. Hence, they require a circuit breaker for protection and control. ∙ Regarding the current-carrying capacity of the conductors connecting the capacitors: there are several arrangements, depending on whether the capacitor is connected in parallel with individual appliances or not. ∙ The provision of a discharge path to allow any charge to be removed via an appropriate resistor by a parallel connection across the capacitor terminals. The provision for discharge is to allow qualified people to work on the associated equipment. A warning notice is required and should state something like:

WARNING: ENSURE THAT CAPACITORS ARE COMPLETELY DISCHARGED BEFORE WORKING ON EQUIPMENT.

The discharge times for capacitors are one minute for those rated up to 650 V and five minutes for those rated above 650 V. At the end of this time, the capacitor should be not more than 50 V across the terminals.

4.8.5  Series R–L circuits In a series circuit, the current is common to all parts. The total voltage is the phasor sum of the individual voltage drops. In Figure 4.43, the voltage drop VR across the resistor is in phase with the current. The voltage drop VL across the pure inductor is 90° out of phase with the VZ VXL current. In an inductive circuit, the current lags the voltage or the voltage leads the current. The two voltage drops VR and VL are out of phase. This means they cannot be added numerically but must be added as phasors. VR Iref Since the current in a series circuit is the common φ value, it is used as the reference phasor. The voltage phasors are drawn as shown in Figure  4.43, with Figure 4.43  Series R–L circuit 240

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VL leading I by 90°. The result of the two voltages VR VXL VZ and VL represents the total voltage V. The angle φ represents the angle of phase difference between the applied  voltage  and the current (meaning that the applied voltage leads the current by φ). With an actual inductor, the winding itself might 202V provide the circuit resistance and there might be no added external resistance. The power losses due to 230V the winding resistance (copper losses) and the core (iron losses) will be real. Accordingly, the lagging phase shift of the current due to the inductance will not be a full 90°—it will be a value corresponding to a combination of both the inductive reactance and the equivalent resistance of the circuit. VR Iref φ 110V Figure  4.44 illustrates one practical use for an inductor in an a.c. circuit. It provides a way of reducing a 230 V supply to 110 V for a projector Figure 4.44  Series R–L ballasted lamp lamp with minimal power loss and  heat generation. The inductor also helps to smooth the current to remove spikes that might damage the lamp. The voltage VR is in phase with the current, and the values of V, VR and VL can be obtained using a voltmeter. Using these values, the phasor diagram can be constructed as shown in Figure 4.44. As the inductor is impure, the voltage does not lead the current by 90° but by an angle less than that (i.e. φL). The voltage VRL is the equivalent voltage drop. For the purposes of circuit analysis, the resistance RL in Figure 4.44 is assumed to be of a value that allows for both iron and copper losses. The value will not necessarily equal the resistance of the windings. The power loss associated with it is the sum of both iron and copper losses. For example, 6 W of iron loss and 4 W of copper loss will show on a wattmeter as 10 W. Figure 4.44 shows the relationship between the respective voltages in this series R–L circuit. The current I lags behind the applied voltage V by φ.

4.9  R–L–C series a.c. circuits 4.9.1  Series R–L–C circuits In Figure  4.45 the voltage VR is in phase with the current, VL leads the current by 90° and VC lags the current by 90°. The two voltages VL and VC are 180° out of phase with each other. Thus the voltage drop across the total reactance is VL − VC, as shown in Figure  4.45. The  total voltage V is the phasor addition of VR and (VL − VC) and φ is the phase angle. The current is lagging the applied voltage by φ°. If VC had been greater in value than VL, the current would have led the voltage by some angle.

VXL VXC VZ φ

VR

Iref

VXC

Figure 4.45  Series R–L–C circuit

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4.9.2  Calculation of total impedance for a series R–L–C circuit EXAMPLE 4.14 A resistance of 30 Ω is connected in series with an inductive reactance of 60 Ω and a capacitive reactance of 20 Ω. What is the impedance of the circuit? ____________ Z = ​  ​R      ​​  2​  +  ​​(​​​XL​  ​​  − ​XC​  )​​​ ​​​​  2​ ​ (1) ______________ ​ = ​  ​3      0​​  2​  +  ​​(​​60  − 20​)​​​​  2​ ​ (2) _________ 2 2 ​ = ​  ​3   0​​  ​  +  ​40​​  ​ ​  (3) ​​ ​      ​  __________ ​  ​  ​  ​  ​  ​  ​​​ ​= √ ​  900 +       1600 ​ (4 ) _____ ​= √ ​  2500 ​     (5 )

√ √ √

​ = 50 Ω

(6 )

EXAMPLE 4.15 A circuit that has 20 Ω in series with 0.25 H and 80 μF is connected to a 230 V 50 Hz supply. Determine the impedance of the circuit, the current and its phase angle. ​XL​  ​​ = 2πfL ​ = 2 × 3.142 × 50 × 0.25

(1) (2)

​ = 78.5 Ω

(3)

1 ​XC​  ​​ = _____ ​     ​  2πfC

(4)

1 ​ = _____________________ ​        ​ 2 × 3.142 × 50 × 80 × 10−6

(5)

​ = 39.8 Ω (6) ___________ Z = ​  ​R      ​​  2​  +  ​​(​​​XL​  ​​  – ​XC​  )​​​ ​​​​  2​ ​ (7) _________________ =​ ​  ​  ​2      0​​  2​ ​ ​  ​ +  (78.5 –  (8)​​​​ ​​             ​  ​     ​  ​  ​  ​  ​ 39.8​)​​  2​ ​​  ​  __________ ​ = ​  ​2      0​​  2​  + ​38.7​​  2​ ​ (9) __________ ​= √ ​  400 +       1498 ​ (10) _____ ​= √ ​  1898 ​     (11)

√ √ √

​ = 43.6 Ω

(12)

(X) θ = ​tan​​  −1​ ​ ___ ​  R

(13)

(38.7) ​ = ​tan​​  −1​ ​ _____  ​     20

(14)

​ = 62.7°

(15)

4.9.3  Calculation of voltage drop for cables using the values for reactance and a.c. resistance When current flows along a conductor in a d.c. circuit, the resistance of the conductor, although minimal, has an impact on the voltage of the other terminals of the connected equipment due to the voltage drop resulting from 242

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this resistance. The same applies to Point Electrical Service line of attachment grid R&X an a.c. circuit as the conductors will exhibit some degree of resistance and Consumer reactance. The resistance is due to the R&X mains R&X material, cross-sectional area, length and temperature. The reactance is Main R&X due mostly to the capacitive reactance switch between the conductors. There will Circuit also be some inductive reactance, breaker Earth Neutral but this will be minimal on account Final of the extremely low amount of turns sub circuit (generally fewer than one). Main The capacitance is affected by earth R&X R&X the distance between conductors, stake the dielectric characteristics of the insulating material and the length. Therefore, different insulation types and configurations will have different Load reactance. For example, the reactance of PVC, XLPE, flexible cable and Figure 4.46  Single phase installation MIMS are listed separately. The spac­ ing between single-core conductors is not only greater than multicore but there is also an extra layer of insulating material. Multicore is usually separated by an earth conductor. The values for calculating the impedance of the conductors in a wiring system are tabled in AS/NZS 3008.1:2017. This is the standard that provides all the data for the selection of cables for a.c., up to and including 0.6/1 kV. To determine the voltage drop of cables, Tables 30 to 33 deal with reactance and 34 to 39 deal with resistance. Also,  the type of cable has to be determined and the operating temperature of the insulation needs to be considered. Table 3.2 in AS/NZS 3000:2018 and Table 1 in AS/NZS 3008.1:2017 contain information on temperatures for cables. Figure 4.46 shows a simple single-phase installation with one load protected by one circuit breaker. If we assume that the voltage at the circuit breaker is 230 V, even with the voltage drop as the result of the impedance (resistance and reactance) of the circuit leading up to the circuit breaker, we can determine the value of voltage at the terminals of the load. This is done by calculating the value of the voltage drop as a result of the final sub-circuit conductors. (The final sub-circuit is the wiring from the circuit breaker to the load.) The values in the tables are for Ω/km. To determine the value of reactance or resistance, the value has to be divided by 1000 to get the Ω/m and then multiplied by the length.

A 10 A motor is connected to a circuit breaker in the main switchboard by a final sub-circuit of 1 mm2 V90 Thermoplastic multicore (TPS) twin and earth. The final sub-circuit is 50 m long. Determine the voltage drop of the final sub-circuit conductors and the voltage at the terminals of the motor. The conductors are made of copper. Step 1. Determine the operating temperature of the 1 mm2 V90 Thermoplastic multicore (TPS) twin and earth. This can be done using either Table 3.2 in AS/NZS 3000:2018 or Table 1 in AS/NZS 3008.1:2017. The normal use for V90 Thermoplastic insulation is 75°. (continued) 243

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Step 2. Consult the table and column in AS/NZS 3008.1:2017 for the reactance of 1 mm2 V90 Thermoplastic multicore (TPS) twin and earth. AS/NZS 3008.1:2017 Table 30 is for all cables, excluding flexible cords, flexible cables, MIMS cables and aerial cables. Column 9 is for multicore PVC cables with circular conductors. From this table, the value of the reactance is 0.119 Ω/km. Step 3. Determine the total reactance for the 1 mm2 V90 Thermoplastic multicore (TPS) twin and earth. The final sub-circuit active (Xfsc active) Ω / km ​​ = _____   ​  ​  ​Xfsc active  ​ × L 1000 ​  ​  0.119 ​​       ​ ​​​   = _____   ​   ​ × 50 1000   = 0.00595 Ω Where L is the length of the final sub-circuit. The final sub-circuit active reactance (Xfsc active) is the same as the final sub-circuit neutral reactance (Xfsc neutral). Therefore, the reactance of the final sub-circuit (Xfsc total) is: ​  ​Xfsc total ​​ = ​Xfsc active ​  ​​  + ​ X​ fsc neutral​​  ​​​ ​       ​ ​ =​  0.00595 +  0.00595 ​​

​ = 0.0119 Ω Step 4. Determine the table and column in AS/NZS 3008.1:2017 for the resistance of 1 mm2 V90 Thermoplastic multicore (TPS) twin and earth. AS/NZS 3008.1:2017 Table 35 is for multicore with circular conductors. Column 4 (75°) is for copper conductors. From this table, the value of the reactance is 25.8 Ω/km Step 5. Determine the total resistance for the 1 mm2 V90 Thermoplastic multicore (TPS) twin and earth. The final sub-circuit active (Rfsc active) Ω / km ​​ = ​ _____ ​ × L   ​Rfsc active ​  1000 ​    ​  25.8  ​​ ​​    ​​ ​ = ​ _____   ​     ×  50 1000 ​ = 1.29 Ω Where L is the length of the final sub-circuit. The final sub-circuit active resistance (Rfsc active) is the same as the final sub-circuit neutral resistance (Rfsc neutral). Therefore, the reactance of the final sub-circuit (Rfsc total) is: ​Rfsc total ​  ​​ = ​Rfsc active ​  ​​  + ​ R​ fsc neutral​​ ​​

​     ​​ ​ ​ ​   =​  1.29 + 1.29 ​ = 2.58 Ω

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Step 6. Determine the impedance of the final sub-circuit (Zfsc) _________________ ​Zfsc ​  ​​ = √ ​   (​   X​f​  sc total​​  2​​ ​ + ​R​ ​fsc total​​  2​​)​  ​ _________________ ​​ ​ ​      =​  √ ​   (​   0.0119​​  2 ​​ ​  + ​2.58​​  2​) ​​ ​ ​ = 2.58003 Ω Step 7. Determine the voltage drop in the final sub-circuit conductors (Vdfsc) as a result of this impedance of the current drawn. ​Vd​ fsc​​ = I  ×   ​Z​ fsc​​ ​​

     ​ ​ =​  10 × 2.58002744 ​  ​​​ ​ = 25.8003 V

Where I is the current drawn by the load (motor) Step 8. Determine the voltage at the terminals of the motor (Vload) ​  ​​  − ​Vd​ fsc​​ ​Vload ​  ​​ = ​Vsupply ​​

​ ​     ​​ ​ ​   =​  230 − 25.8002744 ​ = 204.1997 V

This value of voltage drop is too excessive and an alternate arrangement must be used for the motor to operate correctly.

4.9.4  Comparison of current-limiting characteristics of inductors and resistors While a resistor and an inductor will both limit current in a.c. circuits, inductors have several advantages. As discussed later in this chapter, resistors consume power. So when they are used to limit current, they reduce the efficiency of the systems through the resulting power loss. Inductors are made of a coil of wire and generally have a comparatively low amount of resistance. This means they only consume a small amount of power. They also have a high level of inductive reactance that opposes a.c. current flow. The other main advantage of inductors over resistors is opposition to change in current. With a high inrush current, for example under short circuit conditions or when a fluorescent tube is ignited, the back EMF generated from the rapid increase in current will oppose the current flow and reduce its magnitude. This is one of the major reasons for inductors being used as line reactors in power supply and quality systems. It is also why they are used as ‘ballasts’ in older fluorescent tube light fittings. (A ballast is a device placed in series with the load to limit the amount of current in an electrical circuit.)

4.9.5  Practical examples of R–L–C series circuits Series R–L–C circuits are generally limited to electronic applications such as tuning circuits in radios. However, a similar circuit can be used as a low-pass filter in electrical supplies. By using a series R–L–C circuit with the appropriate values of reactance, frequencies higher that 50 Hz can be filtered out of the supply. At one time, series R–L–C circuits were used in car ignition systems. They created the high-voltage arc that ignited the fuel via the spark plugs. 245

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4.10   Parallel a.c. circuits φ

IR

Vref

ITotal

IXL

Figure 4.47  Parallel R–L circuit φ

IR

Vref

φ1

IXL+R

ITotal

ITotal

IR

φ

Vref

Figure 4.49  Parallel R–C circuit IXC

IR

φ

ITotal

IXC ITotal

Figure 4.50  Parallel R–L–C circuit

Most a.c. equipment requires a supply voltage that is fixed (such as 230 V). This means that most workproducing equipment or loads that are connected in electrical installations are connected in parallel. For example, when a lighting or socket outlet circuit is connected with more than one light or socket outlet, they are all connected in parallel. This is done by looping all active and neutral connections in the active and neutral terminal at each light or socket outlet. Another significant piece of electrical circuitry that is connected in parallel is power factor correction equipment (covered later in this chapter).

4.10.2  Parallel R–L circuits

Figure 4.48  Parallel R–Z circuit

IXC

4.10.1 Introduction

Vref

In a parallel circuit, the voltage is common to all the components. The total current comprises the individual components, as shown in Figure 4.47. In drawing the phasor diagram, the voltage V is used as the reference phasor. Assuming R and L are both pure values, then: ∙  IR is in phase with V ∙  IXL lags V by 90° ∙  Itotal is equal to the phasor sum of IR and IXL (as shown in Figure 4.47, where Itotal lags V by φ). Practical inductors have some series resistance associated with them. A more common circuit would be as shown in Figure 4.48, where the series resistance of the inductor is large enough to affect the phase angle of the inductive phasor (that is no longer 90°). The current IR is in phase with V but the current IXL, through the inductor, lags the voltage by φL. As the inductor is a series R–L circuit, the angle φL R = Cos−1​​ ___ ​  L ​  ​​. ( ZL ) The phasor addition of IR and IXL+R represents the total current Itotal, which lags the voltage V by φ.

4.10.3  Parallel R–C circuits An R–C parallel circuit is shown in Figure 4.49. For all practical purposes, the resistor current IR is in phase with the applied voltage V. The capacitor current leads both by 90°. The total current is the phasor sum of the two individual currents and leads V by φ. 246

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4.10.4  Parallel R–L–C circuits The total current in this type of circuit is equal to the phasor addition of IR, IL and IC (see Figure 4.50). When L and C are pure quantities, the two currents IL and IC are 180° out of phase and can therefore be subtracted (IL − IC). In this case, Itotal lags the voltage by φ. A greater value of IC could cause the total current to lead the applied voltage.

4.10.5  Capacitors in parallel When two capacitors are placed in parallel, it is as if both the area of the capacitor plates and the total capacity are increased. The current flow is increased as capacitive reactance (Xc) is inversely proportional to capacitance (C). The capacitors in parallel on an alternating-current circuit have the same characteristics as resistors in parallel. Each parallel path allows current flow according to its reactance. Two equal-sized capacitors would each draw their usual current, but the total current flow would be double the current flow to a single capacitor. The total opposition to current for the parallel network is: 1  1  ____ 1  1  … ____ 1 ​​ ______    ​     ​  + ​     ​  + ​ ____    ​  +   ​     ​​  = ​ ____  ​X​  Ctotal​​

 ​X​  C1​​

 ​X​  C2​​

 ​X​  C3​​

​X​  Cn​​

In the following example, the same capacitor values and supply voltage have been used as in Example 4.15, so that the results can be compared. The results will differ.

EXAMPLE 4.16 Two 8 μF capacitors are connected in parallel to a 100 V 50 Hz supply. Find the current flowing through each capacitor and the total current flowing. 1 ​XC​  ​​ = _____ ​     ​  (1) 2πfC 1   = ________________ ​       ​ (2) 2 × π × 50 × 8 × 10−6   = 397.9 Ω​

(3)

V I = ___ ​    ​  ​XC​  ​​

(4)

100   = _____ ​    ​  397.9

(5)

  = 251 mA (6) ​​                ​  ​  ​  ​  ​  ​ ​ ​ ​  ​  ​  ​  ​ 1 ​XC total ​  ​​ = _______ ​ ___    ​   (7) 1 ___ ​  ​X1C1 ​    ​​ ​  + ​  ​XC2 ​    ​​ ​  ​​

1   = ________ ​ ____  1  ​  1 ​  397.9    ​  + ​ ____    ​  397.9

(8)

  = 198.9 Ω​

(9)

V I = ________ ​     ​   ​XC TOTAL ​  ​​

(10)

100   = _____ ​    ​  198.9

(11)

  = 502.8 mA

(12)

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4.10.6  Inductors in parallel If two pure inductors are connected in parallel, each draws its own current from the supply and the line current is the phasor sum of the separate currents. Each current lags the voltage by 90°. Therefore, they are in phase with each other and can be added arithmetically. The total inductive reactance is therefore reduced in proportion to the increase in current. This allows us to use the same type of formula as for parallel resistors: 1  ​​ ​​XLtotal ​  ​​ = ________________ ​ ___      ___ 1 1 1 1 ___ ​  ​XL1​   ​​ ​  + ​  ​XL2​   ​​ ​  + ​ ___ ​XL3 ​   ​​ ​  + …  ​ ​XLN ​    ​​ ​  where: XLtotal = total reactance  XL1 = reactance 1  XL2 = reactance 2  XL3 = reactance 3 XLN = more reactances The same method is used to find the total inductance of a circuit that has inductors connected in parallel: 1  ​​ ​​Ltotal ​  ​​ = _____________ ​ __      __ 1 1 1 1 __ ​  ​L1​    ​ ​​  + ​  ​L2​    ​ ​​  + ​ __ ​L3​    ​ ​​  +  …  ​  ​LN​    ​​​   where: Ltotal = total inductance  L1 = inductance 1  L2 = inductance 2  L3 = inductance 3 LN = more inductances

EXAMPLE 4.17 Two inductors, one with an inductive reactance of 10 Ω and the second with an inductive reactance of 8 Ω, are connected in parallel across a 230 V 50 Hz supply. (a) What is the total inductive reactance? (b) What is the total current? 1 ​XLtotal ​  ​​ = ______ ​ ___  1  ​  ​  ​X1L1​    ​ ​​  + ​ ___ ​XL2 ​    ​​​   1 ​ = ____ ​ __    ​  1 ​  10  ​  + ​ _18 ​  ​​

​​

(1 ) (2 )

​ = 4.44 Ω​ (3 )     ​     ​  ​  ​  ​  ​  ​  ​ V ___ I = ​    ​  (4 ) ​XL​  ​​ 230 ​ = ____ ​     ​  4.44

(5 )

​ = 51.75 A​

(6 )

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4.10.7  Parallel circuit impedance In parallel circuits with the voltage as reference, the current phasors must be added vectorally to find the total current. The impedance, reactance and resistance are all proportional to the inverse of the respective current. Therefore, just as parallel resistors in a d.c. circuit cannot be simply added together, the impedance triangle method for series circuits must not be applied to parallel circuit impedances. The recommended method is to calculate the current flow in each component and add them by the phasor/ vector method. This uses either the graphical method or, preferably, a mathematical method involving R–P and P–R conversions or trigonometry. See Example 4.18.

EXAMPLE 4.18 A resistance of 115 Ω is connected to a 230 V 50 Hz supply, in parallel with an inductive reactance of 77 Ω and a capacitive reactance of 120 Ω. What is the total current and the impedance of the circuit? What is the phase angle of the total current? V ​IR​  ​​ = __ ​   ​  R 230 ​ = ____ ​   ​  115 ​ = 2 A V ​IL​  ​​ = ___ ​    ​  ​XL​  ​​ 230 ​ = ____ ​   ​  77 ​ = 2.99 A​ V ​IC​  ​​ = ___ ​    ​  ​XC​  ​​ 230 ​ = ​ ____ ​  120 ​ = 1.92 A​

(1) (2) (3) (4) (5) (6) (7) (8) (9)

​I    ​  ​ ​​    =​  ​IL​  ​​  ​ ​ − ​ (10)​​​ X ​​         ​  ​  ​  I​ C​  ​​​  ​  ​  ​  ​  ​  ​  ​  ​ = 2.99  − 1.92 (11) ​ = 1.07A (12) _______ ​IZ​  ​​ = ​  ​​I ​​  2R​​  ​​  + ​​I​​  2X​​  ​​ ​  (13) _________ ​ = ​  ​2   ​​  2​  + ​1.07​​  2​ ​  (14) ​ = 2.268 A (15)

√ √

V Z = __ ​   ​  ​IZ​  ​​ 230 ​ = _____ ​    ​  2.268 ​ = 101.4 Ω ​I​  ​​ Φ = ​tan​​  −1​ ​ __X ​  ​IR​  ​​ 1.07 ​ = ​tan​​  −1​ ​ ____  ​     2 ​ = 28.15°

(16) (17) (18) (19) (20) (21) 249

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4.10.8  Practical examples of parallel circuits All equipment that is connected by the end user of a.c. circuits must have the same voltage applied to it. So all electrical equipment connected to final sub-circuits is connected in parallel. Other circuits in the electrotechnology industry require parallel connection. They include:

∙ power factor capacitors connected in parallel with the equipment load (or with the incoming supply) ∙ high-pass filtering that allows 50 Hz a.c. through but opposes low frequency interference ∙ shunting circuits that shunt over-voltage current such as lightning strikes and high voltage injection (through equipment failure) to earth.

4.11   Power in an a.c. circuit 4.11.1  Power in a resistive circuit If the values v of voltage and i of current are taken at a given instant, then v × i = P is the instantaneous power. By taking the product of v and i for a number of instantaneous values, we can plot a curve of power for each cycle of a.c. In Figure 4.51, only one cycle is shown—any one cycle represents what any other cycle will do. The curves for voltage, current and power are shown as generated by a computer program from the maths. The following points are particularly important:

1. 2. 3. 4.

The power curve is sinusoidal in shape, which agrees with the laws of trigonometry. There are no negative values of power—a negative multiplied by a negative becomes positive. The power curve completes two cycles for each complete cycle of current or voltage. As the power curve is a sine wave, the area underneath it is identical to the area between it and a line drawn to just touch the peak value of power. Therefore, the power used is half what the peak values would have 1 1 suggested. This proves that the values for RMS must be _______ ​​     ​​  and ​​ ______    ​​  . √2Vmax √2Imax If values of IRMS = 1 A and VRMS = 1 V, power is the rate at which energy is used. Therefore, there is no RMS value of power, but an absolute value. ​P = ​VRMS ​  ​​  × ​I​ RMS​​= 1 × 1 = 1W​ Using maximum values, which are 1.414 times RMS values, gives an answer of twice the actual power used: ​P = ​Vmax ​  ​​  × ​I​ max​​= 1.414 × 1.414 = 2W​

Vref IR

Power IR

Vref

This result confirms the need to use RMS values when working with alternating current. For purely resistive circuits, Ohm’s Law and the power law both work using RMS values of voltage and current: V ​ ​​  2​  ​V = I × R and P = V × I = ___ ​   ​ = ​I​​  2​R​ R

Figure 4.51  Resistive a.c. circuit

But with a.c., V and I must always be measured in RMS values.

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For sinusoidal waveforms only, if peak values are used to obtain a power rating, the average power value obtained is always half that of the peak power value. That is, average power equals half maximum power. Substituting maximum values in the power equation gives: ​​P​  avg​​ = 0.707  × ​V​  max​​  ×  0.707  × ​I​  max​​ = 0.5 ​P​  max​​​

4.11.2  Power in a capacitive circuit As with inductors, capacitors charge and discharge. The energy stored in the capacitor in one quarter-cycle is returned in the next quarter-cycle. Therefore, the average power in a pure capacitive circuit is zero. In Figure 4.40, the shaded power waveform is the result of multiplying the instantaneous values of voltage and current. When both are positive, the capacitor is charged; when both are negative, the capacitor is charged in the opposite polarity. But when one is positive and the other negative, the charge is returned to the power supply. As the charge is the same size as the discharge, no power is consumed. There is as much of the power curve above the zero line as there is below it. The average power in a purely capacitive circuit is zero.

4.11.3  Power in an inductive circuit Inductors store energy as a magnetic field, which is returned to the circuit when the field collapses. This happens every half-cycle. As there is no resistance (in theory), there are no losses and all the energy is returned. Figure 4.39 shows the applied voltage as the red sine wave and the back EMF as the green sine wave. When the resistance either does not exist or is negligible, the back EMF is equal to the applied voltage and is of opposite polarity (or it is out of phase by 180°). The back EMF is proportional to the change in current flow. Therefore it is out of phase with the current by 90°. Similarly, the current is also out of phase with the applied voltage by 90°, with maximum current flow occurring when the applied voltage changes polarity (that is, when it crosses zero). In Figure 4.39, the power is represented by the shaded sine wave. We can see that it has twice the frequency of the voltage or current and that there are two positive pulses of power. Generally we would consider this to be energy that has been used; now we must consider it to be energy that has been stored in the inductor. But the negative pulses of the power curve do not mean that we have discovered negative power. Rather, they mean that we have found energy that has been returned to the circuit. That means that the sign of the power waveform reverses every quarter of a cycle, showing that power is alternately fed into and returned from the inductor. As the current rises, energy is used to produce the magnetic field. As the current falls, the magnetic field collapses and the energy is returned to the supply. Over a complete cycle, the positive and negative sections of the power waveform cancel each other. As a result, the average power consumed by a pure inductor is zero. Figure 4.39 shows that the power wave is sinusoidal if the voltage and current waveforms are sinusoidal. It also shows that the frequency of the power wave is twice that of the line frequency.

4.11.4  Power in a.c. circuits A purely resistive load consumes power, while a purely inductive load consumes no power. When resistance and inductance are combined in one circuit, there will be a value of power consumed that is dependent on the resistance, or resistive load, in the circuit.

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Vtotal

Power Average Power

I +X−

+X+

−X+

Vtotal

−X−

VR

Iref

45°

Itotal VXL

Vtotal

Figure 4.52 shows the waveforms for voltage, current and power in a series R–L circuit where I lags V by 45°. As there is more positive than negative power, the resultant or average power will be positive. It will be a lesser value than for a purely resistive value load, but a greater value than a purely inductive load.

True power (P)

The applied voltage is split into two components at right angles to each other, as shown in Figure 4.52 in Figure 4.52  Power in an a.c. R–L circuit the phasor diagram. VR is in phase with the current, while VL is leading the current by 90° and is shown at 90° to VR. Previously it was stated that, in a purely resistive circuit, V and I are in phase and the power consumed is found from P = V.I. This is still true as long as the resistive or in-phase component of voltage is used. That is: ​P = ​VR​  ​​.I​ V The ratio ____ ​​  R  ​​ is equal to the Cosine of the angle of lag φ and it is usual to express the power consumed in terms Vtotal of the line voltage V. That is: ​V​  ​​  ___ ​  R ​ = cos φ ​ ​​    ​​   V ​  ​  ​  ​  ∴ ​V​ R​​ = V cos φ Since P = VRI, then also P = V cos φ.I that is, ​P = VI cos φ​ In electrical power work (which mainly deals with sinusoidal waveforms), ‘cos φ’ usually applies to the power factor (or PF). However, the general expression for power factor for all wave shapes is the symbol lambda (λ). For electrical work, this symbol is synonymous with the expression cos φ (i.e. PF = cos φ = λ): ​P = VI cos φ = VIλ​ Although you could use lambda (λ) to represent cos φ, using the term cos φ in your formulas will help you remember what lambda and the formula mean.

Apparent power (S) For circuits that have both resistance and reactance, the product of the measured line voltage and line current produces a value greater than the power consumed. Therefore, it cannot be expressed in watts. The value is known as the ‘apparent power’. This is useful in dealing with electric machinery, as will be seen. Apparent power is measured in volt-amperes (VA). Many a.c. machines, particularly alternators and transformers, are rated in VA to give an indication of both core and iron size and the current rating of the windings. The current rating of the windings is greater than the current required for the power consumed. For example, an alternator could be rated at 100 kVA yet only deliver 80 kW: ​S = VI​ 252

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Reactive power (Q) Reactive power is found from the product of the line voltage and the reactive proportion of the line current that does not consume power. A capacitor exhibits only reactive power. This is because the current flowing is leading the voltage by 90° and the true power is zero. Reactive power is sometimes called ‘wattless power’ for this reason. It is measured in volt-amperes reactive (var): ​Q = VI sin φ​

S = VI Q = VI sinφ

φ P = VI cosφ

Figure 4.53  Power triangle

True power, apparent power and reactive power can be represented by a power triangle, as shown in Figure 4.53. True power equals the apparent power in volt-amperes multiplied by the power factor of the circuit. If cos φ is calculated from 0° to 90°, the power factor will vary from 1 for a purely resistive circuit to 0 for a purely reactive circuit. This means that the power factor can only vary from 1 to 0, with PF = 1 being a resistive circuit and PF = 0 being a purely reactive circuit. Similarly, if sin φ is calculated from 0° to 90°, the reactive power ratio will vary from 0 for a purely resistive circuit to 1 for a purely reactive circuit.

4.11.5  Power losses An inductor is a coil of wire that has resistance. If an iron core is used, eddy current and hysteresis losses are produced when an a.c. current is applied. For example, a 40 W fluorescent lamp ballast typically has a resistance of 36 Ω, draws 0.4 A and consumes 10 W. The power loss due to the resistance of the windings is called ‘copper loss’: ​P = ​I​​  2​R = 0.4 × 0.4 × 36 = 5.76 W​ The remaining 4.24 W loss is due to eddy currents and hysteresis in the iron core. This is known as an ‘iron loss’ because the losses occur in the iron core. The total losses in the inductor equal the sum of the copper and iron losses. Since practical inductors consume some power, they must consist of both pure inductance and pure resistance.

4.11.6  Defining ‘power factor’ and ‘phase angle’ The power factor (PF or λ) is the factor or ratio by which apparent power is multiplied to obtain the true power, or the actual power being consumed. The phase angle is a value for sinusoidal waveforms which corresponds to the Cosine of the angle between voltage and current. For all electrical power work with sinusoidal waveforms: R  ​Power factor (PF ) = cos φ = ​ __ ​​   Z The relationship between true power and apparent power can also lead to obtaining a value for the power factor: true power  ​Power factor (PF) = cos φ = _____________    ​    ​​  apparent power P  ​PF = cos φ = ​ __  ​​  S 253

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EXAMPLE 4.19 Determine the power factor and phase angle of a ballast that has 1.8 Ω of resistance and an inductance of 150 mH at 50 Hz. ​XL​  ​​ = 2πfL ​ = 2 × π × 50 × 0.15 ​ = 47.12Ω ________ ​​    ​        ​  ​  ​ ​​ ​ ​ ​ZL​  ​​ = √ ​​   (​R​​  2​  + ​​XL​  ​​​​  2​  ) ​​  _____________ ​= √ ​​   (​   1.8​​  2​  + ​47.12​​  2​  ) ​​ ​ = 47.16 Ω Power factor (PF ) = cos φ R ​ = __ ​   ​  Z ​  ​  ​  ​  ​  ​  ​  ​​ 1.8 ​ = _____ ​    ​  47.16 ​​

​ = 0.0381 Phase angle (φ) = ​cos​​  −1​(PF  ) ​ ​       ​​ ​ =​  ​cos​​  −1​(0.0381  )​ ​​

​ = 87.81°

EXAMPLE 4.20 Determine the power factor and phase angle of a 4.5kW motor that draws 30 A when supplied with 230 V a.c. ​Smotor ​  ​​ = ​Vsupply ​  ​​  × ​I​ motor​​ ​​

​ ​       ​​ ​ ​ =​  230 × 30 ​ = 6.9 kVA Power factor (PF ) = cos φ P ​ = __ ​   ​  S ​  ​  ​  ​  ​  ​  ​  ​​ 4500 _____ ​ = ​   ​  6900 ​​

​ = 0.652 Phase angle (φ) = ​cos​​  −1​(PF  ) ​​

​ ​       ​​ ​ ​ =​  ​cos​​  −1​  (0.652 ) ​ = 49.29°

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4.11.7  Methods for measuring single-phase power, energy and demand Unlike the case with d.c., a voltmeter and ammeter M L cannot be used to measure true power in a.c. This W is because the product of these two values will give V2 V1 apparent power unless the load measured is purely resistive. However, a wattmeter (or dynamometer) can be used, as with d.c. This is due to the current winding Load measuring the average instantaneous value of current and therefore providing a reading that indicates the true power. If the load is purely reactive, the average Figure 4.54  Connection for the wattmetter current will cancel out and be zero. The current coil consists of winding of a relatively large cross-sectional area and low amount of turns. The potential coil is a winding of small cross-sectional area and high amount of turns. The terminals on the wattmeter are typically labelled M (mains) and L (load) for the ammeter connection and C (common) and V (voltage) for the voltage connection. Alternative labels are A1 and A2 for the ammeter and V1 and V2 for the voltmeter. Mixed combinations of these two systems also exist. Figure 4.54 shows the connection for the wattmeter with:

∙ M connected on the line side ∙ L connected to the load ∙ V1 (C) connected as a common connection to M ∙ V2 (V) connected to the other side of the load to the L connection.

More sophisticated digital wattmeters are available. These have many other functions such as multiple ranges and memory storage. Power analysers have true, apparent and reactive power measurement functions. They typically measure the current component with a tong clamp or flexible current probes fitted around the cables to be tested. Electrical energy is measured by a dynamometer with a time-logging function called a kilowatt hour meter. Older versions of kilowatt hour meters used a rotating disc to turn a set of gears which clocked the energy usage. These systems are generally being replaced by electronic ‘smart’ meters that can monitor multiple tariffs for different demand periods of the day. They are also able to communicate remotely with electricity retailers. Some power analysers also have time-of-use capabilities, data logging and communication facilities.

4.12   Power factor improvement 4.12.1  Effects of low power factor Broadly speaking, the lower the value of the power factor, the greater the current required to supply the same true power. The extra current flowing brings the following factors into play:

1. 2. 3. 4. 5. 6. 7. 8.

larger cross-sectional area conductors are required larger transformers higher-rated switch gear fuses of a higher current rating higher voltage drops along conductors extra copper losses decreased efficiency such as higher losses and more fuel used higher generating and capital costs. 255

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The effects of a low power factor mean that rating electrical equipment by power consumption is not always satisfactory. Some electrical equipment is rated by the volt-ampere (VA) method. The voltage determines the insulation required and the current determines the size of the conductors. For example, Figure 4.55 describes a transformer designed for 250 V and 40 A. The rating of this transformer is 250 × 40 = 10000 VA = 10 kVA.

EXAMPLE 4.21 If a 1 kW load is connected to a 250 V a.c. supply, find the current flowing at: (a) unity power factor (φ = 0°)  (b)  power factor = 0.8 (φ = 37°)  (c)  power factor = 0.4 (φ = 66°). P = VI cos φ P ∴ I = _____ ​     ​  ​Vcos φ ​  ​​

 (1)  (2)

1000 ​IA​  ​​ = _______ ​    ​   (3) 250 × 1 ​ = 4 A  (4) ​​             ​     ​  ​  ​  ​  ​  ​  ​​​ 1000 ________ and  ​IB​  ​​ = ​    ​   (5) 250 × 0.8 ​ = 5 A  (6) 1000 and  ​IC​  ​​ = ________ ​    ​  250 × 0.4 ​ = 10 A

P = 1000 W

 (7)  (8)

V = 250 V 4A I = —— 0°

S = 1250 VA

S = 2500 VA NB: True Power remains constant

5A I = —— 37°

VREF

If the transformer was used to supply an electric furnace with a unity power factor (PF = 1), it could supply a maximum of 10 000 × 1 = 10 kW of power. If it was also used to supply a load at 0.8 power factor, the maximum power it could supply would be 10 000 × 0.8 = 8 kW. When a transformer, or any electrical equipment, is rated in VA, a value is given that is independent of the power factor of the load.

4.12.2 Causes of low power factor

10A I = —— 66°

Figure 4.55  Power factor effect on current

Many circuits are inductive and as a result cause currents to lag. A circuit with a leading current (i.e. a capacitive circuit) is rare, although the effect can occur in long-distance transmission lines. The major causes of a low power factor are lightly loaded electric motors and transformers, and fluorescent lighting circuits. Motors and transformers should be designed to run at or near full load. For fluorescent lighting circuits using iron core ballasts, capacitors are added to the circuit to improve the power

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factor. Modern electronic ballast types are designed to produce a PF nearer to unity. Electricity generating authorities have conditions-ofsupply requirements for the use of equipment at poor power factor values.

10 9 8

PF = 0.8 φ = 37.9° ITotal

7 6 5 4

4.12.3  Power factor correction

3 2 1

Resistive Current

0 0 - | - 10 ° - | - 20 ° - | - 3 0 ° - | - 40 ° - | - 50 ° - | - 6 0 ° - | - 70 ° - | - 8 0 ° - | - 9 0 °

For economic reasons, the recommended value Figure 4.56  Power factor versus total current of the power factor is 0.9. Below 0.9, the current increases rapidly; above 0.9, the cost of the equipment necessary to correct the power factor is not worth the overall benefit gained (see Figure 4.56). Reduced power factor, perhaps due to oversized motors operating at less than full load, causes a sharp rise in current. This is shown in Figure 4.55, where the total current is plotted against the phase angle from the resistive current to ten times the resistive Figure 4.57  Motor with PF correction current at around 85° (or a PF of 0.1). To correct the power factor, it is necessary to reduce the phase angle between the line current and voltage. This needs to be done IC without  affecting the values of voltage or load current. Most low power factor problems are caused by inductive loads, such as induction motors and  transformers. One way of improving the IR VRef power  factor in this type of circuit is to connect a capacitor in parallel with the load, as shown in Figure  4.57. The effects of doing that are shown in Figure 4.58. IL remains the same and each load operates at its own power factor, but the overall power factor of the combined circuit is improved. A pure capacitor is IZ(with Capacitor) a load that operates at a leading zero power factor and, when connected across an inductive load, tends to oppose the lagging effect of the inductance, but IC without consuming any power. For example, a 230 V single-phase installation supplies a number of motors requiring 10 IL IZ(without Capacitor) kW of power. On single phase, this results in Figure 4.58  PF correction phasor diagram a load current of 43.5 A. If the power factor of the load is 0.6 (cos 53°), the total current in the line will be 72.5 A. Correcting the PF to 0.8 (cos 37°) would reduce the current to 54.5 A, a decrease of ~20% for the same true power. This illustrates the need for improving the power factor. 257

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EXAMPLE 4.22 A single-phase 230 V 50 Hz induction motor draws 15 A at 0.6 power factor. Determine the line current and power factor when an 80 μF capacitor is connected across the line. ​IR​  ​​ = ​IZ​  ​​  × PF ​ = 15 × 0.6 ​ = 9 A

 (1)  (2)  (3)

​ = ​cos​​  −1​(PF)

 (4)

θ = ​cos​​  −1​  0.6 ​ = 53.13°

 (5)  (6)

​IXL ​  ​​ = ​IZ​  ​​  × sin (φ) ​ = 15 × sin (53.13) ​ = 12 A 1 ​XC​  ​​ = _____ ​     ​  2πfC 1 ​ = _______________ ​       ​ 2π × 50 × 80 × 10−6 ​ = 40 Ω

 (7)  (8)  (9)  (10)  (11)  (12)

V ​       ​​ =​  ___ ​  ​   ​ ​ ​ ​ ​  ​​  ​ ​ ​  ​  ​  ​ ​  ​   (13)​​​ ​​ ​I          ​       ​      ​  XC ​XC​  ​​ 230 ​ = ____ ​   ​   (14) 40 ​ = 5.75 A  (15) ​IX​  ​​ = ​IXL ​  ​​  − ​IXC ​  ​​ ​ = 12 − 5.75 ​ = 6.25 A ______ ​IZ​  ​​ = ​  ​I ​  2R ​ ​  + ​​I​​  2X​​  ​​ ​  _________ ​ = ​  ​9   ​​  2​  + ​6.25​​  2​ ​  ​ = 11 A

√ √

​I​  ​​ PF = __ ​  R ​  ​IZ​  ​​ 9 ​ = ___ ​    ​  11 ​ = 0.82

 (16)  (17)  (18)  (19)  (20)  (21)  (22)  (23)  (24)

Important points here are:

1. 2. 3. 4. 5. 6. 7.

Although an extra component (the capacitor) has been added, the line current has been reduced. The in-phase or power component of current (IR) has retained its original value. The motor current and power factor remain unaltered. The power factor of the resulting combined load has been improved. The power consumption remains at its original value. The volt-ampere rating of the combined circuit has been reduced. The reactive power rating of the combined circuit has been reduced.

φ

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The purpose of using capacitors to improve the power factor is to provide a leading current. This will counteract the lagging current drawn by the load but not increase the value of power consumed. Supply authorities try to keep as high a value of power factor as is economically possible. They do this by regulating the minimum allowable value of power factor for any load connected to the supply. Consequently there is regular demand for power factor correction capacitors. Power factor improvement using a capacitor can be calculated as shown in Example 4.22. However, in that example, the power factor using the suggested capacitor still did not improve beyond the 0.8 usually required by supply authorities. A 100 μF capacitor might give an acceptable PF value, but that would just be another guess. A better method would be to calculate the value of capacitance required to improve the overall power factor to an acceptable specified value. Example 4.23 shows a method of doing that. In this case, a PF of 0.85 was chosen to ensure that the improved PF is better than 0.8. A 31.8 μF capacitor would have to be specially made, which would be very expensive. In this case, a 32 μF capacitor would do the job with a little to spare. In practice, this might be made up of four 8 μF capacitors in parallel, or perhaps a 35 μF capacitor (if that value is available). Power factor correction is sometimes achieved by the reactive power approach. The value of current flowing in the capacitor, multiplied by the voltage across it, gives the reactive power or var value. For example, in Example 4.23 the motor took 230 V at 10 A or 2.3 kVA. The true power is found from P = VI(PF) or 230 × 10 × 0.65 = 1.495 kW. If the power factor is improved to 0.85, then the true power will remain the same. But the kVA will be reduced, and therefore the line current will be reduced. If P = VI cos φ for either PF values, it follows that: ​​VI​  1​​(​PF​  1​​) = ​VI​ 2​​(​PF​  2​​)​ The voltage is the same each time and so cancels out, giving us a formula for the improved line current: ​PF​  ​​  ​​I​  2​​ = ​I1​  ​​​ ____ ​  1  ​  ​= 10 × 0.65/0.85 = 7.647 A.​ ( ​PF​ 2​​) This tells us how much the current will improve at the specified new power factor: ​PF​  ​​  ​​I​  2​​ = ​I1​  ​​​ ____ ​  1   ​ ​​ ( ​PF​ 2​​)

EXAMPLE 4.23 A motor takes a current of 10 A at 0.65 power factor, lagging, from a 230 V 50 Hz supply. What size of capacitor is required to improve the power factor to 0.85 lagging? IR = IZ × PF

 (1)

​ = 10 × 0.65

 (2)

​ = 6.5 A

 (3)

φ = cos−1(PF)

 (4)

−1

​​            ​ ​    ​  ​  ​  ​  ​  ​  =​  cos ​  0.65  (5)​​​ ​ = 49.45° IXL  (@ 0.65PF ) = IZ × sin (φ)

φ

 (6)  (7)

​ = 10 × sin (49.45)

 (8)

​ = 7.6 A

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φ(@ 0.85PF) = cos−1(PF)

 (10)

−1

​ = cos 0.85  (11) ​ = 31.8°  (12) IX(@ 0.85PF) = IZ × sin(φ)  (13) ​ = 10 × sin (31.8)  (14) ​ = 5.3 A  (15) ∴ IXC = IXL − IX  (16) ​ = 7.6 − 5.3  (17) ​ = 2.3 A  (18) V X =​  ___ ​    ​​   ​  ​  ​  ​  ​  ​  ​  ​  ​  ​  ​  ​   (19)​​​ ​​                  ​     C    IXC 230 ​ = ____ ​   ​  2.3 ​ = 100 Ω 1 C = _____ ​       ​ 2πfXC

 (20)  (21)  (22)

1 ​ = ____________ ​       ​  (23) 2π × 50 × 100 ​ = 31.8 × 10−6   = 31.8 μF

 (24)  (25)

The reactive power is calculated from Q = VI sin φ and φ is cos−1(PF) so reactive power can also be found from Q = VI sin(cos−1(PF)). Using trigonometry, this can be simplified to: _________ ​Q  =  VI​ √ (1  − ​PF​​  2​  ) ​​  Therefore at 0.65 PF and 10 A: ​Q = 230  ×  10  ×  sin(​cos​​  −1​(0.65))=  1747 var​ And at 0.85 PF and 7.647 A: ​Q = 230  ×  7.647  ×  sin(​cos​​  −1​(0.85)) = 927 var​ Therefore, the reactive power needed to make that improvement is 1747 − 927 = 821 var of capacitive load, or leading reactive power. That means a capacitive current of I = var/V = 821/230 = 3.57 A in parallel with the load current.

EXAMPLE 4.24 A 480 V single-phase supply feeds an installation that draws 54 A at a power factor of 0.55. What will the current be if the power factor is improved to 0.8? Determine the kvar rating of the capacitor required to improve the power factor to 0.8.

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P ​F​  ​​ ​I2​  ​​ = ​I1​  ​​  × ​ ____1 ​  ​PF​ 2​​ 0.55 ​ = 54 × ​ ____ ​  0.8

 (1)  (2)

​ = 37.125 A

 (3)

2

​Q1​  ​​ = VI 1 − ​PF​​  ​

 (4) ________ ​ = 480 × 54 × ​  1    − ​0.55​​  2​ ​   (5) ​​       ​ ​     ​  ​ ​  ​  ​  ​  ​  =​  21.6 kvar  (6)​​​

√

​Q2​  ​​ = VI 1 − ​PF​​  2​

_______ ​ = 480 × 37.125 × ​  1    − ​0.8​​  2​ ​ 

√

​ = 10.695 kvar ​QC​  ​​ = ​Q1​  ​​  − ​Q2​  ​​

 (7)  (8)  (9)  (10)

​ = 21.3 − 10.695

 (11)

​ = 10.905 kvar

 (12)

Where the values of reactive power required are economically beyond the range of available capacitors, another means of power factor correction is needed. A type of motor called a ‘synchronous’ motor can, under certain conditions, draw a leading current. Synchronous motors are usually installed in large industrial premises and used to drive air compressors or other similar machines that require a constant service. While doing that, they also provide a leading current to correct or improve the overall power factor. For installations requiring 20 Mvar (20 Mega var) or more of power factor correction, the synchronous motor is often installed without a load connected to it. Then, it is usually called a synchronous capacitor or condenser.

4.12.4  Requirements regarding the power factor of an installation and power factor improvement equipment As we have seen, AS/NZS 3000:2018 outlines the safety requirements for the installation of capacitors. However, as power factor is performance-based (not safety-based), there is little further reference to the subject. The requirements for power factor correction are instead stated in the local supply authority service and installation rules. These are the documents adhered to by supply authorities responsible for the safety, security and maintenance of jurisdictions’ electricity grids. Some of the organisations that produce these rules are private, others are governmental. It varies by jurisdiction. The requirements that apply to the installation of power factor equipment generally only apply to installations that are charged in kVA hours instead of kW hours. These installations have primarily been non-domestic. This situation is changing, though, with the evolution of the grid and the supply of electricity in Australia. The performance factors that generally apply to these rules include: ∙ AS/NZS 3000:2018 should be adhered to for the switching and isolation requirements for capacitor installations ∙ the power factor should be maintained between 0.9 lagging and unity and should never become leading ∙ steps in the kvar rating of the capacitor bank should not be excessive, and should be, for example, limited to 50kvar increments ∙ series resonance should be avoided ∙ harmonics and spikes in the power supply should be avoided and measures put in place to control their effects on the grid and other customers. 261

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4.12.5  Determining power factor The power factor of a circuit can be obtained by using a voltmeter, ammeter and wattmeter. Figure  4.59 shows the circuit for measuring the power factor of a single-phase a.c. motor. The power factor can then be found from: Figure 4.59  Power factor measurement

P  watts  ​Power factor (PF) = ​ __ ​ = ___________ ​     ​​   S  volt-amperes

EXAMPLE 4.25 A single-phase motor draws 2.7 A on 230 V and a wattmeter in the circuit reads 450 W. Find the power factor and phase angle. P PF = __ ​   ​  S

 (1)

450 ​ = ________ ​     ​   (2) 230 × 2.7 ​​     ​ ​    ​  ​  ​  ​  ​  =​  0.72  (3)​​​ φ = ​cos​​  −1​  (PF ) ​ = ​cos​​  −1​  (0.72) ​ = 43.6°

 (4)  (5)  (6)

The power factor can also be measured by using a power factor meter (cos φ), as shown in Figure  4.60. The meter is connected like a wattmeter and the scale is calibrated in values of power factor.

Calculation

Figure 4.60  Power factor meter

In a series circuit, the power factor can be obtained by using the values of resistance and impedance.

Phasor diagrams Another method of obtaining the power factor is by drawing a phasor diagram to scale, measuring the phase angle and then using a calculator to find the Cosine of the angle.

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EXAMPLE 4.26 An inductor draws 20 A on 230 V d.c. and 10 A on 230 V a.c. Calculate the angle of lag when on a.c. V ​Rd.c. ​  ​​ = __ ​   ​  I

 (1)

230 ​ = ____ ​   ​  20

 (2)

​ = 11.5 Ω

 (3)

V ​Zac ​  ​​ = __ ​   ​  I

 (4)

230 =​  ____ ​  ​   ​  (5)​​​ ​​         ​ ​    ​    ​  ​  ​  ​  ​  ​  10 ​ = 23 Ω R φ = ​cos​​  −1​ ​ __ ​  Z

 (6)  (7)

11.5 ​ = ​cos​​  −1​ ​ ____ ​    23

 (8)

​ = ​cos​​  −1​  0.5

 (9)

​ = 60°

 (10)

4.13   Harmonics and resonance effect in a.c. systems 4.13.1 Harmonics All waveforms, with the exception of pure d.c., comprise sinusoidal waveforms. A single a.c. wave has only one sine wave, called the fundamental. All other waveforms, such as triangle and square, have additional sine waves of differing frequency and amplitudes. This perhaps surprising fact can be proven both experimentally and mathematically. Figures  4.61 and 4.62 show the original sine wave, called the ‘fundamental wave’, and two harmonically related waveforms. We will take the 50 Hz fundamental wave to be 50 Hz. In Figure  4.61, the second harmonic is 2 × 50 or 100  Hz at half 50 Hz the amplitude in this case. The third harmonic 100 Hz 150 Hz is at 150 Hz and one-third the amplitude. The contributing waveforms are shown in shades of red. Showing more harmonics would make things unnecessarily complicated. The combined waveform, coloured blue, shows the result of adding the fundamental wave to nine harmonics to produce what becomes a sawtooth waveform. A perfect sawtooth waveform would consist of an infinite number of harmonics. Figure 4.61  Sine waves added to form a sawtooth wave

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Electrical Principles

50 Hz

50 Hz

250 Hz

150 Hz

Figure 4.62  Sine waves added to form a square wave

50 Hz

Ripple caused by interference from 1000 Hz sine wave of 1/20th amplitude

In Figure  4.62, the fundamental wave is added to the third harmonic at 150 Hz at one-third the amplitude; it is added to the fifth harmonic at 250 Hz and one-fifth the amplitude. Here too, the contributing waveforms are shown in shades of red. The combined waveform (coloured blue) shows the result of adding the fundamental wave to nine odd harmonics from the 3rd to the 19th, to produce what you will see becomes a square waveform. A perfect square wave would consist of an infinite number of odd harmonics only. Finally, in Figure  4.63, a 50 Hz waveform is shown experiencing interference from another sine wave 20 times the fundamental frequency or 1000 Hz, at 1/20 the amplitude. We will see later that harmonics can be useful or harmful, depending on how they are applied. Radio and TV would be impossible without them; but their presence in transformers or in the distribution system can cause serious trouble.

4.13.2  Sources in a.c. systems that produce harmonics

Power-consuming loads connected to the electrical grid can be broadly separated into two groups: linear Figure 4.63  Sine wave modified by a 1 kHz sine wave and non-linear loads. Linear loads are generally the older technology that is resistive and/or reactive. This includes heaters, induction motors, halogen lamps and transformers, and these generally have little effect on the shape of the sinusoidal a.c. waveform. Non-linear loads are usually electronic and involve a degree of ‘cutting up’, a term that describes high-frequency switching of the a.c. waveform to achieve different voltage, current and frequency levels. Cutting up the fundamental 50 Hz sine wave results in other frequencies being generated in the supply. Equipment that uses non-linear technology is more modern, efficient and compact. Examples include switched-mode power supplies (in computers and other small electronic appliances), electronic ballasts, electronic low-voltage transformers, variable frequency drives (in motor speed control circuits) and inverters (including solar photo-voltaic and battery types).

4.13.3  Problems that may arise in a.c. circuits as a result of harmonics Harmonics can cause problems that are confusing and hard to diagnose and rectify. These problems can be separated into two main groups: those associated with the harmonic order and those associated with the harmonic sequence. The harmonic sequence group can be split into three smaller groups: positive, negative and zero-sequence harmonics. Positive sequence harmonics include the fundamental, the 4th, 7th, 10th, etc. In motors they produce magnetic and current fields that rotate in the same direction as the fundamental frequency. Negative sequence harmonics include the 2nd, 5th, 8th, 11th, etc and. In motors they produce magnetic and current fields that rotate in the opposite direction to the fundamental frequency. Zero-sequence harmonics include the 3rd, 6th, 9th, 12th, etc. They have no effect on the rotating magnetic and current field but can cause additional I2R power losses in the machine. The harmonic order can simply be divided into two groups: even and odd. Even harmonics tend to cancel each other and consequently have a less alarming effect than odd harmonics. Three-phase non-linear loads produce odd harmonics that are not multiples of three. Single-phase non-linear loads 264

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produce zero-sequence harmonics (3rd, 6th, 9th, etc.) accompanied by other odd order harmonics. The odd harmonics that are multiples of three (3rd, 9th, 15th, etc.) in three-phase systems can combine in the neutral and cause it to heat up. Other effects of these third-order harmonics include overheating the supply transformer and nuisance-tripping circuit protection devices. The main ways of overcoming the effects of harmonics on an electrical installation are: removal of the source; increasing the neutral conductor size in three-phase systems or supplying each phase with a separate neutral; and the use of inductor/capacitor filters that can be tuned to reduce harmonic current flow at desired frequencies. The inductors that are used for this are called ‘line reactors’.

4.13.4  Methods and test equipment used to test for harmonics Harmonics can be measured with oscilloscopes, power analysers or clamp meters. Using an oscilloscope or power analyser, harmonics can be detected either by looking at the wave shape or by analysing the harmonic order. The clamp meter option involves comparing the difference in the neutral current and requires the use of two meters, a standard RMS clamp meter and a clamp meter with multiple frequency and true RMS capabilities. The difference between the readings from each device will indicate if there is any harmonic, as compared with out-of-balance current.

4.13.5 Resonance When an electrical circuit has its power factor corrected to unity, the current is brought into phase with the voltage. Although it could still contain both capacitive and inductive reactances, it behaves as a purely resistive circuit. Capacitive reactance and inductive reactance are both determined by the frequency. When they are exactly equal, the circuit is said to be ‘resonant’. Resonance is the frequency that conserves energy. At resonance, energy passes back and forth between the reactances at the resonant frequency, just as a bell rings at its resonant frequency. In both series and parallel resonant circuits, capacitive reactance is equal to inductive reactance. The energy stored in the magnetic field of the inductor for one part of a cycle is transferred to the electrostatic field of the capacitor in the next part. This energy transfer produces different effects in series and parallel circuits.

4.13.6  Series-circuit resonance Since at resonance XL = XC, then XL − XC = 0 That is:

___ ​Z  = ​ √ ​R​​  2​ ​  or Z  =  R​

As the impedance is equal to the resistance, the current flow from the supply will be calculated by Ohm’s Law as I = V/R. However, as the same current will flow between the inductor and the capacitor, the reactive components will generate voltages according to Ohm’s Law and the reactance of each component: V = IXL = IXC. The voltage across the reactive components will cancel each other out. But the voltage on each will be equal and may be many times the circuit terminal voltage. The major characteristics of the series resonant circuit are a power factor of unity and a minimum impedance: _______________ ​Z  = ​ √  ​   R​​  2​  + ​(​XL​  ​​  − ​X​ C​​  )​​  2​ ​​ The series resonant circuit should be avoided for general electrical work, unless special precautions are taken. One precaution is ensuring that adequate series resistance is in the circuit, if necessary adding resistance to ensure that the current (and therefore the voltage across the reactors) is limited. Where circuits are operated such that voltages higher than the supply voltage are generated, the circuit must be insulated for those higher voltages and suitably rated components must be selected. 265

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EXAMPLE 4.27 A 10 Ω resistor, 0.25 H inductor and a 40.52 μF capacitor are connected in series across a 230 V 50 Hz supply. Calculate the current flowing in, and voltage drop across each component. R = 10 Ω  (1) ​XL​  ​​ = 2πfL  (2) ​ = 2 × π × 50 × 0.25  (3) ​ = 78.54 Ω  (4) 1 ​XC​  ​​ = _____ ​     ​   (5) 2πfC 1 ​ = ___________________ ​         ​  (6) 2 × π × 50 × 40.52 × 10−6 ​ = 78.54 Ω  (7) ____________ Z = ​  ​R      ​​  2​  + ​(​XL​  ​​  − ​XC​  ​​  )​​  2​ ​  (8) ___________________ 2 2 ​ = ​  ​1      0​​  ​  + ​(78.54  −  78.54)​​  ​ ​  (9) ​ = 10 Ω  (10) V ​​                          ​      ​  ​  ​  ​  I     =​  __ ​   ​ ​ ​ ​ ​  ​ ​ ​  ​  ​ ​ ​  ​   (11)​​​ Z 230 ​ = ____ ​   ​   (12) 10 ​ = 23 Ω  (13)

√ √

​VR​  ​​ = IR ​ = 23 × 10 ​ = 230 V

 (14)  (15)  (16)

​VXL ​  ​​ = ​IX​ L​​ ​ = 23 × 78.54 ​ = 1806 V

 (17)  (18)  (19)

​VXC ​  ​​ = ​IX​ C​​ ​ = 23 × 78.54 ​ = 1806 V

 (20)  (21)  (22)

A useful characteristic of the series resonant circuit is that the capacitive reactance is equal to the inductive reactance at only one frequency. Other frequencies above or below resonance experience higher impedances due to the reactance no longer cancelling out. They will therefore be attenuated. Knowing that at resonant frequency (f0), XC and XL are equal, the formula for resonant frequency can be developed, as: ​XL​  ​​ = 2πfL 1 ​XC​  ​​ = _____ ​     ​  2πfC at resonance ​ X​ L​​ = ​XC​  ​​ 1 ∴ 2πfl = _____ ​     ​  2πfC    ​​        ​  ​  ​  ​  1  ​​​ ∴ f × f = _________ ​     ​  2πL × 2πC 1 ∴ f = ​  _______ ​     ​ ​  2πL2πC 1 ∴ f = _______ ​     ​  2π√LC

√

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where: f = resonant frequency XL = inductive reactance XC = capacitance reactance

4.13.7  Parallel circuit resonance

1000

AS/NZS 3000:2018 and local service installation rules have strict guidelines about equipment that might generate harmonics. In AS/NZS 3000:2018, the main guidelines relate to the current rating and associated particular

1 FR = 2π LC 1μF 1000 Ω 1H

0

4.13.8  Standards relating to harmonics

Impedance (Z) in Ω 2000 3000

4000

When an inductor and capacitor are connected in parallel and their respective reactances are equal, the reactive currents are equal, but are 180° out of phase with each other. Theoretically, the current drawn from the supply would be zero, while a comparatively high circulating current would oscillate between the inductor and capacitor at the supply frequency. But in practice, though, an inductor has some finite value of resistance. The parallel resonant circuit appears as a pure resistance, and some current in phase with the voltage would flow from the supply. The resonant frequency in a parallel circuit with zero resistance is found using the same formula as for series resonant frequency. For a practical circuit, inductive reactance is actually a series circuit of resistance and inductive reactance. Although the resonant frequency of a parallel resonant circuit is not exactly as calculated from the series formula, the difference may be less that any error in calculation. For parallel resonant circuits operating on very high frequencies, the inductive reactance can be achieved with very short lengths of conductors. The resistance can then be ignored. When the supply frequency to a parallel resonant circuit is varied, the resistance in the circuit is unchanged. But the impedance will be a maximum only at the resonant frequency. At resonance, energy is being transferred from the electromagnetic field to the electrostatic field and back again via the circulating current. The circulating current cannot be related to the input current from the supply. The supply current at resonance is at a minimum because the impedance is at its maximum. The current is sufficient only to make up the losses in the circuit. The lower the losses, the lower the value of input current. In electronic circuits, a capacitance in parallel with an inductance can be used to get the highest possible impedance for a particular frequency across that parallel section. Making either the capacitor or the inductor adjustable means a particular resonant frequency can be chosen. When a variety of frequencies (such as different radio stations) is presented to a parallel circuit, only the resonant frequency is passed to the next part of the circuit. (This is the method used in tuning a radio to a set frequency.) In other words, the non-resonant frequencies are presented with a low-impedance path to earth and are thus removed from the circuit. Test equipment sometimes uses the principle of parallel resonance for measuring capacitance. Frequency-dependent transducers use the phenomenon as a means of monitoring and Z for R = 1000 Ω regulating frequency. Other circuits use the property Z for R = 0 Ω of resonant circuits as a metal detector.

0

25

50

75

100

125

150 175 200 Frequency in Hz

225

250

275

300

Figure 4.64 

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size of the conductors. This is especially important in the neutral conductor, where these harmonic currents can be cumulative. Clause 3.5.2 outlines these requirements. It notes that a harmonic current bigger than 40% of the phase current is enough to warrant a change in the cross-sectional area of the conductor(s). It also explains that the third harmonic can make it necessary for a neutral that is larger than the associated actives to carry the harmonic current. The service and installation rules focus more on the effect that harmonics have on the network and other customers. These include switched mode power supplies and there are requirements for inverters to be limited. This is to prevent harmonic distortion (which changes the RMS values) and other unwanted effects such as data corruption and frequency relay switching.

4.13.9  Standards relating to resonance AS/NZS 3000:2018 and the service and installation rules set requirements about the effects of resonance in an installation. Series resonance can cause overvoltage within the circuit, which would be a safety concern. AS/NZS 3000:2018 clauses 1.5.11 and 2.7 state that, where danger to persons or property can occur, the installation should be protected to prevent harm from overvoltage. This requirement can be satisfied by either insulation/separation or by protective devices. Parallel resonance can cause excessive currents and conductors carrying them need to be sized correctly. The service and installation rules generally require some measures to be in place to avoid resonance with the network that can cause high inrush currents. Effective measures include de-tuning reactors and resistors.

4.14   Three-phase systems 4.14.1 Introduction Three-phase electricity is the standard for power generation, distribution and industrial use around the world. d.c. is still used, and single-phase a.c. is commonly used in domestic and many commercial situations. Two-phase electricity has mostly disappeared, except for centre-tapped SWER transformers. Many industrial electricians will work on three-phase plants, motors and transformers for most of their working day. Others will work on three-phase motors, refrigeration and air-conditioning units. Having three phases is the natural way of producing electricity. It is very efficient. Having more than three phases is bad economics.

4.14.2  Efficiency in generation and distribution The alternating-current electrical system has some major advantages over direct current (d.c.), but it has one considerable disadvantage: low efficiency in generation, distribution and machine loads. This is a result of the voltage and current passing through zero twice each cycle. When no voltage is generated, no power is delivered. That equals wasted time. Power taken from the driving machinery also decreases to zero one hundred times per second, creating 100 Hz mechanical vibrations in the machine (see Figure 4.65). One way of improving a.c. efficiency is by generating a second a.c. voltage so that the peak of the second waveform occurs at the same time as the zero crossing of the first. This is called a ‘two-phase’ system. Generating two a.c. voltages at 90° phase angle to one another improves the efficiency to 90%. This might lead us to wonder what happens if another phase is added (see Figure 4.66). Instead of a phase angle of 90°, three phases would need to be balanced across 360° (360°/3 is 120°, which is mathematically the best phase angle difference for three-phase power). The three-phase (or 3Ø) system has an 268

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efficiency of around 96% (see Figure  4.67). There is no disadvantage to using three phases instead of two as a two-phase system requires at least three wires and usually uses four. The same applies to three or four wires. That is why two-phase systems are so rare today. Systems using more than three phases require an extra wire for each extra phase. So, although they slightly increase efficiency, they also increase the costs of transmission and distribution. The threephase system is the most efficient yet economical system. (Systems with more than one phase are called ‘multiphase’ or ‘polyphase’.)

4.14.3  Power efficiency and number of phases The power output of an a.c. generator (also called an alternator) is limited by the mechanical power delivered by the machine. If you ignore the other losses for the sake of this discussion, then the efficiency is given by: Output  ​Efficiency % = _________________ ​   ​​  = ​  ×  10​0  Input

Lost efficiency Power generated

Voltage

Figure 4.65  ac sine wave showing power lost Lost efficiency Power generated VA

VB

Figure 4.66  Total power with a second phase

In theory, a perfect machine would work at full Lost efficiency output over the full cycle of generation, and therefore the full revolution of the driving machine.  The only real Power generated generator that does this is a pure d.c. generator. In fact, VB VA VC all generators, d.c. included, generate a sine wave in the individual conductor. This is because it rotates within a magnetic field. d.c. generators approximate a d.c. voltage by using many coils of wire that are switched by a commutator so that the current always flows in the same direction in the external circuit. d.c. is approximated by using 12 or more phases, each being generated by its own coil. Perfect d.c. power Figure 4.67  Total power with a third phase is mathematically the same as an alternator using an infinite number of phases. A phasor diagram helps to understand the efficiency of an alternator. But as phases represent rotating vectors, no phasor can represent d.c.. The d.c. must be shown as the result of an infinite number of phases. In Figure 4.68, d.c. power is represented by the semicircle. The reason for this will become clear as we work through polyphase systems. The straight line (P1) that passes from the bottom to the top of the semicircle represents the power produced by a single-phase a.c. generator. This does not tell us much yet but when the power phasors for a two-phase system, a three-phase system and a four-phase system are viewed, the losses are represented by the difference between the semicircle and the phasors for that system. The power phasors P2, P3 and P4 respectively show the individual phase power that must be added vectorially to be equal to the power of the single-phase system. The phasors for each system with an increasing number of phases approximate the semicircle more accurately. The efficiency is represented by how accurately the phasors approximate the semicircle. 269

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d.c. in a phasor diagram can be drawn as a circle, or in the case of power is represented by a semicircle where the diameter is the power of a sine wave of the same (RMS) voltage. Therefore the efficiency of the sine wave is determined by the ratio of vector lengths: Psine Eff = ——— x 100% Pd.c.

P3 P3

P1 P3

1. Single-phase alternator (1 phase)

P1

PDC

Generated power = P1(proportional to vector P1) Average power in an ac system is 63.7%. 2 x 100%. i.e. P1 = 2 Radii, Pd.c. = π Radii. Eff = — π In a single-phase system therefore, the generation efficiency is 63.7% of the peak power. In the following multiphase systems, each generated power is a sine wave and therefore all values should be multiplied by 2 63.7% = 0.637 = — π.

P2 P1

P2

2. Two-phase alternator (90° phase difference) Generated power = P2 (in two windings added vectorially to equal P1) The phasors are at 90° to each other, and 45° to P1, P so the power = 2 x —1 (added vectorially) 2 Total power = 2 x P1 = 1.414 P1 2 x 2 = 90% Power efficiency = — π That is, total available power output for a two-phase machine is 90% efficient or 26.3% greater than the single-phase machine.

P4 P4 P1

P4 P4

3. Three-phase alternator (120° phase difference) Generated power = P3 in each of three windings; (added vectorially to equal P1) The three phasors are at 120° to each other, one parallel to P1 and two at 60° such that the vector sum becomes ... P3 P3 1 —— — P1 = — 2 + P3 + 2 = 2P3 or P3 = 2 P1 3 Total power = — 2 P1 2 3 Power efficiency = — πx— 2 = 95.49% (˜96%) That is, total power available is 95.48% or 50% greater than that for a single-phase machine. 4. Four-phase and greater… In general terms, efficiency is the vectorially added lengths of each of the phases divided by the length of the d.c. arc, which is π Radians or 180°. Using the laws of trigonometry, a formula can be derived to calculate the efficiency of any number of phases (n) … π Sin( — n) Eff = n/π x 100% π Sin((π– — (Radians) n )/2 Therefore: Four-phase Eff = 97.45% Five-phase Eff = 98.36% Six-phase Eff = 98.86% Ten-phase Eff = 99.59% 100-phase Eff = 99.996% The increases in complexity and costs outweigh the increase in efficiency.

[

]

Figure 4.68  Phase systems comparison

4.14.4  Two-phase systems In a two-phase system, two coils are physically displaced by 90° mechanical (written as ‘90°M’), as shown in Figure 4.69; the result is that the two output voltages have a 90° electrical phase difference (written as ‘90°E’). Three-phase systems are more efficient and have almost completely replaced two-phase systems in Australia, although there may still be SWER systems in use to supply rural properties on the fringe of the electrical grid.

4.14.5  Three-phase systems A three-phase system has three generating windings, each out of phase with the other two by 120°E. Figure 4.70(a) illustrates a simplified three-phase alternator with three windings A, B and C at 120°E intervals. Figure 4.70(b) shows the waveforms generated by the three windings, illustrating the phase shift between waveforms. Figure 4.70(c) shows the phasor diagram of the three phasors. The phasor of the A-phase voltage VA is shown as the reference phasor. This is drawn horizontally to the right, i.e. at 0°. The phasor of the B-phase voltage VB is drawn 120° after VA, putting it at the bottom left of the diagram. The phasors rotate in a counterclockwise direction, so lagging phasors are clockwise from the reference phasor. The phasor of the C-phase voltage VC is drawn 240° after VA. This puts it at the top left of the diagram. It is also 120° counterclockwise from VA, which completes the cycle.

Advantages of a three-phase system 1. For the same size or weight, a three-phase machine can produce higher outputs than a single-phase machine. 2. A three-phase machine can be smaller than a single-phase machine for the same power output. 3. The power delivered to (or taken from) a three-phase system has a more constant value. In a single-phase system, the power pulses at twice the line frequency. With three phases, the power pulses are six times the line frequency, with far less amplitude than single-phase power. Since the power is more constant, the torque of a rotating machine is more constant. This results in much less vibration from the machine. 270

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4. With one type of three-phase connection, there are two voltages available: 230 V and 400 V. 5. In a distribution system, the total quantity of material needed for three conductors is less than that required for the equivalent singlephase system. This is due to higher efficiency.

4.14.6  Generating a three-phase supply A three-phase supply is produced by an electric machine that contains three windings. These windings are separated by 120°E, as shown in Figure 4.70. This causes them to naturally produce three voltage waveforms 120° apart. The three phases follow in a fixed sequence, known as the ‘phase sequence’ or ‘phase rotation’. First, the three phases must be identified to allow the sequence to be stated and loads to be balanced across them. In some applications, the letters A, B and C are used as A-phase, B-phase and C-phase. For general-purpose supply and distribution identification in Australia, the phases are given the colour coding red, white and blue (prior to 1981, the colours were red, yellow and blue). As the phasors rotate, they pass through the reference position in the order red, white, blue. This sequence must be followed in connecting equipment on three-phase circuits, so that motors rotate in the expected direction. When three-phase phasors are drawn, the usual practice is to draw the red phasor (A) in the reference position; if it helps, either the white (B) or the blue (C) phasor may be used as the reference as long as the sequence is still correct. Phases may also be marked as L1, L2 and L3, meaning Line 1, Line 2 and Line 3. European standards often use U–V–W or u–v–w to represent the three phases.

Three-phase winding arrangements

VA phase VB phase

VA VB

VA

VA–B

VA–B (If A and B are joined at one end of each winding.) VB

Note that at any instant in time, VA–B is equal to VA plus VB

Figure 4.69  Two-phase system

Figure 4.70  A three-phase machine

24-slot stator wound as 24 coils in sets of 2 coils per pole per phase, ie... 2 x 3 phases x 4 poles = 24 coils.

Unlike d.c. machines, the poles in a three-phase machine generally overlap. This is a factor in balancing the current and power of a three-phase machine. Figure 4.71 shows a typical 24-slot stator lamination set. To use this for a three-phase, four-pole electric Figure 4.71  A three-phase induction motor winding motor, there must be three sets of coils for four poles fitted into 24 slots. (Four-pole here means that there are four sets of coils (poles) for each phase.) This would usually result in a winding of 3 × 4 × 2 coils, meaning that two coils form one pole for one phase. Phase A is drawn in red, with one side of the coils on the outside and the other on the inside of the laminated stator. Phase B is white and phase C is blue. The motor is four-pole. Each phase occupies one-third of the total number of slots. A four-pole machine has 720°E in one complete rotation (360°M). 271

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4.14.7  Three-phase machine alternator construction An alternator basically consists of coils rotating in a magnetic field. There is a more advantageous form where the a.c. windings are stationary and the magnetic field system rotates. The same principles apply to both single- and three-phase alternators. The only real difference is whether there is one winding or three identical windings.

4.14.8  Three-phase sine wave construction The construction of the three sinewave curves for a three-phase system follows the same method as that of a single sine wave (discussed previously). The phase displacement of 120°E between the phases has to be factored in. The conventional sine wave set for three-phase is illustrated in Figure 4.72. The sine waves for the B- and C-phases are the same sine wave drawn 120° and 240° after the A phase. An alternative method, as used in this book, is to use a computer program to draw the three phases. Grapher or Plot are suitable programs, but an internet search should locate free software.

4.14.9  Three-phase connections Three-phase voltages are produced by mechanically interconnecting three sets of windings to form a three-phase a.c. source. (As there are three separate voltages, each could be used as a single-phase source.)

4.14.10  Phase sequence If a magnet is rotated anticlockwise within the coils in Figure 4.71, the voltage generated in each set of coils will reach a positive peak value in the order red–white–blue (or ABC, in which case the alternator is said to have a phase sequence of ABC). If the magnet were driven clockwise, the phase sequence would be ACB. In a threephase system, where the three voltage sources are connected to feed a three-phase load, the phase sequence can be important. This is the case in rotating machinery, as the sequence can affect the direction of rotation.

4.14.11  Determining the phase sequence of a three-phase supply By convention, the phase rotation produced by a set of windings U1/U2, V1/V2, W1/W2 will produce a phase sequence ABC, as described above. But in a complex system such as an electrical grid, this sequence can become mixed up. So, to maintain a safe operating system and prevent short circuits, voltage checks must be made. These should also be carried out to ensure that all connections (both those within the grid and those to installations and loads) have no potential difference between them. For example, if a conductor labelled as A or red phase is to be connected to a parallel conductor that is also labelled as A or red phase, the voltage between the two conductors should be zero. This is because both are at the same potential. But if the marking of one of the cables was incorrect, a voltage of 400 V would be present across the two cables. It is also important to maintain phase sequence within an installation where three-phase machinery is to be connected in multiple places. It is especially important when the equipment is connected via a plug and socket: if the phase sequence is the same throughout the entire installation, when equipment is connected to different sockets, the machine will still rotate in the same direction. A-Red B-White C-Blue A phase rotation meter can be used to determine the phase sequence of an installation. The analogue version of this device is a three-phase motor that simply rotates clockwise or anticlockwise, depending on the sequence of the socket it is connected to. Ensuring that the meter rotates in the same direction when connected to the same conductors in each socket means that each Figure 4.72  Three-phase waveforms socket will have the same phase rotation. 272

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4.15   Three-phase star connections 4.15.1  Three-phase star connections One method of forming a three-phase system is to connect the three similar ends of the windings together, as shown in Figure 4.73(a). Either the start or finish ends of the windings can be used. The three phases are said to be ‘star connected’ (or ‘wye connected’), and the common connecting point is called the ‘star point’, due to the shape of the diagram. An alternative method of drawing and labelling the windings is shown in Figure 4.73(b). Once again, similar ends are connected to the star point. The three actives (or lines) are connected to the phase windings A, B, C, as shown in Figure 4.73(b). The voltage across these lines is called the ‘line voltage’ (Vline or VL). The current flowing through the lines is called the ‘line current’ (Iline or IL). The neutral, which is common to the three actives, is connected to the star point. (The neutral is usually earthed and is not considered to be a line.) The voltage across a single-phase winding is called the ‘phase voltage’ (VP). This distinguishes it from the line voltage. The line voltage is not equal to the phase voltage, as two phase windings are connected across each pair of lines. The current flowing through the phase winding is called the ‘phase current’ (IP). The three phases are shown in Figure  4.74 as red, white and blue (or A, B and C). The line voltages are shown as A–B, B–C and C–A, with appropriate amplitude and phase angle to the phase voltages. The line voltage at any point in time is the voltage between the two-phase sine waves. So VA−B is equal to VA − VB. A ruler or dividers can be used to check this. The greatest voltage difference occurs at 30° before the first named phase voltage reaches maximum. VA−B maximum occurs at 60°, while VA is maximum at 90°. This is the conventional sequence, but if the line voltages are given as A–C, C–B and B–A, the line phasors will be 180° to those shown. Nothing will be changed electrically, as this is simply a naming issue.

When coil polarity is important, a dot denotes the start of the winding C A

B

C

C A

A

B

(a)

(b)

B

(c)

Figure 4.73  Three-phase star (wye) connection

C

Vphase

C

A

A

Vline B

B

A–B

B–C

A-Red

C–A

B-White

C-Blue

Figure 4.74  Phase vs line voltage

−VA VC−A

VA−B

VC VB

−VB

VA

VB−C −VC

VA−B = VA − VB = 1 0° − 1 120° = 1 0° + 1 60° = 1.732 30° i.e.= 3 30°

Figure 4.75 Vline to Vphase ratio

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VA–B VB–C VB –VC

–VB

VA VA–B

VC–A

VC

VC–A

–VA VB–C If VC is reversed, VA–B is unchanged, but VB–C and VC–A are the same value as phase voltages and 90° to their previous phase angles. (Original phasors in grey.)

Figure 4.76  One phase reversed

Line A is in series with winding A, so the current is the same. There is only one path for the current. As this applies to all three phases, in a star-connected system the line current equals the phase current: ​For a star (wye) system :  ​I​ L​​ = ​I​  P​​​ Vline is equal to the phasor difference between the two phase voltages. This can be estimated graphically or calculated accurately by phasor (vector) addition. Using the methods shown in section 4.5.3, the two-phase voltages are subtracted to show that the line voltage is 1.732 of the phase voltage and leads the phase voltage by 30°.

4.15.2  Effect of phase reversal on a star system If one phase winding is reversed, the start ends of the three windings are now no longer 120° apart. If phase winding C is reversed, for example, the phase voltage of C has a phase shift of 180°. The waveforms of the three-phase voltages then have a displacement of 120° between A and B, and 60° between A and C and C and B, as shown in Figure 4.76. Although the phase voltages are equal, they are not in the correct phase sequence. Two of the line voltages are reduced to the same value as the phase voltages. The load is no longer balanced and motors will be likely to run backwards.

4.16   Three-phase, four-wire systems 4.16.1  Purpose of the neutral conductor in a three-phase, four-wire system In a balanced three-phase, four-wire system there is no need for a neutral. This is because these systems have equal current flowing in and out of each of the phases. As a result, the phase voltage of each phase will also remain equal across each phase. If the single-phase load that is connected to each phase is identical, to meet the voltage requirement of these loads they simply need to be connected to each phase and joined together at their tails. However, if each of the single-phase loads is different, a different phase voltage will be present on each phase. For this reason, the star point of the loads is connected to the star point of the supply via the neutral conductor. This provides a zero-volt point for each phase and maintains the voltages, regardless of the loads. The neutral conductor also provides a current path for the unbalanced load current where the phasor difference of the three phases is the magnitude of current flowing in the neutral.

4.16.2  Effects of a broken neutral With single-phase loads on three-phase, four-wire systems, the neutral must not be open circuited. One major reason for this is personal safety. With equipment operating on one phase at 230 V, an open-circuit neutral can prevent it from working. Although the equipment appears to be without power, it still has the active conductor connected. A person could contact the active conductor, complete the circuit via the body to earth and be electrocuted. With the Multiple-Earthed Neutral (MEN) system, a break in the neutral can also create a hazard. The potential of earthed appliances can sometimes rise to levels approaching that of the mains voltage. 274

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4.16.3  Balanced loads

Infinite grid frame

40 0V

With three-phase unbalanced loads, a broken neutral has several effects. The voltage across the lightest load increases; the voltage across the heaviest load decreases; and the voltage across the third phase may shift either up or down. At the same time, the power factors of the individual line currents may also be affected. Any load located before the neutral break is not affected. Singlephase loads and unbalanced three-phase loads after the break will be affected. These are illustrated in Figure 4.77. To prevent the neutral from being opencircuited, neutral switches and links in substations are often locked or bolted. Neutrals are never fitted with fuses under normal installation conditions.

230V 20W

>230V >230V

360°

With balanced loads, the line currents are 120° out −0.5A of phase with one another. Figure 4.78 shows the waveform diagram for a balanced load with three−1A phase currents, IA, IB and IC. I K L M At the point K, the current IA is a maximum at +1 A and the currents IB and IC are both −0.5 A. Figure 4.78  Current in a balanced system At point L, the current IA is zero, IB is +0.866 A and IC is −0.866 A. Although the three currents are all changing in value and direction, the phasor sum of the instantaneous currents is zero (IA + IB + IC = 0). Therefore, the current flowing through the neutral in a balanced circuit is also zero. The same result can be obtained from the phasor sum of the line currents using RMS values. Two types of load can exist in a three-phase system: balanced and unbalanced. If the current and phase angle in all three phases are equal, the system is ‘balanced’ or a ‘balanced load’. These are typically individual threephase loads where the impedance of each phase is the same. Examples include three-phase motors and heaters. (see Figure 4.79) If the current and/or phase angle of each of the single phases are not equal, the system is called ‘unbalanced’ or an ‘unbalanced load’. Examples include a three-phase main switchboard and three-phase distribution for houses (see Figure 4.79). This is more common in three-phase systems, where multiple combinations of single-phase equipment are connected and a complete balance is unlikely. While a balanced three-phase system should always be the ultimate aim, local service rules have a degree of tolerance for unbalanced loads For a balanced load (e.g. a three-phase motor) the neutral current is zero. This means the neutral wire is unnecessary and is usually omitted unless it is needed for control devices. If a distribution system is subject to load changes on one phase, this puts the system out of balance. A neutral conductor must be installed. The two requirements for a balanced load are: there must be the same current loading on each phase; and each current must have the same power factor. When both requirements are met, the neutral current is zero. When the two conditions for balance are not met, a system is said to be ‘unbalanced’ and a current may flow in the neutral (see Figure 4.80). By convention, the generated voltage is assumed to be positive when acting from the star point to the line terminal. The phase current is also regarded as positive when flowing in the same direction. The value of IN is equal to the phasor sum of IRA, IWB and IC, but the direction of current flow in the neutral wire is reversed. 275

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Electrical Principles

Typical balanced loads

Typical unbalanced loads

3 Phase motor

3 Phase main switch board

2Ω @ 0.6

2Ω @ 0.6 2Ω @ 0.6

L1 P1 P2

Stove

L2 P3 P4 Air con.

Heater P5 P6 Hot water

3 Phase hot water heater 3 Phase distribution 12Ω 12Ω

12Ω

A B C N

House 1

House 2

House 3

House 4

Figure 4.79  Example of a balanced and unbalanced load

The current in a neutral conductor of any threephase, four-wire system is equal to minus the phasor sum of the line currents.

vC IC

— ​​I​ R ​​​ =

—

—

—

−[​​I​ R ​​​   + ​​I​ W ​​ ​ + ​​I​ B ​​ ​ ]

The bar ‘—’ in the formula above represents vector quantities. IA + IB + IC

θC 180° IN

IA

θB

IB

IA + IB

vB

Figure 4.80  Neutral current in an unbalanced three-phase system

vA

4.16.4  AS/NZS 3000 requirements regarding neutral conductors Clause 3.5.2 of AS/NZS 3000:2018 states that the current carrying capacity and associated cable size of the neutral conductor shall be the same as the active conductor for single-phase circuits and the same as the largest associated active conductor. The harmonic content of the load supplied by multiphase mains, submains and final subcircuits must also be considered, especially the third

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EXAMPLE 4.28 Find the value of current flowing in the neutral conductor in a three-phase, star-connected distribution system where the phase currents are: A phase 125 A at PE 0.79 lagging power factor B phase 147 A at PE 0.85 lagging power factor C phase 215 A at PE 0.80 lagging power factor Step 1. Convert power factors to phase angles (Note that lagging is negative.) ​φA​  ​​ = c​ os​​  −1​  0.79 ​ = − 37.8°

 (1)  (2)

​ B​  ​​ = ​cos​​  −1​  0.85 φ  (3) ​​     ​      ​  ​  ​  ​  ​​​ ​ = − 31.8°  (4) ​φB​  ​​ = ​cos​​  −1​  0.80

 (5)

​ = −36.87°

 (6)

Step 2. Select an appropriate scale to draw the three-phase phasor diagram (e.g. 2:5) Step 3. Using VA as a reference, plot all three-phase voltages with a phase displacement of 120° Step 4. Plot IA lagging VA by 37.8° Step 5. Plot IB lagging VB by 31.8° Step 6. Plot IC lagging VC by 36.87° Step 7. Add the two phasors IA and IB Step 8. Add the phasor IC to the resultant of the addition of IA and IB. Step 9. Plot in 180° in the opposite direction of the resultant of the sum of IA, IB and IC. This is the current phasor for IN. Step 10. Measure the angle between IN and VA (the reference) and scale the measured value of IN to get the resultant – IN = 69A ∠ 102° VC

IC

IA + IB + IC θC θB IB

θN θA

VA

IN IA

IA + IB

VB

Figure 4.81  Calculation of neutral current in an unbalanced three-phase system

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Electrical Principles

harmonic and odd multiples of the third, which can result in higher current in the neutral. In the instance of these harmonic current the neutral conductor must be sized accordingly to accommodate these currents. The neutral conductor of a multiphase circuit can also be reduced in size as long as there is either a detection device connected and arranged to prevent the neutral current exceeding the current carrying capacity, or the multiphase circuit is predominantly supplying multiphase equipment and the current carrying capacity of the neutral is not exceeded by out of balance and harmonic currents.

4.17  Three-phase delta connections and interconnected systems 4.17.1  Three-phase delta connections The windings of a three-phase alternator can also be connected as shown in Figure 4.82(a). This forms a closed loop with dissimilar ends joined, and the lines are connected to the junctions. An alternative method of drawing the windings and connections is shown in Figure 4.82(b). This system is called a ‘delta’ connection because of the similarity in shape with the Greek letter Δ (delta). Each phase winding is now connected across a pair of lines, so the phase voltage is equal to the line voltage: For a delta system: VL = VP Each phase winding is also connected in parallel across the other two phase windings, which are in series with one another. A quick check should confirm, however, that the vector sum of the other two windings is equal in voltage and phase to the first winding, noting winding polarities. The phase currents in Figure  4.83 are IA, IB and IC and the line currents are I1, I2 and I3. If the phase currents are of equal value, then by vector addition the C–A C line current is equal to √3 times the phase current: A

B

C A–B B

A

(a)

(b)

A star connection gives the line voltage a phase shift, causing it to lead one of the phase voltages by 30°. A delta connection causes the line current to lead one of the phase currents by 30°. This effect is put into use when larger numbers of phases are required (as with large industrial rectifiers, where filtering costs become prohibitive).

Figure 4.82  Three-phase delta connections

IC

A

L1

IA

−IB IA–B = IL2

IC C

IB

IB

IA B

(a)

L2 L3

That is, IL = √3IP (delta). Also IA − B leads IA by 30°, so IL leads IP by 30°.

(c)

B–C

For a delta system: IL = √3IΡ

IA 30°

IB

4.17.2 Limitations and uses of open delta connections

IC (b)

Figure 4.83  Line current versus phase current in delta

Three-phase systems can be connected by using two windings. The start of one winding is connected to the end of the other. The three phases are connected

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to each free end of the windings and this junction. This form of connection is referred to as ‘open delta’ or ‘v’ connection. It is relatively cheap as only two windings are required. However, as the power in a closed three-phase system is: ​​P3phase ​  ​​  =  √3  × ​V​ L​​  × ​I​ L​​  ×  pf​ Or ​​P3phase ​  ​​ = 3  × ​V​ L​​  × ​I​ P​​  ×  pf​ (note: VL = VP in a closed delta system) and as the path for current in an open delta system is limited to √3 IP with one of the windings missing. This equates to a power of: ​​Popen delta ​  ​​  =  √3  × ​V​ L​​  × ​I​ P​​  ×  pf​ So, the ratio open to closed delta equals: √3  × ​V​ L​​  × ​I​ P​​  ×  pf ________________ ​​         ​​ 3  × ​V​ L​​  × ​I​ P​​  ×  pf

and as VL × IP × pf cancels out on both sides the ratio is: √3 ___ ​​   ​​    3

which equals 57.735%.

Primary – closed delta

Secondary – closed delta IL

IL

A

a VL

VL IP

IP

C

c b

B Primary – open delta

Secondary – open delta

IL

A

IL

VL

a VL

IP

IP

C

c

B

b

Figure 4.84  Open delta connection

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Electrical Principles

A

400V

400V

So, the major limitation of an open delta system is that it is only able to deliver 57.735% of the power of a closed delta system. Although this limits the uses of the system, it does provide a cheaper option when initially installed. It can be upgraded to a closed delta system later.

400V

400V 800V (a)

C

B (b)

4.17.3  Effect of phase reversal on a delta system

If the ends of one-phase winding are reversed, a phase shift of 180°E occurs. This causes the voltage on that phase to be added to the sum of the other two phases. This in turn produces a voltage that is twice the phase voltage. In a 400 V delta system, the resulting voltage is not zero, which would allow the delta loop to be closed safely; it is in fact 800 V which, if closed, would cause a circulating short circuit and a very large current to flow. The phasor diagrams for line currents I2 and I3 are identical but naturally 120° phase shifted. Because this higher voltage is generated within the closed circuit of the windings, heavy circulating currents will flow in them, causing them to burn out quickly. Great care must be taken when the phase windings are connected in delta to ensure that dissimilar ends are joined. A simple method of testing the connections is to leave one junction open, as shown in Figure 4.85, and connect a voltmeter across the open winding ends. If the connections are correct, the voltmeter will read zero. If one phase winding is reversed, the meter will register a voltage equal to twice the phase voltage. Figure 4.85  One-phase reversed

4.17.4  Loads in typical power systems Three-phase power systems are connected in star or delta, depending on circumstances and requirements. Where the load current in each phase has minimal difference, delta systems are used as they require one less conductor. Examples include generators, motors and high-voltage transmission and distribution systems. Alternatively, star-connected systems are used where there is a higher difference between phase currents and where single-phase loads are required. For this reason, all low-voltage consumer supplies and associated distribution systems are connected in either four-wire, three-phase or two-wire, single-phase. Some older low-voltage supplies also were connected with two phases using three-wire (two phases and neutral). Star- or delta-connected systems are also used to vary the output of a three-phase load or restrict start-up and inrush currents in motors. In Figure 4.86, the top diagram is of a three-phase delta-connected motor supplied from a star-connected threephase 230/400 V supply. As the impedance of each winding of the motor is 10 Ω, the current can be determined in each winding of the motor: ​Vsupply line ​  ​​ ​Imotor phase ​  ​  ​​ = _________    ​  ​Zmotor phase ​  ​​ ​​

​    ​  400 V  ​​ ​  ​ ​ = _____ ​   ​  10 Ω ​ = 40 A

That is to say that there is 40 A flowing in each of the windings in the motor. But as delta-connected loads have two current ratings, the line current to the motor will be: ​Imotor Line ​  ​​ = ​√3  × ​I​ motor phase​​​ ​​

​      ​ ​ =​  √3 × 40 ​​ ​ ​ = 69.28 A

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And as the phase and line currents are equal in star-connected systems, the supply will have a line current and a phase current in the windings of 69.28 A in both. In the lower diagram of Figure 4.86 if we consider a three-phase heater connected in either star or delta we can see the difference in power output. As the phase voltage in a star-connected 400 V system is 230 V, the current in each element of the star-connected heater is: ​V​  phase​​ ​I​  phase​​ = ​ _____      ​ R ​  ​  ______  ​​  ​​ ​​  230V ​ = ​     ​  11.5Ω ​ = 20A And as the line current is equal to the phase current, the power is (assuming a unity power factor): Pstar = √ 3 ×  VLine × ILine × power factor ​ ​ ​​ ​      ​​ ​    =​  √ 3 × 400 V × 20 A × 1 ​ = 13 856.4 W The same load connected in delta will have a phase current of: ​​ V ​  ​ phase ​​ = ______ ​  ​Iphase ​   ​  ​Zphase ​  ​​ ​​

​  ​  400 V​  ​  ​​ ​ = ______   ​   ​  11.5 Ω ​ = 34.78 A

Star connected supply

Interconnection of star and delta

VP = 230V

VL = 400V

Delta connected motor

Z = 10 Ω

Z = 10 Ω

Z = 10 Ω

3 phase heater was connected in: Delta

Star R = 11.5 Ω VL = 400V

R = 11.5 Ω R = 11.5 Ω

R = 11.5 Ω

VL = 400V R = 11.5 Ω R = 11.5 Ω

Figure 4.86  Typical combinations of three-phase interconnected systems

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And ILine is: ​Imotor Line ​  ​​ = ​√3  × ​I​ phase​​​  ​​​ ​ ​ ​      =​  √3 × 34.78 ​​

​ = 60.25 A So the three-phase power for the delta-connected heater is: ​​ = √ ​ 3  × ​V​ Line​​  × ​I​ Line​​ × power factor​ ​Imotor Line ​  ​​

​ ​  =​  ​  √3 × 400 V × 60.25 A × 1 ​     ​ ​     ​​ ​ = 41 742.42  W

From this, we can see that the same heating elements in the two different configurations can produce two different levels of heat. It is important to note that the power in delta is three times the power in star.

4.18   Energy and power requirements of a.c. systems 4.18.1  Power transmission Infinite grid The distribution grid is so large in comparison to most loads that it appears to be infinite, not only visually, but in most calculations as well. If a load took 100 A on each phase in a 400/230 V three-phase system, this might seem like a large load; however, a relatively small 500 MW power station can supply over 100 000 A per phase at 230 V. The entire grid has a much greater capacity than that. What this means when doing calculations for loads on the grid is that the voltage, frequency and phase difference between lines are fixed. They cannot be changed by any relatively small load that we apply. This makes calculations much easier for electricians (although engineers may still have to consider supply impedances in their calculations). The infinite grid means fixed voltage (400/230 V), frequency (50 Hz) and phase separation (120°).

4.18.2 Transmission Electrical power can be transmitted using low voltage and high current. But higher current results in higher transmission losses, according to the formula P = I2R. So, to reduce what are known as ‘I2R losses’, transmission lines generally use high voltage and low current. Energy is consumed in a power grid relative to the ‘load’ or current used. For the same power, the line current can be reduced by increasing the transmission voltage. This also allows for a reduction in conductor size for transmission lines and still produces a lower power loss in the line. In economic terms, the higher the voltage used for transmission, the lower the cost of installing and maintaining the transmission lines. For long distances between the source of supply and the consumer, voltages up to 576 kV are used for power transmission and distribution. (Typical voltage values vary from state to state, and even within states.) Transmission system voltages are far higher than the voltages required by the average consumer; therefore, the local distribution voltage is transformed in stages at substations and sometimes in pole transformers. Figure 4.87 shows a simplified distribution network. Most main transmission and sub-transmission lines are duplicated, and alternative routes provided, so that different localities can be fed by other lines and substations in the event of essential maintenance or breakdowns. 282

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Some systems are ‘ring fed’, which means that the distribution lines form a complete circle. The reason for this is that, in the event of a fault, a small section of the ring can be shut down while the remaining sides remain online; a smaller number of consumers are affected. Electricians must be aware of ring feeds, as two disconnections must be made to render the section safe.

4.18.3  SWER distribution Rural areas are generally a special case, where load units are comparatively small and their points of application are widely dispersed. One method of providing electrical power in these areas is the Single-Wire Earth-Return (SWER) system. Figure 4.88 shows an isolating transformer connected to the sub-transmission lines. The secondary voltage of the transformer is connected to a single conductor that traverses the countryside. The voltage of this line can vary between states or localities. If the isolating transformer is omitted and the SWER line is fed directly from one conductor of a three-phase 33 kV line, the phase voltage to earth is 19 kV. In some localities, the other phases are led out in different directions. This provides a balancing effect on the line. Due to the high voltage, both the line currents and the ‘earth-return’ currents are small. These ground currents effectively prevent the system from being used in larger population centres. This is because, in areas where large amounts of metal are buried in the ground, electrolytic corrosion is a problem. Special bonding arrangements might have to be set up to limit the amount of corrosion, and excessive metal would therefore make a SWER line uneconomical. Transformers are provided at the point of distribution. There are two secondaries on a SWER transformer which can be connected in parallel to supply 230 V or in series for 460 V at half the current.

Power Station

Transmission Lines

Terminal Station

132–576kV Step-up 11,16,26kV Transformer

Subtransmission Lines

Distribution Substation

Consumers Installations 400/230V Local Distribution Network

11/33/66kV Step-down Transformer

Stepdown Transformer

NOTE: Fault Protection, Earthing and Switching details not shown for higher voltage levels. Refer to supply authority training notes

400/230V 3-phase

400/230V 2-phase

L1 L2 L3 N

230V single phase

Figure 4.87  Electric power distribution Subtransmission Lines

Distribution Substation

11/33/66kV Stepdown Transformer

Consumers Installations Local Distribution Network L1 L2 400/230V L3 3-phase N

SWER Distribution Line Typically 16kV or 19kV

230V single phase

230/460V two phase

Optional Isolation Transformer

Figure 4.88  Single-Wire Earth-Return (SWER) distribution

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Electrical Principles

4.18.4  Three-phase distribution For general purposes, three-phase power may be supplied using either a three-wire or a four-wire system. A three-wire system is one that uses only the three line conductors, as shown in Figure  4.90(a). The phase windings are shown connected in delta, but they can also be connected in star, with or without the star point earthed. A four-wire distribution system is one that uses the three line conductors plus the neutral. The neutral is connected to the star point of the phase windings and earthed, as shown in Figure 4.90(b). For the supply authority, it is no great problem to supply power with star or delta systems. For the consumer, the star system is safer and more versatile because it provides a choice of voltages and an earth reference point. Single-phase loads present Figure 4.89  A SWER consumer transformer a problem to an otherwise balanced three-phase Shutterstock/Roman Tiraspolsky system but are more convenient and safer for smaller consumers. (a) A Voltage drop is a major problem in power L1, A, Red distribution because it causes consumers furthest from the supply to receive power at a reduced voltage. 3-Wire System — No Neutral or Earth Various techniques are used to try to overcome this. B C One method that works for small groups of consumers L2, B, White L3, C, Blue is to supply them from a centrally located transformer (b) A L1, A, Red fed by a high-voltage primary feeder (a feeder being a grid supply line). Radiating from the central point 4-Wire System — Neutral &/or Earth are the secondary or supply mains, consisting of three lines and a neutral. Characteristically, the mains B C L2, B, White become smaller in size as the distance from the L3, C, Blue N, N, Black transformer increases. This method is typical for very small country towns. Figure 4.90  Three-wire vs four-wire For higher-density distribution, as in the suburbs of a larger town, it is more common to have each block of consumers supplied from a transformer, and have the mains from various blocks interconnected. This means that any one consumer can be supplied from a number of sources. This method has the disadvantage of needing more protection devices for the transformers, and it becomes more difficult to isolate sections of mains for maintenance purposes.

4.18.5  Three-phase power Star connection The power consumed by a load connected to a single-phase a.c. supply is found by using the formula: P = VIcosø. If three identical loads are connected in parallel to one supply, the total power used is 3 × VIcosø. This means that three loads of the same size use three times the power of one load in three-phase systems. Three loads on the three phases use three times the power of one load, at least when working with phase voltage and phase current. In general, it is easier to measure line values rather than phase values, and use the former instead. 284

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In a star-connected system, IL = IP and VL = √3.VP. Substituting line values for phase values: ​V​  ​​  ​P = 3 × ​ ____ ​  L   ​  ​  × ​I​ L​​  ×  cos  ø  =  √  3​VL​  ​​ ​IL​  ​​  cos  ø​ ( √ 3) This is usually expressed as: ​PT = √3VL IL cos ø​ where V and I are assumed to be line values.

Delta connection If the three individual loads are connected in delta, the power consumed is still: ​P = 3  × ​V​  P​​ ​I​  P​​  ×  cos ø (for a balanced condition)​ In a delta system, VL = VP and IL = √3IP. Substituting these: ​V​  ​​  total power  P = 3 × ​ ___ ​  L   ​  ​  × ​I​ L​​  ×  cos  ø ( √3)       ​​ ​​​ ​  ​  ​ = √  3​VL​  ​​ ​IL​  ​​  cos  ø In general terms: ​PT = √3VL IL cos ø​ where V and I are assumed to be line values cos ø​ ​= power factor. This formula is the same as for a balanced star-connected load. Thus it is applicable for both star- and delta-connected balanced three-phase loads. It is not to be used for unbalanced loads.

EXAMPLE 4.29 A three-phase 400 V motor draws 12 A at 0.85 lagging power factor. How much power is consumed? PT = √3VL IL cos ø  (1) ​ = 3 × 400 × 12 × 0.85  (2) ​​ ​      ​  ​  ​  ​  ​​​ ​ = 7067 W (7.1 kW )  (3)

4.18.6  Power and energy meters In the days of mechanical instruments, power meters required two coils: one for voltage connected across the circuit and one for current to be connected in the circuit. Their combined magnetic field would cause the meter to register power. The instrument was reasonably reliable and accurate. It was also fragile, sensitive to temperature changes and required occasional recalibration. Energy meters were similar, although generally fixed in use, and were almost free of recalibration. Electronic instruments are good at addition and subtraction and can even emulate square and square root functions. But multiplication of two rapidly varying values is difficult and accurate only over a narrow band of values. It took digital electronics and computerised instrumentation to really replace analogue instruments. Power being consumed in a circuit is measured with a wattmeter, and these are often constructed with a dynamometer movement. This type of movement usually has two internal electrical circuits. 285

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6 7 8 4 5 9

10 Moving coil V+ Power (responds to source load voltage)

0

1

2

3

Electrical Principles

Pointer

M

Coil spring

Moving coil

Fixed coil V+

M

R

Load

L V Fixed coil (responds to load current)

(b) Connections. The moving coil with the series resistance R carries a current proportional to load voltage. Meter deflection is proportional to the product of voltage and current, which is power. This meter may be used for a.c. or d.c. measurements

V

L

(a) Exploded view

Figure 4.91  A dynamometer movement

4.18.7  Methods of three-phase power measurement One wattmeter (four-wire system) The single wattmeter is connected between one line and neutral in a three-phase, four-wire system (see Figure 4.92). The total power drawn from a three-phase supply is found by adding the separate values of power consumed by each phase. In the case of a balanced load: ​​P​  total​​ = 3 ​P​  A​​ = 3 ​P​  B​​ = 3 ​P​  C​​= three times the wattmeter reading in any of the three lines​ For an unbalanced load, the wattmeter has to be connected or switched into each phase in turn and the individual power readings added: ​​P​  total​​ = ​P​  A​​  + ​P​  B​​  + ​P​  C​​​

Advantages

1. One wattmeter only is required. 2. It is suitable for both balanced and unbalanced loads.

Disadvantages

1. A neutral connection is required for the wattmeter. 2. It is not accurate for unbalanced fluctuating loads. 3. The wattmeter has to be connected or switched into each phase in turn for unbalanced loads. The switch must not break the line when switching.

One wattmeter (three-wire system) With a three-wire system, no neutral is available. As there is a 30° phase shift between line and phase voltages, it is necessary to provide an artificial star point so that the correct voltage at the correct phase angle is applied to the wattmeter. Two impedances, each matching the impedance of the voltage circuit in the wattmeter, must be connected in star with the meter voltage circuit (Figure 4.93), and to the other two lines. Resistors matching the resistance of the voltmeter circuit must be very close approximations for this purpose. 286

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V1

V1 L1

A1

A2

A1

L1

A

A2

A

V2

V2 L2

L2

B 3-phase Load C

L3

B 3-phase Load C

L3 Z1

N

Z2 N

N

Figure 4.93  One wattmeter three-wire

Figure 4.92  One wattmeter four-wire

For balanced loads only: ​​P​  total​​ = 3 ​P​  A​​= 3 times the wattmeter reading​ For balanced and unbalanced loads: ​​P​  total​​ = ​P​  A​​  + ​P​  B​​  + ​P​  C​​​

Advantages

1. One wattmeter only is required. 2. It is suitable for both balanced and unbalanced loads.

Disadvantages

1. Two matching impedances are required to provide an artificial neutral. 2. It is not accurate for unbalanced fluctuating loads. 3. The wattmeter has to be connected or switched into each phase in turn for unbalanced loads. The switch must not break the line when switching.

Two wattmeters (three-wire system) A method for measuring the power consumed in a three-phase, three-wire circuit is shown in Figure  4.94. The two meters have their current windings in any two lines, and both voltage windings are connected to the third line. Neither meter alone indicates the total power in the circuit. But the two meters together, by their algebraic sum, indicate the power consumed. That is: ​​P​  total​​ = ​W​  1​​  + ​W​  2​​​ For a balanced load with unity power factor, both meter readings will be equal. For all other conditions, the meters will show different readings. If the lower-value meter indication is W1 and the higher one W2, as the power factor decreases, W1 registers less and less of the total power. When the power factor is 0.5 with a balanced load, W1 will read zero and W2 will read the total power. Should the power factor fall further (to, say, 0.3), W1 will read even less, meaning that W1 will attempt to read a negative value of power consumption. If the current or voltage connections to the

V1 L1

A1

A2

A

V2 L2 V2 L3

A1

A2

B 3-phase Load C

V1 N

Figure 4.94  Two wattmeter, three-wire

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meter are reversed, the numerical value of W1 can be obtained. But it is a negative value. The total power in this case is still the algebraic sum of W1 and W2. That is: ​P​  total​​ = (− ​W​  1​​  + ​W​  2​​  ) ​  ​     ​​​ ​​ ​ = ​W​  2​​  − ​W​  1​​ Should the power be reduced to zero with a balanced load (pure capacitance or inductance), W1 would read a negative value numerically equal to W2 and the algebraic sum would be zero: ​​P​  total​​ = − ​W​  1​​  + ​W​  2​​ = 0​ This also agrees with the concept of a purely reactive circuit. The two-wattmeter method may be used on three-phase, three-wire systems to obtain load power values whether the load is balanced or unbalanced. The same applies whether it is star- or delta-connected. But it cannot be used on a four-wire, star-connected system because a single-phase component of current might be flowing in the line (and neutral) with no wattmeter current-coil connection. The power being consumed would not be recorded. Only when the three-phase load is balanced is it possible to find the power factor of the load from the wattmeter readings. The Tangent of the angle of lag or lead is found from: [​W​  1​​  − ​W​  2​​  ​tan φ = √3. ​ _________    ​​  ​W​  1​​  + ​W​  2​​  ] (balanced loads and sinusoidal waveforms only) The angle φ is obtained from tan−1 φ, and the Cosine of this angle gives the power factor of the load.

EXAMPLE 4.30 When connected to a three-phase motor, two wattmeters gave readings of 5 kW and 1 kW. Find: (a) the total power being consumed. (b) the power factor of the motor. (a) ​PTotal ​  ​​ = ​W1​  ​​  + ​W2​  ​​      (1) ​​

(b)

=​  5 + (−        (2)​​​ ​ ​    ​  1)​  ​ = 4 kW      (3)

__ ​W1​  ​​  − ​W2​  ​​ φ = ​tan​​  −1​​​ √ ​​​  3 ​ ​      _ ​​  ​​​ [ ​W1​  ​​  + ​W2​  ​​]

__ 5 − (− 1) φ = ​tan​​  −1​​​ √ ​​​  3 ​ ​      _ ​​  ​​​ [ 5 + (− 1)]

 (4)  (5)

__ 5 + 1 φ = ​tan​​  −1​​[√ ​​​  3 ​ ​      _ ​​  ​​  (6) ​​           ​      ​  ​  ​  5 − 1 ​  ​  ]​  ​  ​​​ __ 6 φ = ​tan​​  −1​ ​[√ ​​​  3 ​ ​      __ ​ ​ ]​​  (7) 4 ​ = ​tan​​  −1​  [2.598  ]

 (8)

​ = 68.9°

 (9)

∴ PF = 0.3593

 (10)

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Advantages

1.  Only two wattmeters are required. 2. It is useful for both balanced and unbalanced three-phase, three-wire loads. 3. The power factor can be obtained for balanced loads. 4.  No neutral connection is required.

Disadvantages

1. 2. 3. 4.

It is suitable only for three-phase, three-wire loads. Care must be used in determining the polarity of W1. The power factor cannot be obtained for unbalanced loads. It is not suitable for power or power factor readings with three-phase, four-wire systems.

Three wattmeters (three-wire system) With a three-wire system, no neutral is available; an artificial neutral must be provided. However, if identical wattmeters are used, the three voltage circuits can be connected to provide a star point, as shown in Figure 4.95: ​​P​  total​​ = ​W​  1​​  + ​W​  2​​  + ​W​  3​​​ V1

Advantages

1. It is suitable for both balanced and unbalanced loads. 2. It is convenient for obtaining total power. 3. It is more accurate than one wattmeter for fluctuating loads.

L1

A1

A2

A V1

V2

A1

L2

A2 V1

V2

A1

L3

Disadvantage

V2

1. Three wattmeters are needed.

Three wattmeters (four-wire system) The three-phase, four-wire system is basically three separate supplies with only a common neutral. The total power is obtained by connecting three wattmeters, as shown in Figure 4.96: ​​P​  total​​ = ​W​  1​​  + ​W​  2​​  + ​W​  3​​​

Advantages

1. It is suitable for both balanced and unbalanced loads. 2. It is convenient for obtaining total power. 3. It is more accurate than one wattmeter for fluctuating loads. 1. Three wattmeters are needed.

Electronic three-phase power meter A typical electronic power meter measures all three lines’ voltages (VAB, VBC and VCA) and current to determine the power. For higher current measurements, Current Transformers (CTs) are used (see Figures 4.97 and 4.98). Total power is measured by linear electronics in some instruments. They use operational amplifiers to calculate

N

Artificial Neutral

Figure 4.95  Three wattmeter, three-wire V1 L1

A1

A2 V2

L2

A V1

A1

A2 V2

L3

V1 A1

A2

B 3-phase Load C

V2

N

N

Figure 4.96  Three wattmeter, four-wire CT1

L1

Disadvantage

A2

B 3-phase Load C

A CT2

L2

CT3

L3 N

B 3-phase Load C N

V1V2V3N

A1 A2 A3

W, VA, var, PF, Ø, etc., Meter

Figure 4.97  Electronic three-phase power meter

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power continuously before displaying data on an analogue meter or digital readout. Digital instruments may use analogue-to-digital converters to measure voltage and current, and zerocrossing comparators to measure phase angle. From those values, digital electronics calculate power, reactive and apparent power, PF and phase angle. The most recent instruments use computer technology to improve on digital instruments. This gives greater accuracy and more functions and features. These include frequency, Total Harmonic Distortion (THD), true RMS measurement and possibly even the ability to display the waveforms or phasors. Figure 4.99 shows a technician using a power-analysing instrument. Figure 4.98  Panel power meter

Advantages   1. It suits any type of load or system, three- or four-wire.   2.  It can measure V, I, W, VA, var, PF, Ø, F, THD etc.   3.  No calculations are required.   4.  Some units show waveforms and/or phasors.   5.  It has robust construction.   6.   It offers good environmental protection, often IP56 or better.   7.  Once set up, measurements are selected by push button.

Disadvantage Figure 4.99  Fluke power analyser in use © Fluke Australia, www.fluke.com.au

  1. 

It may require a battery!

4.18.8  Volt-Ampere Reactive (var) measurement In power stations operating under normal conditions, the values of voltage and current are generally too high and unwieldy to be used directly with portable instruments. Potential Transformers (PTs) and Current Transformers (CTs) must be used to avoid these high-energy circuits. The constant measurement of voltage, current, power, VA and var, as well as PF, phase angle and frequency means that the CTs and PTs have to be permanently installed in the conductors. The instruments have to be installed in a suitable location such as a power station control room. Reactive power measurement is often required when a power station supplies a grid system. There may also be more than one generating station supplying power to the same grid. It can be desirable to know the amount of reactive power that may be circulating between power stations and the grid. To keep track of this, a readout is provided in a power station’s control room. Under ‘Conditions of supply to consumers’, supply authorities try to ensure that the overall power factor is no worse than 0.8 lagging. This reduces the amount of var circulating in their supply mains. Somewhat ironically, at the same time, due to the capacitive effect between long-distance transmission lines, the power station also has trouble with leading power factors. The var load travels up the transmission lines with a circulating current and can cause unwanted rises in voltage at the end remote to the power station. The problem can be exacerbated with underground transmission lines. 290

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4.18.9  Handheld wattmeters Handheld wattmeters are similar in size and shape to a multimeter. Battery powered, they operate electronically and provide a digital readout. Range selection is by a rotary switch. The meter uses RMS values of current and voltage, irrespective of the actual waveform. It has an accuracy of around 5% of the readout, a figure which is sufficiently accurate for a portable instrument. The rotary switch has three sections: voltage, current and power. Maximum ranges are up to around 750 V and 20 A, giving a power range from 400 W to 15 kW. The instrument has the added advantage of being comparatively accurate from 15 Hz to 1 kHz. Because there are three groups of readings, individual readings of voltage, current and power can be obtained. Some models also indicate the displacement, if any, between voltage and current.

4.18.10  Bench-type wattmeters Equipment of the bench type has a far higher degree of accuracy than the portable version, and is usually never taken into the field. Expensive to purchase, bench-type wattmeters are kept in a workshop for better protection. They are usually 230 V mains-powered, but later models are electronically operated. With an analogue Figure 4.100  Types of power factor correction capacitors readout, the operating frequency is usually from d.c. © Aerovox, www.aerovox.com (f = 0) to around 15 kHz. Current ranges are up to 10 A, with a maximum voltage of 1000 V. This gives a maximum power range from 250 mW to 10 kW.

4.18.11  VA and var meters VA is of course simply the product of V and I, which digital electronics with computerised instrumentation __________ can 2 2 2 easily calculate. var is calculated using Pythagoras’ theorem, or (VA) = P + var , i.e. var = √ ​​   (VA2 − P2) ​​  . The point here is that once P has been measured, VA and var are relatively easy to calculate inside the instrument if a microcomputer is used.

4.18.12  Power factor meters The same method as above can be used to calculate power factor. However, another method in analogue electronics used the zero-crossing point of sine waves. That is, when the voltage waveform crosses zero in the positive direction, a circuit called a ‘flip-flop’ goes positive. Then, when the current waveform crosses zero and goes negative, the flip-flop goes negative again. That should happen 180° later. The time that the gate is on for is smoothed to make a voltage that is proportional to the power factor. Half the voltage is a power factor of unity, while less than half is leading and more than half is lagging.

4.18.13  Energy meters (kWh meters) Energy meters are power meters that integrate the power over time. In other words, the energy meter adds the power to increase a value that is stored in memory. Most energy meters are much more complex than that, being able to record a vast amount of data for later harvesting by technicians. 291

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4.18.14  Frequency meters Digital electronics are perfect for frequency measurement. Of course the circuit could count the cycles every second and give a readout each second, but they are too fast for that. Digital instruments can actually count the period of the cycle and invert the result to give an answer in hundredths of a hertz, 50 times a second.

4.18.15  High-frequency wattmeters Wattmeters intended for use on frequencies well above powerline frequencies use different principles of operation. Shutterstock/By Matee Nuserm Most rely on the heating effect of the current flowing in the circuit. The heat produced generates a voltage proportional to the temperature of a thermocouple. The voltage is then processed and indicated on a meter, whether analogue or digital. Figure 4.101  Power factor correction capacitor

4.18.16  Ultra-high-frequency wattmeters For frequencies in excess of 300 MHz, parallel-line meters are used. One of the parallel lines has the load current flowing through it. The other line has a voltage induced in it. This voltage is rectified and read against the scale of a meter calibrated for that frequency.

4.18.17  Total harmonic distortion meters While not something that is typically shown on power meters, total harmonic distortion (THD) can be readily monitored with modern technology to display harmonics, spikes and other issues with power supplies. Harmonics can have disastrous effects within an electrical installation and technicians need to be familiar with the use and operation of THD meters.

4.18.18  Power factor improvement Power factor improvement is theoretically the same for three phase as it is for single phase. The major difference is in the location of the power factor improvement equipment. For single phase, this is more often in the equipment connected at the supply terminals; for three-phase installations, the power factor equipment can be a separate component that is usually located close to the point of supply. Three-phase power factor correction equipment is also generally three- or four-wire when incorporated into three-phase components.

4.19   Fault loop impedance 4.19.1  Fault loop impedance of an a.c. power system When a fault occurs in an installation, there is the risk of the exposed conductive parts of the installation becoming live. That would be dangerous. The provision of an earth connected to all the exposed conductive parts of an installation creates a low impedance conductive path to conduct this hazardous current. Under fault conditions, this is the conductive path that ensures that the circuit protection operates (open circuits) and de-energises the fault. This path is called the ‘Fault Loop Impedance’. It consists of:

1. 2. 3. 4.

The impedance of the windings of the electrical supply transformer. The impedance (resistance and reactance) of the supply authority service line active. The impedance (resistance and reactance) of the consumer mains active. The impedance (resistance and reactance) of the submain active (if any).

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5. The impedance (resistance and reactance) of the final sub-circuit active. 6. The impedance (resistance and reactance) of the fault, which is generally negligible for the determination of the fault look impedance. 7. The impedance (resistance and reactance) of the final sub-circuit protective earth. 8. The impedance (resistance and reactance) of the submain earth (if any). 9. The impedance (resistance and reactance) of the M.E.N. connection, which is generally negligible for the determination of the fault look impedance. 10. The impedance (resistance and reactance) of the consumer mains neutral. 11. The impedance (resistance and reactance) of the supply authority service line neutral.

Figure 4.102 highlights the fault loop impedance of the installation under fault conditions. AS/NZS 3000:2018 has guidance and examples of general arrangements for installations. These determine appropriate conductor size and associated protection ratings. The particular requirements for fault loop impedance is covered in paragraphs B4 and B5. Paragraph B4.4 outlines the components of the fault loop and states that it is determined by the sum of the impedances of all these components (calculation B3). B4.4 also states a demarcation point between the ‘easily known’ and the ‘not so easily known’ parts of the fault loop. The ‘easily known’ part is referred to as the ‘internal fault loop impedance’ (Zint); the ‘not so easily known’ part is referred to as the ‘external fault loop impedance’ (Zext). The boundary between these points is the protective device that the final sub-circuit originates from. Zext is upstream from the protective device and includes the components that may be known. These include the submain and consumer mains impedance as well as perhaps less well known components such as service line, distribution, supply transformer and transmission impedance. These are the responsibility of the supply authority as they are beyond the point of supply (or point of attachment). Zint however directly relates to the circuit under scrutiny, and the impedance is in the control of electrical workers. A simple diagrammatic representation of the fault loop impedance is shown in figure B5. Under fault conditions, it is assumed that there will be at least 80% of the supply voltage at the protective device. This is the case even with an excessive voltage drop due to the high fault current. This means the acceptable internal fault loop impedance (Zint) can be calculated when designing a circuit by the formula in Paragraph B5.2.1 in AS/NZS 3000:2018: 0.8  × ​U​  o​​ ​​Z​  int​​ = _______ ​     ​​  ​I​  a​​ Electrical grid

Point of attachment

Service line R&X

Consumer mains

R&X

R&X

Earth

R&X Main switch Circuit breaker

Neutral

Final sub-circuit Main earth stake

R&X

R&X

Load

Figure 4.102  Fault loop impedance under fault conditions

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where: Uo is the nominal phase voltage (230 V) Ia is the value of current required to trip the protective device.

4.19.2  Determining fault loop impedance using resistance and reactance values The impedance of cables can be determined by tables 30 to 39 in AS/NZS 3008.1:2017 for voltage drop. The same method can be applied to determine the fault loop impedance for the final sub-circuit. The difference is that the protective earth conductor for the final sub-circuit must be considered instead of the neutral. This is because the neutral is excluded from the fault circuit under the worst-case-scenario fault condition.

EXAMPLE 4.31 A 25 A single-phase socket outlet is connected to a circuit breaker in the main switchboard by a final subcircuit of 4 mm2 V90 Thermoplastic multicore (TPS) twin and earth. The final sub-circuit is 27 m long. Determine the fault loop impedance of the final sub-circuit. The conductors are made of copper. Step 1. Determine the operating temperature of the 4 mm2 V90 Thermoplastic multicore (TPS) twin and earth using either Table 3.2 in AS/NZS 3000:2018 or Table 1 in AS/NZS 3008.1:2017. The normal use for V90 Thermoplastic insulation is 75°. Step 2. Determine the size of the protective earth conductor using Table 5.1 in AS/NZS 3000:2018. The minimum protective size of protective earth for the 4 mm2 active conductor is 2.5 mm2. Step 3. Determine the table and column in AS/NZS 3008.1:2017 for the reactance of 4 mm2 V90 Thermoplastic multicore (TPS) active and 2.5 mm2 earth. AS/NZS 3008.1:2017 Table 30 is for all cables, excluding flexible cords, flexible cables, MIMS cables and aerial cables. Column 9 is for multicore PVC cables with circular conductors. From this table, the value of the 4 mm2 active reactance is 0.102 Ω/km and the earth reactance is 0.102 Ω/km. Step 4. Determine the total reactance for the 4 mm2 V90 Thermoplastic multicore (TPS) active and 2.5 mm2 earth. The final sub-circuit active (Xfsc active) Ω / km ​​ = ​ _____ ​ × L   ​Xfsc active ​  1000       ​​ ​​ ​  ​  _____ 0.102 ​ = ​     ​ × 27 1000 ​​

​ = 0.002754 Ω where L is the length of the final sub-circuit. The final sub-circuit protective earth (Xfsc earth) Ω / km ​​ = _____ ​    ​Xfsc earth ​   ​ × L 1000 ​​

      ​​ ​​ ​  ​  _____ 0.102 ​ = ​     ​ × 27 1000 ​ = 0.002754 Ω

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Step 5. Determine the table and column in AS/NZS 3008.1:2017 for the resistance of 4 mm2 V90 Thermoplastic multicore (TPS) active and 2.5 mm2 earth. AS/NZS 3008.1:2017 Table 35 is for multicore with circular conductors Column 4 (75°) is for copper conductors. From this table, the value of the final sub-circuit active resistance is 5.61 Ω/km. From this table, the value of the final sub-circuit protective earth resistance is 9.01 Ω/km. Step 6. Determine the total resistance for the 4 mm2 V90 Thermoplastic multicore (TPS) active and 2.5 mm2 earth. The final sub-circuit active (Rfsc active) Ω / km ​​ = _____ ​    ​Rfsc active ​   ​ × L 1000 ​    ​  5.61 ​​​ ​ = _____ ​     ​  × 27 1000 ​​

​ = 0.15147 Ω where L is the length of the final sub-circuit. The final sub-circuit protective earth (Rfsc earth) Ω / km ​​ = _____ ​    ​Rfsc earth ​   ​ × L 1000 ​​

   ​​​ ​  ​  _____ 9.01 ​ = ​     ​  × 27 1000 ​ = 0.24327 Ω

Step 7. Determine the impedance of the final sub-circuit (Zfsc) ______________________________________ ​Zfsc ​  ​​ = √ ​   ​(     ​[​Xfsc active ​  ​​  + ​X​ fsc earth​​  ]​​  2​  + ​[​Rfsc active ​  ​​  + ​R​ fsc earth​​  ]​​  2​)​ ​ _________________________________________ 2 2 ​​     =​  √ ​   (​     [0.002754  ​​               +  0.002754  ]​​  ​​  + ​[0.15147  +  0.24327 ​]​​  ​) ​​​​ ____________________ ​= √ ​      (​0.005508​​  2​  + ​0.39474​​  2​  ) ​ ​ = 0.39477 Ω

4.19.3  Measuring fault loop impedance of typical circuits There are two methods for measuring fault loop impedance:

1. Using a fault loop impedance tester. This type of tester is connected to a live circuit under normal conditions. It measures the complete fault loop impedance (Zs). Values obtained using a fault loop impedance tester should be compared to Table 8.1 in AS/NZS 3000:2018 for verification of compliance. These are known as HOT values as the circuit is energised and can be up to the temperature limits stated in AS/NZS 3000:2018, Table 3.2. 2. Using an ohmmeter. This is the method outlined in AS/NZS 3017 Electrical Installations—Verification Guidelines. This method gives a value of RESISTANCE for the Internal part of the fault loop (Zint), and the values obtained should be compared to AS/NZS 3000:2018 Table 8.2. The values in Table 8.2 are 64% of the values in Table 8.1 due the reduction in voltage at the protective device (80%). As the conductors are de-energised, they are at ambient temperature and their resistance is further reduced by 80%. Thus they are known as COLD values. 295

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4.19.4  Fault loop impedance testers Under existing self-regulatory conditions for electrical workers, the worker can be expected to check the fault loop conditions for an installation. The fault loop is the path from the installation’s main earth back to the supply point where the main neutral is also grounded. Fault loop impedance testers are designed to give an indication of the impedance of that path. The tester itself may be a combination of insulation resistance tester and continuity tester. It may perform other functions such as testing the Figure 4.103  Fault loop tester operation and effectiveness of any residual current device in the installation. The loop test places a known resistor between one phase of the installation and measures both the no-fault voltage and the voltage under simulated fault conditions. This is then processed in the instrument, providing a reading in ohms impedance for the loop back to the supply via the earth return. For safety and residual current devices, a good earth return is generally considered a must. Particularly with the later electronic devices, the testing of the loop impedance can cause tripping at least (and a possibility of damage to the device itself). In either case, the effects of an interruption to the supply service can vary from a minor nuisance in domestic cases to a major problem involving safety in an industrial installation. Figure 4.103 shows a typical fault loop impedance tester. This instrument also has the ability to test for prospective fault levels within an installation. Typically these testers have two types of leads: one with a male plug for testing socket outlets and one with alligator-type clamps for testing electrical equipment and apparatus.

4.19.5  Procedures for testing fault loop impedance When using a fault loop impedance tester, the tester is connected to an energised circuit and a reading taken. However, WHS regulations stipulate de-energised testing in most circumstances. AS/NZS 3017 provides guidance and procedures for safe de-energised testing. Testing the fault loop impedance of circuits supplying socket outlets NOT protected by RCDs is mandatory in AS/NZS 3000:2018. It must be done prior to connecting the circuit to the supply. AS/NZS 3017:2018 outlines a detailed step-by-step process for doing this, which is essentially:

1. Verify that the circuit to be tested is isolated from the supply. 2. Connect the active and protective earth conductor of the circuit to be tested at the origin of the circuit (in the switchboard that the circuit originates from). 3. Measure the resistance between the active and protective earth contacts on the furthest point on the circuit. 4. Compare the reading to the values in AS/ZNS 3000:2018, Table 8.2. Table 8.2 also has values for the individual active and protective earth conductors (Rph and Re). An experienced tester can reduce the time taken for testing by incorporating the testing to verify the resistance of the protective earth conductor’s resistance with the test to verify fault loop impedance.

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Solve problems in a.c. circuits  Chapter 4

Summary ∙ A conductive loop rotating in a magnetic field produces an alternating voltage waveform. ∙ When the field is uniform and the speed of rotation is constant, the shape of the waveform is sinusoidal. ∙ An alternator is a generator that produces a voltage of alternating voltage polarity and current flow. ∙ There are two types of alternators: conductors rotated inside a stationary magnetic field and a magnetic field rotated through stationary conductors. ∙ The direction of the induced voltage can be determined from Fleming’s right-hand rule. ∙ The magnitude of the voltage can be found from: e = Blv sin θ ∙ The output voltage of an alternator can be increased by increasing the number of conductors. ∙ The output voltage of an alternator can be increased by increasing the magnetic flux. ∙ The output voltage of an alternator can be increased by adding an iron core to the alternator. ∙ The iron core rotates within a magnetic field and therefore generates a current within the metal, which gives rise to iron losses (eddy currents and hysteresis). ∙ As operating frequency is usually fixed, the speed of the machine is also fixed (f = np/120). ∙ One cycle of alternating current occupies 360°E (electrical degrees). It is not always equal to mechanical degrees. ∙ Phasors are rotating vectors. ∙ Phasors that are ‘in phase’ have a zero angle between them. ∙ Phasors that have a difference of angle between them are ‘out of phase’. ∙ The ‘reference phasor’ is one that is common to all parts of the circuit. ∙ Phasors rotate counterclockwise (CCW). ∙ Phasors ahead of the reference phasor are ‘leading’ the reference value. ∙ Phasors behind the reference phasor are ‘lagging’ the reference value. ∙ Phasors cannot be added arithmetically unless they are in phase. ∙ Phasors that are out of phase must be added vectorially, using the graphical method or trigonometry. ∙ Phasors may be given in polar form of value and angle, e.g. 230 V ∠ 45°. ∙ Phasors may be given in rectangular form, in which case the horizontal and vertical values may be added arithmetically, e.g. [100,50] + [86.6, − 50] = [186.6,0]. ∙ To add phasors given in polar form, they must be converted to rectangular form using: P ∠Φ = [Pcos Φ),Psin(Φ)] ∙ To convert rectangular to polar form, use: [X,Y] = √(X2 + Y2)∠tan–1(Y/X) ∙ Every repeating regular waveform is made up of sine waves of varying amplitude and frequency. ∙ Harmonics are sine waves at multiples of the original (fundamental) frequency. ∙ Harmonics may be detrimental to power-supply systems and electrical machines. ∙ With alternating current, the current might not be in step with the voltage, in which case it is said to be ‘out of phase’. ∙ For resistive circuits, current is in phase with the voltage. ∙ For purely inductive circuits, the current lags the voltage by 90°. ∙ For purely capacitive circuits, the current leads the voltage by 90°. ∙ For circuits containing resistance and reactance, the phase displacement of the current depends on the relative proportions of each component in the circuit. 297

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Electrical Principles ∙ The angle of phase displacement is the ‘phase angle’, symbol φ. ∙ The opposition to a.c. current flow in a capacitor or inductor is known as ‘reactance’, symbol X. ∙ ‘Inductive reactance’ is found from XL = 2πfL. 1 ∙ ‘Capacitive reactance’ is found from XC = ______ ​​     ​​  . (2πfC) ∙ The total opposition to an a.c. current flow is called ‘impedance’, symbol Z. ∙ Impedance is made up of resistance, capacitive reactance and inductive reactance. ∙ In a series circuit, Z = √(R2 + (XL − XC)2). ∙ In a parallel circuit, IZ = √(IR2 + (IL − IC)2). ∙ In series circuits, current is the reference phasor. ∙ In parallel circuits, voltage is the reference phasor ∙ Out-of-phase phasors must be added vectorally. ∙ The Cosine of the angle between the voltage and the current (φ) is called the ‘power factor’ of a circuit. ∙ For single-phase, the power consumed in a circuit is dependent on the power factor: P = VI cos φ. ∙ When V and I are in phase, φ = 0° and cos φ = 1 and P = VI. ∙ When V and I are 90° out of phase, φ = 90° cos φ = 0 and P = 0. ∙ A power triangle can be used for an a.c. circuit by the components ‘true power’ (P), ‘apparent power’ (S) and ‘reactive power’ (Q). ∙ The power factor is equal to true power divided by apparent power: PF = P/S ∙ A low power factor leads to ‘wattless’ components of current flowing in distribution lines. ∙ Low PF causes poor voltage regulation, excessive line losses, excess fuel consumption and unnecessary loading of alternators. ∙ The power factor can be obtained by measuring with a voltmeter, ammeter and wattmeter and then calculating the P value: PF = ___ ​​    ​​  VI ∙ The power factor can be measured directly with a power factor meter. ∙ 0.9 is considered the lowest acceptable power factor by supply authorities in NSW. This could vary across states and territories. ∙ For individual loads, capacitors are connected in parallel to improve the power factor. ∙ For larger loads, power factor correction can be made using leading current synchronous motors. ∙ Power factor correction var can be calculated by subtracting the maximum acceptable var (e.g. @0.8) from the maximum var without correction. ∙ If inductive reactance is equal to capacitive reactance, the circuit behaves as if it were purely resistive and is said to be ‘resonant’ at that frequency. 1 ∙ The resonant frequency can be calculated from: f = __________ ​​     ​​  . (2π√(LC)) ∙ Resonance can cause dangerous voltages in series circuits and dangerous currents in parallel circuits. ∙ Single-phase alternators do not use the whole cycle of the driving machine, so that a sine wave is only 63% efficient. ∙ Two-phase systems have two voltages locked together at 90°E and efficiency increases to 90%. ∙ Three-phase systems have three voltages locked together 120°E apart and efficiency increases to 94.5%. ∙ Four-phase systems have too little advantage over three-phase systems to be of any economic interest. ∙ Three-phase systems are more cost-efficient than any other multiphase system. ∙ Three-phase systems are more mechanically efficient than two-phase or single-phase systems. ∙ The phase sequence of a three-phase system determines whether systems can be connected and the direction of rotation of induction motors and similar machines. 298

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Solve problems in a.c. circuits  Chapter 4 ∙ Three-phase motors can start without additional circuitry due to three-phase systems having a phase sequence. ∙ Phases are designated A, B and C and by the colours red, white and blue. ∙ Lines are designated L1, L2 and L3 or in European technology U, V and W. ∙ Three-phase systems have two possible connections—star and delta. Both have advantages and have different current and voltage ratios. ∙ Both star and delta systems can be either balanced or unbalanced. ∙ An unbalanced delta system tends to be unstable. ∙ Windings have to be connected correctly in star, or reduced voltages occur. ∙ Windings have to be connected correctly in delta, otherwise high voltages occur at open terminals or high circulating currents occur if the triangle is closed. ∙ Three-phase balanced system power is found from: PT = √3VL IL cos power factor.

where V and I are line values and cos ϕ is the

∙ In unbalanced systems, the power in each load must be added to find total power. ∙ With a star-connected system in balance, there is no neutral current. ∙ If a broken neutral occurs in a star-connected system, voltages and currents change, with the greatest load reducing in voltage and the smallest load increasing in voltage. ∙ Local (consumer) power is usually distributed with star-connected systems. Delta-connected systems are more usual in high-power transmission. Loads such as electric motors can be connected in star or delta configurations at appropriate voltage levels. ∙ In remote areas, SWER systems are sometimes used to save money. Only one active wire is used and the earth is used as a return conductor. There are usually two voltages available to the consumer: 230 V and 460 V. ∙ There are several methods by which three-phase power can be measured. The same methods can apply to the measurement of var, provided due attention is paid to the phase relationship of the voltage used. ∙ Modern measuring instruments have a far greater selection of available measurements, including V, I, P, Q, S, PF, ø, F, THD etc. ∙ High energy level circuits reduce the risk of shock or dangerous arcs by using CTs and PTs. ∙ Terms used are: ∙ ‘Periodic function’—any wave that repeats itself. ∙ ‘Periodic time’—the time taken in seconds to complete one cycle (t = 1/f) seconds. ∙ ‘Frequency’—the number of times a wave repeats itself in one second (unit = hertz). ∙ Vmax and Imax the maximum voltage or current of the sine wave. The same goes for the peak value. ∙ Vp–p and Ip–p—peak-to-peak value equals twice the maximum value. ∙ ‘Average value’—0.637 of maximum for a sine wave. ∙ ‘RMS value’—0.707 of maximum for a sine wave. ∙ ‘Instantaneous values’—v = Vmax.sin θ for voltage and i = Imax.sin θ for current.

Questions Exercises 4.1 Define the terms ‘period’, ‘maximum value’, ‘peak-to-peak value’, ‘instantaneous value’, ‘average value’, ‘rootmean-square (RMS) value’ in relation to a sinusoidal waveform. 299

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Electrical Principles 4.2 Explain the terms ‘SOH CAH TOA’ and ‘Pythagoras’ theorem’ as relating to a right angle triangle. 4.3 What is meant by the terms ‘in phase’ and ‘out of phase’? 4.4 Compare the relationships between voltage and current if a.c. is applied to pure resistance, inductance or capacitance. 4.5 Draw a phasor diagram of a resistor drawing 1 A from a 230 V supply. 4.6 Draw a phasor diagram of an inductor drawing 1 A from a 230 V supply. 4.7 Draw a phasor diagram of a capacitor drawing 1 A from a 230 V supply. 4.8 Why does a practical inductor never cause the current to lag by 90°? Draw a circuit to represent a practical inductor. 4.9 Calculate the current and power drawn from a circuit consisting of three resistors (100 Ω, 47 Ω and 22 Ω) connected in series across a 100 V 50 Hz supply. 4.10 Describe the dangers of a series resonant circuit when it is connected to a 230 V 50 Hz supply. 4.11 Determine the voltage drop in a 2.5 mm2 twin and earth cable supplying a 20A single phase load. The cable insulation is V90 TPS and the circuit length is 37 m. 4.12 A 30 Ω resistor in series with a 0.1 H inductor are placed across a 230 V 50 Hz supply. What are the total current, total power and phase angle between the current and supply voltage? 4.13 In a circuit containing a 0.5 H inductor in parallel with a 100 Ω resistance supplied by 100 V at 50 Hz, calculate the current in each component and the total current. 4.14 When does a parallel resonant circuit draw minimum current from the supply? 4.15 Explain why a pure inductor does not consume power. 4.16 What is the power factor? Give its maximum and minimum values. 4.17 Explain the differences between true power, apparent power and reactive power. 4.18 What are the effects of poor power factor on a distribution system? 4.19 Explain how a capacitor can correct poor power factor. 4.20 What is used in a high power plant to correct a low power factor? 4.21 Calculate the total current, phase angle and power factor for a 230 V 50 Hz series circuit consisting of a 33 Ω resistive element, a 0.3 H inductive coil and a 100 μF capacitance. 4.22 A 230 V 50 Hz circuit passes 1.6 A at a power factor of 0.8. Calculate the phase angle, true power, apparent power and reactive or wattless power. 4.23 At what frequency will a series circuit resonate if it has an inductance of 25 mH, 100 μF and a resistance of 10 ohms? What is the impedance at resonance? 4.24 A single-phase motor draws 1150 W from a supply of 230 V 50 Hz. A power-factor meter reading in the circuit is 0.54. Determine the current taken from the supply. 4.25 A 400 V single-phase alternator is rated at 32 kVA. What would be the maximum safe power output for this machine at: (a) unity power factor? (b) a power factor of 0.8? 4.26 What is the third harmonic for a 50 Hz a.c. sine wave? 4.27 A single phase 230 V installation has a total loading of 20 kW at a power factor of 0.6. Calculate the size of the capacitor, in kvar, to correct the installation so that it has a power factor of 0.9. What is the current draw from the supply with the new power factor and what is the current rating of the capacitor used for the power factor correction? 4.28 Explain why the three-phase system is better than one, two, four or more phases. 4.29 Explain how three phases are produced in an electric machine to produce the 230 V 50 Hz three-phase power supply. 4.30 Explain the differences between star and delta connections. Nominate voltages and currents in each system for current Australian practices. 300

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Solve problems in a.c. circuits  Chapter 4 4.31 Explain the purpose of the neutral conductor in: (a) a balanced load; and (b) an unbalanced load. 4.32 Draw a circuit showing methods of measuring power in a balanced three-phase system. 4.33 Draw a circuit showing methods of measuring power in an unbalanced star-connected, three-phase distribution system. 4.34 A three-phase alternator has three separate 220 V windings. Calculate the line and phase voltages for: (a) star connection; and (b) delta connection. 4.35 A three-phase alternator has a line voltage of 400 V. Find the phase voltage and current for a balanced load consisting of 3 × 100 Ω resistors connected in: (a) star connection; and (b) delta connection. 4.36 A three-phase, star-connected alternator supplies an induction motor at a line voltage of 400 V. The current in each delta-connected motor coil set is 40 A. Find: (a) the line and phase voltages and line current of the motor (b) the phase voltage and current in each phase of the alternator. 4.37 A three-phase, delta-connected alternator supplies a star-connected induction motor at a phase voltage of 230 V. The current in each coil set is 25 A. Find: (a) the line and phase voltages and phase current of the alternator (b) the line voltage and current in each phase of the motor. 4.38 A 220 V three-phase motor can be connected in star or delta (with 220 V on each coil set). What are the power supply options for this motor? 4.39 A three-phase machine is connected in delta. If the line currents are 5 A each, find the phase current in each winding. 4.40 Three heating elements can be connected in star or delta to a three-phase, 400/230 V system. If in star connection and 10 A flows in each resistor, determine: (a) the resistance of each heating element (b) the power drawn by the three elements connected in star (c) the power drawn by the three elements connected in delta. 4.41 In a three-phase, four-wire system, the line currents are each 100 A. The power factors in the three lines are: (a) 0.9; (b) 0.8; (c) –0.9 (leading). Determine what, if any, current flows in the neutral conductor. 4.42 The power input to a 400/230 V three-phase induction motor is measured by the two-wattmeter method. The wattmeters show readings of 13.5 kW and 7.5 kW, both positive. Calculate the line current, power input and power factor of the motor. 4.43 A factory supplied by a 400/230 V three-phase system has three lighting circuits, each consisting of 120 40 W fluorescent lamps with a power factor of 0.99 on a 20 A breaker. (a) Is that too many lamps on a 20 A circuit? (b) What is the actual power supplied to the lighting circuits? (c) If 20 lamps fail to operate on B-phase and 30 lamps fail to operate on C-phase, what are the circuit currents and neutral current? 4.44 A diesel locomotive generates 2500 Hp (1865 kW). The three-phase alternator generates 2800 V which is divided into 6 three-phase traction motors. If each traction motor takes 56 A per phase at full rated load with a PF of 0.8: (a) What is the load drawn from the alternator? (b) How efficient is the diesel electric process? 4 .45 Three resistors of 10, 20 and 30 Ω are connected to a 400/230 V, three-phase supply in: (a) star configuration (b) delta configuration. Find the line current and total power drawn from the supply in each case. 4.46 List the cicruit components that make up the fault loop impedance of a final sub-circuit that has a short of negligible impedance from the active to the earthed frame of an appliance. 301

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Electrical Principles 4.47 When designing and/or installing a final sub-circuit, the installer generally only has to consider the internal fault loop impedance. What device is the demarcation point where the internal fault loop can be determined from? 4.48 What is the normal operating temperature of X90 cable? 4.49 When a 25A ‘C’ curve breaker supplying a final sub-circuit was checked for fault loop impedance, a measurement of 1.3 Ω was taken (with the circuit turned on). Is this value acceptable as per AS/NZS 3000? 4.50 Through the use of the tables in AS/NZS 3008, what is the fault loop impedance of 25 m of 6 mm2 twin and earth V90 multicore cable?

302

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Solve problems in single- and threephase low-voltage machines: Part 1 Single- and threephase transformers

5

CHAPTER OBJECTIVES • • • • • • • • • • •

define the terms transformer, primary winding, secondary winding and magnetic core explain the operating principle of a two-coil transformer define transformation ratio, turns ratio, voltage ratio, current ratio and impedance ratio sketch the phasor diagram of a transformer under no-load conditions sketch the phasor diagram of a transformer under on-load conditions define and calculate iron losses, copper losses, transformer losses and transformer efficiency describe and calculate transformer voltage regulation describe typical single-phase transformer construction describe typical three-phase transformer construction describe typical testing of transformers for commissioning and parallel operation describe special use transformers such as potential transformers, current transformers, autotransformers, variacs, isolation and hi-reactance types.

5.1   Transformer construction 5.1.1  Types of laminations and core construction A transformer consists of a common magnetic circuit linking the primary and secondary windings. The form of construction is determined by the arrangement of the laminations and the way they are stacked together. Figure 5.1 shows two methods for making up the stack for a transformer core. Figure 5.1(a) shows U–I shaped laminations, which are stacked in alternate directions to make a core-type magnetic circuit. Figure  5.1(b) shows E–I-shaped 303

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Electrical Principles

(a) Core

(b) Shell

laminations, which are also stacked in alternate directions to make a shell-type magnetic circuit. Either type can be stacked from simple rectangles of lamination sheet— the preferred method for larger transformers. Although there are several variations of these types of construction, transformers can generally be classified as one of these two types: U–I or E–I. Transformers are also separated into groups known as ‘core’, ‘shell’ and ‘toroidal’ (see Fig.5.1).

Core With the core-type transformer, the windings surround the laminated core (see Figure 5.2(a)). To provide a uniform flux density throughout the magnetic core, the crosssectional area of the core is uniform.

(c) Toroidal core

Figure 5.1  Core, shell and toroidal NB Split magnetic path

(a) Core

(b) Shell

Figure 5.2  Windings—core and shell

A1 A2

Toroidal core wound over 360 degrees

Shell The shell-type construction has the magnetic core surrounding the windings (see Figure  5.2(b)). Because the core provides a parallel magnetic path for the flux, the centre limb is twice the cross-sectional area of the outer limbs, maintaining uniform flux density throughout the iron core. By comparison, the core-type construction has a lighter core of smaller cross-sectional area, but a greater length of magnetic circuit. It also has a relatively greater number of turns, but these have shorter mean length. The core type, with its larger window space, is more suitable for higher voltages requiring many turns and a larger space for insulation. The shell type is particularly suited for moderate voltages requiring fewer turns, less insulation, larger currents and lower frequencies, with corresponding flux densities.

Toroidal

The toroidal core is formed from a continuous ribbon of thin metal tape made from a special alloy. It is wound tightly around a former and consolidated under pressure into a solid mass. Toroidal cores must be wound by a special machine that passes the coil wire through the centre of the toroid many times. One advantage of the toroidal type is that the windings are spaced around the whole core, resulting in a shorter, constant cross-section magnetic path, with very low leakage flux (see Figure 5.3). A toroidal core may alternatively be sliced into two C-shaped pieces—the finished article is sometimes referred to as a ‘C-core’. The cut faces are ground to ensure good surface contact between the two halves. Two of these halves are placed around the transformer windings and clamped with a metallic band under moderate pressure to counter the effect of an air gap. For core-type construction using C-cores, one pair of cores is used; for shell-type construction, two pairs are used. It is usual to place a third clamp around the pair of cores after assembly to prevent noise and chafing by vibration. The same variations in single-phase cores apply to three-phase cores. For single-phase, the majority of transformer cores use the shell-type construction, while for three-phase, the majority are of a core-type construction. A three-phase transformer can be obtained using three identical single-phase transformers. But usually a common three-phase magnetic core is used, with three identical sets of primary and secondary windings mounted on it. Figure 5.3  Toroidal winding

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Single- and three-phase transformers  Chapter 5

Three-phase core type The shape shown in Figure 5.4(a) is usually employed in smaller distribution-type transformers. The coretype construction has a shorter length per turn of winding than the shell type but has a longer magnetic path. While similar in appearance to the single-phase shell type, each leg of the core has an equal crosssectional area.

(a) Core type

Core assembled from strips alternating in layers

Three-phase shell type This shape of core overcomes the tendency of the core type to have unequal flux densities (see Figure 5.4 (b)).

Three-phase cruciform or stepped core

(b) Shell-type transformer also assembled from strips

With conductors of large cross-sectional area, it becomes difficult to construct windings that have 90° bends in the conductors. With this shape of core, the windings are wound on circular formers and the core is stepped (in a cross-sectional area) to fill up the inside of the coil as far as possible with transformer laminations. The core is shown in cross-section in Figure 5.4(c), and it can be seen that a great number of different-sized laminations are required. This form of construction is expensive and is generally used only on large transformers.

Three-phase toroidal Generally speaking, these toroidal cores can be obtained in most shapes for three-phase transformers (see Figure 5.5).

(c) Cruciform or stepped core

Figure 5.4  Three-phase core types

5.1.2  Identification of different windings The actual placement of the windings on the transformer core depends on the type of core and the intended use of the transformer. Other factors that influence this arrangement are the operating frequency Figure 5.5  Three-phase C-core formed from rolled and bonded transformer steel strip and the size or power rating of the transformer. Some typical winding layouts are shown in Figure  5.6. While the core-type transformer construction is shown in the diagrams, the winding arrangement applies equally to the shell-type construction. With the concentric method, one winding is wound on the top of the other (primary or secondary) and suitable insulation is installed between the two. A sandwich or pancake-type winding is used where closely coupled windings are required, so that the magnetic leakage can be reduced to a minimum. The sandwich method is also used in large distribution transformers for ease of winding and handling, and also in smaller transformers operating at higher audio frequencies. The type of winding arrangement that is now becoming more common for power transformers is shown in Figure 5.6(c). This is due in part to Australian Standards recommendations for insulation requirements between primary and secondary windings. 305

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Electrical Principles

The same factors that affect windings and cores for single-phase transformers apply to three-phase transformers, although the majority of distribution transformers are wound in the sandwich or pancake S S PS P style. The method lends itself to ease of construction S P P and repair. The degree to which the primary and secondary windings are magnetically coupled depends on the (a) Side by side (b) Sandwich (c) Concentric (cheek to cheek) or pancake intended purpose of the transformer. A transformer is said to be ‘close coupled’ when all the primary Figure 5.6  Winding arrangements flux passes through the secondary turns. If a large proportion bypasses the secondary windings, the transformer is said to be ‘loosely coupled’. There are of course intermediate degrees of coupling. For example, a distribution transformer is less than close-coupled as a form of current limitation, to allow for the event of damage to overhead lines connected to its secondary. However, the degree of coupling for a high-tension transformer for an illuminated sign is far less than that for a distribution transformer. In this case, the on-load voltage must be considerably less than the open-circuit voltage. Australian Standards commonly require a thermal fuse in the windings of transformers used in many household appliances and in items such as plug-pack power supplies. Section view

5.1.3  Methods used to insulate low- and high-voltage transformers Insulation oil plays an important role in many high-voltage transformer insulation systems. The oil acts as a liquid dielectric and coolant. In low-voltage transformers there is no need for insulating oil as heat dissipation is very low. There are several materials currently used to provide insulation for transformers, and these include:

∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙

presspaper and pressboard flexible multi-layer insulation materials prepreg insulation materials mica products flexible electrically conductive surface materials side and top ripple springs slot wedges glass-fibre-reinforced plastic sheets glass-fibre-reinforced pultruded plastic profiles.

5.1.4  Construction of transformer tanks The transformer tank houses the transformer oil and provides physical protection for the coils. It also needs to protect accessories and controls. Changes in the loading can result in alternating tank pressure and, at times, vacuum. These need to be allowed for, to insure against deformations and stress fractures. Polished metallic surfaces inhibit the removal of heat from transformer oil and casings. It has been found that colours such as low-sheen variations of black, green or grey enable the oil to run at lower temperatures than would otherwise be the case. However, highly polished surfaces reflect the heat of the sun more than the above colours do, so reflective shields are sometimes used to shade the transformer.

5.1.5  Transformer auxiliary equipment Figure 5.7 shows the auxiliary equipment that can be found on a basic distribution transformer. 306

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Single- and three-phase transformers  Chapter 5

10 3

6

13

4 5

2

14

12

11

21

16

9 17

15

7

1 19

8

20

Figure 5.7  Transformer auxiliary equipment

5.1.6  Function of transformer auxiliary equipment The following list identifies the auxiliary equipment shown in Figure 5.7. It also provides a brief explanation of the function of each component.

1. Tank. Used to house the windings and cooling oil. 2. Lid. 3. Conservator tank. Used to fill the tank. Also stores oil which has expanded due to temperature increases. 4. The oil level indicator (end of conservator tank). This should be checked so that correct oil levels are maintained. 5. Buchholz relay for detecting gas bubbles caused by an internal fault. 6. Piping to conservator tank and Buchholz relay. 7. Tap changer to change output voltage. 8. The motor drive of the tap changer (can be controlled by an automatic voltage regulator). 9. Drive shaft for tap changer. 10. High-voltage (HV) bushing connects the internal HV coil with the external HV grid. 11. High-voltage bushing current transformers for measurement and protection. 12. Low-voltage (LV) bushing connects LV coil to LV grid. 13. Low-voltage current transformers. 14. Bushing voltage-transformer for metering the current through the passing bushing. 15. Core. Provides a path for the magnetic field. 16. Yoke of the core. 17. Limbs connect the yokes and hold them up. 18. Coils. Primary and secondary coils. 19. Internal wiring between coils and tap changer. 20. Oil release valve. Allows draining of oil for maintenance. 21. Vacuum valve. Allows the air and moisture to be removed from the oil. 307

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Electrical Principles

5.1.7  Types of information stated on a transformer nameplate The following is a list of the standard information on an oil-cooled distribution transformer nameplate. Nameplates are permanently fixed to the side of the transformer and are generally made of brass or stainless steel.

∙ manufacturer ∙ serial number ∙ year of manufacture ∙ number of phases ∙ VA rating (kVA, MVA, etc.) ∙ frequency ∙ voltage rating (primary and secondary) ∙ current rating (primary and secondary) ∙ tap voltages ∙ connection diagram ∙ cooling class ∙ temperature in °C ∙ polarity (if single phase) ∙ phasor or vector diagram ∙ % impedance ∙ approximate weight ∙ type of insulating liquid ∙ conductor material of each winding ∙ oil volume ∙ instructions for installation and operation.

5.1.8  Application of transformers A simple transformer consists of two separate windings, either close together or one around the other. Typically, an iron or ferrite core is used to increase the magnetic field density and efficiency of the transformer. One of the windings (called the ‘primary’) is connected to a source of electrical energy and the other (the ‘secondary’) to a load. The voltage of the secondary can be made to be higher, lower or the same voltage as the primary supply voltage. If higher, it is called a ‘step-up transformer’. If lower, it is called ‘a step-down transformer’. If it is the same voltage, it is referred to as a ‘one-to-one’ or an ‘isolation transformer’. Many transformers are fully reversible in operation, so the winding connected to the source of supply is always referred to as the primary winding. A transformer has no moving parts, so it needs minimal maintenance. Transformers range in volt-ampere size from a few to over a hundred, with efficiencies over 99% in the larger sizes. The level of efficiency is far higher than any other electrical apparatus or mechanical machine, yet, although there are no moving parts, the transformer is usually regarded as an electric machine.

5.1.9  Performing basic insulation resistance (IR), continuity and winding identification tests There are several tests that need to be performed on a transformer prior to putting it into service. These are carried out to ensure that there are no open/short circuits and that the correct connection can be made. An insulation resistance test should be performed between each winding and earth and between each of the windings. A continuity test (using an ohmmeter) should be performed to ensure that there are no open circuits in the windings. A winding identification test (an extension of the continuity test) will show which of the windings is the primary and which is the secondary. 308

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Single- and three-phase transformers  Chapter 5

5.2  Transformer operation 5.2.1  Principles of mutual induction of a transformer The primary and secondary windings and the magnetic core of the transformer are all stationary in relation to each other. The primary winding is connected to an alternating supply, causing an alternating magnetic flux to be produced in the magnetic core—the magnitude of the flux changes over time. The relative motion between the magnetic flux and the conductors of the secondary winding induces a voltage into the secondary winding.

5.2.2  Factors that determine the induced voltage in a transformer winding Transformer operation is based on the principle of mutual induction—that is, the changing current in the primary winding produces the changing flux in both windings, causing a back EMF in the primary winding and an induced voltage in the secondary winding, which is in fact the same as the induced EMF. A small transformer is shown in Figure  5.8(a), and the standard circuit symbol for a single-phase, iron-cored transformer is shown in Figure 5.8(b). Note the two windings are normally wound separately and placed side by side.

5.2.3  Determining the value of a transformer’s secondary voltage and current, given one winding’s electrical details and turns ratio The value of an induced voltage in a transformer depends on three factors: frequency, number of turns and the maximum instantaneous flux. Provided that the current waveform, and consequently the flux distribution, is sinusoidal, the equation for the RMS (root mean squared) value of induced voltage is given by: ​V′  =  4.44​Φ​  max​​ f N​ where: 2π ​​ ​​ ___  ​​  = 4.44 (adjustment for an RMS sine wave) √2 Φmax = maximum instantaneous flux f    = frequency N   = number of turns

Denotes iron core

Winding 1

(a)

Winding 2

(b)

Figure 5.8  Transformer and drawing symbol

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Since transformer cores are usually designed on the basis of permissible flux density, the above equation may be expressed as: ​V′ = 4.44 ​B​  max​​ Af N​ where: Bmax = maximum permissible flux density in Wb ​​      ​  ​  ​ ​​ A = cross-sectional area of core in square metres An important point is that Φ = BA.

Voltage ratio The mutual flux is common to each winding. Therefore, it must induce the same voltage per turn in each winding. ​V​  ′​ ​  If V ​​ ​  1′​ ​​is the total induced voltage in the primary winding having N1 turns, then the induced voltage per turn is ___ ​​  1   ​.​  ​N​  1​​ ​V​  ′​ ​  Similarly, the induced voltage per turn in the secondary winding is ___ ​​  2   ​​.  ​N​  2​​ On no load, the applied voltage V1 and the self-induced voltage ​​V​  1′​ ​​are almost equal and ​​V​  2​​  = ​V​  2′​ ​,​so the above ratios are transposed and usually expressed as: ​V​  ​​ ​N​  ​​ ___ ​​  1 ​   = ​ ___1 ​​  ​V​  2​​

​N​  2​​

That is, on no load, the ratio of the voltages is equal to the ratio of the turns.

EXAMPLE 5.1 A transformer has 1000 turns on the primary winding and 200 on the secondary. If the applied voltage is 250 V, calculate the output voltage of the transformer. ​V​  ​​  ​N​  1​​  ___ ​  1  ​ = ___ ​   ​   ​V​  2​​

 ​N​  2​​

​N​  ​​ ​V​  2​​ = ​V​  1​​  × ​ ___2 ​  ​​ ​    ​  ​   ​​ ​N​  1​​​  ​ 200  ​ = 250 × ​ _________  ​  1000 ​ = 50V

Current ratio When the transformer is connected to a load, the secondary current I2 produces a demagnetising flux proportional to the secondary ampere-turns I2N2. The primary current increases, providing an increase in the primary ampere-turns I1N1 to balance the effect of the secondary ampere-turns. Because the excitation current Io is so small compared with the total primary current on full load, it is usually neglected when comparing the current ratio of a transformer. Therefore, the primary ampere-turns equal the secondary ampere-turns: ​​I​  1​​​N​  1​​ = ​I​  2​​​N​  2​​​

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5.2.4  Identification of voltage and current components of a phasor diagram for a transformer on no-load

Applied magnetic flux (Φ)

Core

W1

W2 I1

V

V′

I2 V2

1 1 Under no-load conditions, the supply voltage is applied to the highly inductive primary winding. Denotes d.c. would cause a larger current to flow, probably start of winding burning out the transformer in a very short time. The Remember the right-hand grip rule! a.c. current, however, produces a self-induced voltage​​ ′ V​  1​ ​,​only slightly less than the applied voltage and in opposition to the applied voltage. Figure 5.9  Non-loaded transformer The only losses are that required to produce the magnetic field and the current flowing through the resistance of the primary winding. The no-load or excitation current is typically very small compared with the full-load current. In many V1 cases, the excitation current can be as low as 1 to 3% of the full-load current. The excitation current causes an alternating flux, called the ‘mutual flux’, to be set up in the core linking both primary and secondary windings, as shown in Figure  5.9. The mutual flux causes a voltage to be Io Ie induced in the secondary winding—the secondary Φ voltage ​​V​  2′​ ​​ —but no current can flow until a load is Im connected. The excitation current can be resolved into two rectangular components called the ‘energy’ and V2′ ‘magnetising’ components, as shown in the phasor diagram of a non-loaded transformer in Figure 5.10. Parallel circuits use the voltage as the reference phasor and series circuits use the current, as in each case the V1′ reference phasor is common to all of the components in the circuit. In transformers, the mutual flux produced by the magnetising component is common Figure 5.10  Phasor diagram for non-loaded transformer to both windings and is used as the reference phasor when drawing phasor diagrams for transformers. The phasor relationships are shown in Figure  5.10. The flux Φ is shown as the reference phasor, and the magnetising component of the excitation current is in phase with it. Both Φ and Im represent the purely inductive part of the circuit, and thus will lag 90°E behind the applied voltage V1. This means that, with flux as the reference phasor, the voltage will be leading the flux by 90°E. The energy component of current Ie that represents the losses in the iron circuit and the small copper losses is resistive and will be represented by a phasor in phase with the voltage. A wattmeter connected in the primary circuit would show power being used to cover these losses. The phasor sum of Im and Ie add up to the no-load current Io. The large angle (perhaps approaching 90°) between V1 and Io indicates a very poor power factor for a transformer on no load. The self-induced voltage ​​V​  1′​ ​​in the primary winding, since it opposes the applied voltage, is 180°E out of phase with V1.

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Applied magnetic flux (Φ) W1

W2 l1

l2

V1 V1′

V2

Load

5.2.5  Principles of power transferred from the primary to secondary when a load is connected using a phasor diagram neglecting impedance drops

When a load is applied to the secondary terminals, a secondary current I2 will flow and its magnitude and phase relationship with the secondary terminal voltage Figure 5.11  Loaded transformer V2 is determined by the type of load. Lenz’s Law tells us that the direction of this secondary current I2 will always be such as to oppose V1 any change in the flux Φ. In Figure  5.11, W1 is the primary winding with the start of the winding marked by a solid dot ‘∙’. I1 I1′ Assume that at a particular instant in time the primary current I1 flows from the start to the end of the Φ1 winding, establishing a flux with a magnetic polarity in a clockwise direction around the iron core as shown. I° This flux is mutual to both coils. Φ The mutual flux causes a reaction current in both coils, which has the effect of opposing the establishment Φ2 of the mutual flux. This can be seen as an opposing V 2′ reactive flux, but the total effect is to reduce the mutual flux, thus reducing the self-induced voltage ​​V​  1′​ ​​ in the primary and allowing more current to flow in both the I2 primary and secondary. V1′ All of these events happen together. The application of a load draws a current in the secondary winding, causing a demagnetising flux and reducing the mutual Figure 5.12  Phasor diagram for loaded transformer flux. The self-induced voltage in the primary decreases; the primary current increases; the mutual flux rises to its original value. In practice, the mutual flux in the iron core of a transformer effectively stays at a constant value for all loads. An increase in secondary load current causes an increase in primary line current. The phasor diagram in Figure 5.12 shows the general case for a transformer on load. Assume for the purposes of the diagram that the secondary voltage is equal to the primary voltage and the connected load is inductive, so that the secondary current I2 lags behind the induced voltage V​  ​​ 2′​ ​​by the phase angle φ2. The equivalent current to supply this load will be the value ​​I​  1′​ ​.​If the transformer were 100% efficient, this value of primary current would be the actual current flowing into the transformer from the supply. Since the excitation current Io is already flowing in the primary windings to cover core losses, the total primary current will be the phasor sum of these two currents (​I​​  1′​ ​ + ​I​  o​​ ) .​The phasor sum of I​ ​​1′​ ​​ and Io gives the actual primary current of I1 flowing at a lagging phase angle of φ1. It should be noted that the excitation current has been enlarged for the sake of clarity and copper losses in the windings are considered negligible.

5.2.6  Selecting transformers for specific applications Transformers with multiple secondaries Sometimes more than one secondary voltage is desired. The choice is then one of having two or more transformers to obtain the voltages or having one transformer with one primary winding and more than one secondary. 312

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It could occasionally be mandatory from a safety point of view to have separate transformers, but it is common (and cheaper) to have one transformer with a slightly larger core and as many secondaries as required. This is illustrated in Figure 5.13, where a transformer is shown with three secondary windings, each having different voltages. These extra windings may be called ‘tertiary’ windings. The current and voltage ratios discussed in Section 5.2.3 still hold true for the individual windings, but it should be remembered that the volt-ampere rating of the transformer will be the sum of the individual ratings of each winding. For example, to use the windings at ratings of 50 VA, 55 VA and 40 VA, the transformer as a whole would have to be rated at the sum of these figures (145 VA). If due regard is given to phasing the windings, it is only one step further to connect all three windings in series and have a total voltage of 322 V. This procedure then produces a winding with taps brought out at various voltages.

Tapped windings

200V

230V 50Hz

110V

12V

Figure 5.13  Tertiary winding transformer

130V 120V 230V 50Hz

110V

For smaller transformers in particular, it is common to see primary and secondary windings with tappings brought out to give a range of voltages 0V from a common point. This method of obtaining various voltages is shown in Figure 5.14. It is also a variation of the autotransformer method Figure 5.14  Tapped windings discussed below. While the taps are shown here on the secondary windings, the method is not restricted to secondary windings. It is also quite common for tapped primary windings to reflect a range of acceptable primary supply voltages, such as 220 V, 230 V and 240 V. Once the ‘turns per volt’ ratio of a transformer is established, it is a straightforward matter of calculating the required number of turns to determine the location of a voltage tap on the winding. A rule of thumb that was at one time commonly used in reference to the cross-sectional area of the laminations in the window in the coil stated seven turns per volt per square inch of iron. Using that rule, winding rooms could convert an existing transformer to a new voltage secondary. (That particular rule related to common laminations of the day, and modern materials will probably allow lower numbers of turns.) The volt-ampere rating of the transformer has to be observed, so converting a 24 V transformer to a 12 V transformer will allow for twice the current output, assuming that the winding conductor is an appropriate CSA.

Autotransformers An autotransformer has a part of the winding common to both the primary and the secondary circuits (see Figure 5.15). The voltage across any number of turns is proportional to the turns per volt established into the primary winding. Therefore, for the sake of simplicity, if a certain transformer has one volt per turn and is connected across a 230 V supply, it would require 230 turns. If, however, it was intended to also provide the correct output voltage at either 220 V or 230 V, there might be a tapping at 220 turns and another at 230 turns. Autotransformers, like other transformers, may be step-up or step-down, meaning the secondary may be a higher or lower voltage than the primary voltage. If a voltmeter were placed between the common V1 N 1 N 2 V2 (neutral) terminal and each of the tappings in turn, the V1 N N 2 V2 1 meter would read 220 V, 230 V and 240 V respectively. A load connected to one of the terminals would be (a) Step-down transformer (b) Step-up transformer provided with that voltage and a current allowed by the volt-ampere rating of the transformer. In this way, Figure 5.15 Autotransformers 313

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a device designed to operate on 240 V could be supplied from a 230 V supply (or 220 V, or 240 V) simply by selecting the appropriate tapping of the primary winding. Autotransformers are usually considered not to have a secondary winding, but the output may be referred to as ‘secondary’, and indeed there may be a secondary—or even tertiary—winding included. Standard AS/NZS3000 indicates the limitations placed on the use of autotransformers for general use. In general it stipulates that, except in special circumstances, the secondary voltage should not vary by more than ± 25% of the primary voltage.

Variac transformers Extending from the concept of an autotransformer, a transformer could have a tapping on every turn, making the range of output voltage almost continuous. ‘Variac’ is a common trade name for a transformer which is an autotransformer that has a toroidal winding with an exposed side cleaned of insulation so a moving ‘wiper’ can be adjusted along the winding, making an apparently continuously variable voltage. In fact, the voltage would only vary in steps according to the volts per turn if the wiper did not cover more than one turn. The circuit diagram for a variac is shown in Figure 5.16, while Figure 5.17 shows the windings and wiper arm.

Isolation transformers An isolation transformer is a type of transformer that has an equal number of turns on the primary and secondary windings. That means that the output voltage is equal to the supply voltage. Isolation transformers have two basic uses. One is providing isolation from the supply voltage so a machine that has a potential earth fault can be tested without dropping out the residual current devices (RCDs). Care must be taken when working in such environments. Another use is in testing circuits with a reduced risk of fault current as the current is limited by the Wiper 3A contact impedance and VA of the transformer. 4A Isolation transformers were once commonly used V1 V1 on worksites to operate power tools with a reduced 230V 1A 180V 45Ω V2 risk of earth faults and are still used in testing RCDs for compliance to the standards. 3A 4A The theory of using isolation transformers is that (a) Step-down autotransformer (b) Variable autotransformer—variac the output is unrelated to earth, and therefore an operator would need to make contact with both sides Figure 5.16  Variable voltage autotransformers of the transformer to cause a shock situation.

High-reactance or flux leakage transformers

Figure 5.17  Variac-style transformer

When designing transformers, the highest-possible efficiency is usually desired and design features are incorporated to reduce the leakage flux. In some applications, however, transformers with poor efficiency may be deliberately designed to meet particular requirements. One such transformer, called a ‘high-reactance’ or ‘leakage’ transformer, produces a very high no-load voltage and a comparatively small short-circuit current. The design is such as to permit a low flux leakage on no-load but a high flux leakage on increasing load. This is achieved by spacing the primary and secondary windings some distance apart on the core

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Magnetic shunts

(a) Core type

(b) Shell type

Figure 5.18  Flux leakage transformer

V2

No load

Secondary voltage

and by using either fixed or variable magnetic shunts (see Figure 5.18). On no load, the primary winding produces a flux in the core which cuts the secondary winding, inducing a voltage in it. The leakage flux is reasonably low because the air gaps in the magnetic shunt circuits produce a reasonably high reluctance in the shunt circuits. The secondary voltage can be calculated using the usual transformation ratio. When the transformer is loaded, however, the secondary current produces a flux that opposes the primary flux, causing some of the primary flux to be diverted through the magnetic shunts, thus reducing the value of flux cutting the secondary turns. This reduces the value of secondary voltage at an increasing rate. Figure 5.19 shows the secondary voltage decreasing as the load current increases. Transformers using this principle are found in such applications as furnace ignition, gaseous discharge lighting and welding machines. Long, narrow cores can achieve the same result as magnetic shunts, with the length of the core governing the degree of leakage. Distribution transformers have a small leakage factor built into them as protection against excessive currents in the event of transmission line failures.

Full load

I 2 (Load current)

Figure 5.19  Flux leakage transformer load curves

Welding transformers Welding transformers (which were not electronically controlled) generally used flux leakage or shunted flux techniques to control the amount of current delivered to the welding rod. Most cheap home welders—and even many high-powered welders—still use this basic technique. Figure 5.20 shows the transformer of a typical home welder, including the flux shunt, which is adjustable for varying the welding current.

5.2.7  Safety features specified in AS/NZS3000 with respect to transformers and isolating transformers Clause 2.7.2 of AS/NZS3000 refers to the requirements regarding protection by insulation or separation— specifically to provision of adequate insulation, screening or separation of windings. Clause 7.4.2 of AS/NZS3000 relates to the source of supply and the installation requirements of an isolating transformer.

Figure 5.20  Flux shunt welding transformer

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5.3  Transformer losses, efficiency and cooling Engineers design transformers for a specified voltage ratio and current (power) capacity, but once a transformer is placed in service, the load placed on it is beyond the immediate control of both the designer and the power supply authority. The actual load depends on the loading of the total number of connected circuits. Transformer design may assume that the individual circuits will not all reach maximum load at the same time, and so the transformer rating will be less than the total potential load. The load circuits may have a power factor different to the design expectations and therefore cause a higher current than a unity power factor. So, transformers are not rated by power but by voltage and current, which is expressed in terms of apparent power, VA. For example, a single-phase transformer capable of delivering 100 A at 500 V would be rated at 500 × 100 = 50 000 VA or 50 kVA. If the power factor of any given load is 0.5, then the maximum safe power output would be 25 kW. Similarly, at a power factor of 0.8 the safe power output would be 40 kW. In both cases, the full-load current would be 100 A. The current rating of the conductors in the windings is dependent on the rate at which the total heat generated in the transformer can be dissipated. The rating limitation of the transformer is a factor of the temperature rise of the unit on load and the ambient temperature. High ambient temperatures result in a lower rating and a low ambient temperature allows a high rating.

5.3.1  Power losses which occur in a transformer Iron losses—eddy currents The magnetic core of a transformer consists of many laminations of high-grade silicon steel of a definite thickness. The power absorbed by the core of a transformer is due to eddy currents and hysteresis, and is called ‘iron losses’. When the alternating flux cuts the steel core, an EMF is induced in each lamination, causing a current B Silicon (called an ‘eddy current’) to flow in the closed electrical steel (low loss) circuit of the lamination. This eddy current flows through the resistance in each lamination, causing heat to be generated in the laminations and therefore in Carbon steel the core as a whole. Although eddy-current losses are (high loss) effectively reduced by using laminations for the core, they are never entirely eliminated.

H

Figure 5.21  Hysteresis curves

Hysteresis  The alternating flux also causes changes in the alignment of the magnetic domains in the magnetic core, with the magnetic polarity reversing one hundred times per second. This change is energy-consuming and heat is produced within the core. The energy loss is referred to as hysteresis loss, the degree of loss being dependent on the nature of the material used for the laminations. Silicon steel has low hysteresis losses, making it suitable for electrical laminations. Figure  5.21 shows a comparison of two hysteresis curves for different

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materials. It can be seen that the silicon steel curve has a smaller area, representing a lower energy loss and reduced heat production.

Copper losses For details on these, see Section 5.3.2.

5.3.2  Tests which allow the power losses of a transformer to be determined

Co

Power

pp

er

los se

s

To ta

l lo

ss

es

To calculate the efficiency of a transformer, it is necessary first to calculate its losses. These present in the form of copper losses and iron losses. Two tests will determine them. The first test will determine the iron losses by measuring the power consumed on no load in what is known as a ‘no-load’ or ‘open-circuit test’. A W The transformer is connected as in Figure  5.22 to a supply at the rated voltage and frequency. The Open primary current on no load is usually less than 3% of V circuit the full-load current, so the primary I2R loss on no load is negligible compared with the iron loss. The wattmeter reading can then be taken as being the total iron loss of the transformer. Another form of loss that occurs in a transformer Figure 5.22  No-load or open-circuit test is copper loss, which is the energy lost in the windings when the transformer is loaded. The resistance of each winding is relatively low, but since the power A1 W dissipated in each winding is proportional to the square of the current flowing through that winding, it follows that the copper loss is significant when the A2 V load current is high. 2 2 The total copper loss is ​​p​  cu​​  = ​I​  1​ ​​  R​  1​​  + ​I​  2​ ​​  R​  2​​,​ where R1 and R2 are the resistance values of the primary and secondary windings respectively. The copper losses are not constant, but change according to the Figure 5.23  Transformer short-circuit test square of the load current. The value of the losses can be obtained by performing the short-circuit test, as shown in Figure 5.23. The typically-shaped curve of copper losses can be seen in Figure 5.24. As Figure  5.23 shows, the secondary winding of the transformer under test is shorted through the ammeter A2. An adjustable autotransformer is used to provide a low-voltage supply to the primary winding of the transformer on test. The output of the autotransformer is increased until the full rated current flows in the primary and secondary Iron losses circuits. The supply voltage to the transformer is low, and the flux in the iron core is also low, so the iron losses are negligible. The power registered on the Load current wattmeter can be taken as the total copper losses in Figure 5.24  Transformer losses the transformer on full load. 317

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5.3.3  Determination of transformer losses and efficiency using test results The efficiency of any machine is expressed as: output  ​η =______ ​   ​​   input A transformer normally has a high efficiency, so the difference between the output and input readings is very small (typically 1 to 3%). The efficiency is usually determined from the losses. output  ______ output  ​η = ​ ______ ​     = ​   ​ + losses​  input  output that is, ​V​  2​​ ​I​  2​​ ​λ​  2​​  __________________ ​​       ​​  (V ​ ​  2​​ ​I​  2​​ ​λ​  2​​  + ​P​  Cu​​  + ​P​  Fe​​)

where: PCu = copper losses ​​    ​  ​   ​​​ PFe = iron losses Assuming the output voltage V2 remains constant, the only variables affecting the efficiency of a transformer are load current and power factor.

EXAMPLE 5.2 11 kV A single-phase ​​ _____   ​​transformer supplies a load current of 30 A at a power factor of 0.8. A short230 V circuit test is performed and the wattmeter indicates that the copper losses at full load are 420 W. An open-circuit test reveals the iron losses to be 320 W. Calculate the efficiency of the transformer. Power out = 230 × 30 × 0.8 = 5520 Power in = Power out + losses = 5520 + 420 + 320 = 6260 ​​           ​  ​  ​  ​​​ output 5520  ____________ _____  η = ​       ​  × 100 = ​   ​   × 100 = 88% output + losses  6260

5.3.4  Relationship between transformer cooling and rating The cooling system of a transformer affects the life of the transformer and its kVA rating. An increase in cooling efficiency will increase the kVA rating. For example, a transformer with an 80°C rise in temperature uses between 13 and 23% less energy than the same transformer operating at 150°C. A small increase in the operating temperature will have a negative impact on the efficiency of the transformer, and its life will be considerably shortened as the heat will chemically alter the insulating materials, causing them to deteriorate sooner.

5.3.5  Methods used for natural and forced cooling of transformers As with any device, a transformer on load generates heat. Transformers generate heat in both the core and the windings. For smaller units, the surface area is great enough to remove the generated heat by convection and 318

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radiation. As transformer size increases, the surface area becomes proportionately smaller than the volume, and eventually the heat being generated cannot be dissipated quickly enough. As a result, the temperature of the transformer begins to rise and additional cooling methods must be used. In general terms, there are two commonly used media for transformer cooling—air and oil. The methods for (and combinations of) these are many and varied.

Filler-breather Dipstick

Transformer oil

Cooling tubes Transformer windings Transformer core

Air cooling For air cooling, the transformer must be provided with ducts between the coils, and between the core and the housing, so that air can be blown through them to remove the heat. The air must be filtered so that dust cannot build up in the ducts, become wet and lead to faults. Air-blast cooling is seldom used in very large transformers, or for voltages above 20 kV. It is used on transformers where economy of space and weight is required, or where oil cooling may be a fire hazard.

Sludge space Drain

Figure 5.25  Transformer cooling

Oil cooling One common method used for cooling is to immerse the transformer in a tank of special transformer oil, providing as large a cooling surface area of the tank as possible by using external tubes, as shown in Figure 5.25. The oil serves the dual purpose of cooling and insulating. It conducts the heat from the core and the windings to the surface of the tank and the external tubes. The heat is then dissipated into the surrounding air, cooling the oil that circulates through the tank by means of natural convection.

Figure 5.26  Transformer heat exchanger

Forced circulation For very large transformers, convection within the oil does not remove the heat quickly enough, so forced circulation methods are needed. The oil is drawn off at the top of the tank, pumped through a water-cooled heat exchanger and then returned to the bottom of the transformer tank. Figure 5.26 shows such a transformer.

5.3.6  Properties of transformer oil Although the basic function of transformer oil is to provide electrical insulation and heat conduction, its other properties should be taken into consideration. The viscosity of the oil determines its flow rate. Its purity will reduce the risk of oxidisation and sludge build-up. The flash point of the oil is the temperature at which it will ignite spontaneously and is typically greater than 140° Celsius. The fire point is the temperature at which the oil will burn and is typically greater than 170° Celsius. 319

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5.3.7  Tests conducted on transformer oil Tests need to be carried out periodically to ensure that the oil in the transformer is fit to provide the cooling and insulating functions. Visual inspections are conducted to check oil colour, levels and evidence of sludge, which can bake itself to the insulation and mechanical structures. A dielectric test will check the breakdown voltage of the oil, which can be reduced with the introduction of contaminants such as water and dirt and other conductive particles. A dissolved gas analysis (DGA) is conducted to determine the performance of the transformer. Gasses extracted from the oil are identified, and these can provide early warning of abnormal transformer operation. An interfacial tension (IFT) test will assess the levels of soluble contamination and oxidising agents in the oil. Over time, the oil will oxidise and the acidity levels will increase. An acid number test will assess the acid levels in the oil. Varnish and paint can also contribute to increased levels of acidity. A power factor test measures the dielectric losses of the oil, or energy that is dissipated as heat. A low power factor indicates that the oil has high levels of contamination or has deteriorated.

5.4 Transformer voltage regulation and per cent impedance 5.4.1  Voltage regulation as applicable to a transformer A transformer is expected to deliver a pre-determined voltage at full load. The two major losses that have been discussed so far are:

1. magnetic losses, which include leakage flux and other magnetic core losses 2. copper losses due to winding resistance.

Because of these, the full-load voltage will tend to be less than the no-load voltage. To obtain a regulation value, the primary input voltage should be maintained at its rated value and the power factor of the load must be known—the regulation value obtained is relevant only at this value of power factor for a particular transformer. Voltage regulation of a transformer can be expressed as a percentage of its full-load voltage (the formula given is really only accurate for single-phase transformers): (​V​  ​​  − ​V​  FL​​) ​voltage regulation = ​ __________ ​  NL  ​       ​ × 100%​ [ ]  ​V​  FL​​ The voltages used are all secondary values. Where a formula differs from the above, it should be checked to see whether equivalent or reflected values are to be used. Care must be exercised when using a regulation value as a basis for comparison with another transformer. Comparisons with transformers of a different load, power factor or voltage ratio are not valid.

5.4.2  Percentage impedance as applicable to a transformer Impedance ratio is very significant to audio and radio technicians, but electrical workers need to understand it, too. The key point is that when the voltage goes down as a result of the turns ratio, the current will go up for the very same reason. The impedance—or resistance, if that makes things clearer—is a result of both changes. Therefore, the impedance ratio is the square of the turns ratio. A typical situation is when a television antenna has been designed with an impedance of 300 Ω but needs to be connected to the coaxial cable that has an impedance of 75 Ω. A transformer is used with a turns ratio of 2:1, therefore the voltage ratio will also be 2:1 and so the output voltage will be half the input voltage. Meanwhile, the V 0.5V1 output current will be twice the input current. Therefore the output impedance will be Z2 = ​​ __2 ​​  = ​​ ___  ​​ = 0.25Z     1 or I 2I1 2 2 Z N a quarter of the input impedance. That is, the ratio of __ ​​  2 ​​ is found from ​​​ ___ ​  2 ​  ​​​  ​​. Z1 (N1) 320

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Single- and three-phase transformers  Chapter 5

5.5 Parallel operation of transformers and transformer auxillary equipment 5.5.1  Polarity markings for an unidentified single-phase double wound transformer To determine the polarities of transformer windings, two terminals are connected together (one terminal of each winding). If the voltmeter reading across the other two connections is greater than the supply voltage, the two voltages are aiding each other and the transformer is said to have dissimilar ends joined. Therefore, the ‘open end’ of the primary is marked as the ‘start’ of the primary and the joined end of the secondary is also marked as a ‘start’ end. If the voltmeter reads less than the supply voltage, then the voltages are opposing each other and the windings have similar ends bridged; both open ends should be marked as starts, shown by a dot (∙).

5.5.2  The need for parallel operation of transformers It is sometimes necessary to operate two or more transformers in parallel. To do this, not only must the output voltages be equal but the instantaneous polarities must be the same. Tranformers can be connected in parallel to supply a load in excess of the rating of the existing transformer, thus reducing the expense of having to replace the original transformer with a larger-capacity transformer. Having a number of transformers in parallel allows maintenance to be carried out on a single transformer without interruption to the supply.

5.5.3  Conditions/restrictions required before two transformers can be connected in parallel Equal voltages If two unequal voltage sources are connected in parallel, a circulating current is set up between them. One transformer becomes a burden on the other and they are unable to supply full power to an external load. Essentially, the turns ratios must be the same for the same style of connection.

Same phase sequence If different phase sequences are connected in parallel, the least that can occur is a short-circuit between the lines. Heavy circulating currents flow, and damage will almost certainly occur to both transformers (and perhaps to the installation).

Phase angle shift The change in phase angle from primary to secondary on both transformers must be identical, otherwise dangerous circulating currents will be generated. Satisfactory parallel operation can occur only when the two transformers belong to the same group and have the same phase shift.

Compatible internal impedance The two transformers must have a compatible range of internal impedance to allow effective load-sharing across the load range. Parallel operation involves two or more transformers connected to a common source of supply and their secondaries connected to a common load. Only when the two transformers match in all important characteristics can they be expected to share the load evenly, or according to design. 321

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A1

Primary

a1

Secondary

Primary

A1

Secondary

a1

5.5.4  Connecting transformers in parallel to supply a single load (loading on transformers operating in parallel)

When drawing sketches of transformers, the dot or a similar system of identification for winding ends A2 Windings a2 is satisfactory. In practice, it is more usual to be confronted with a transformer and a row of terminals, which makes some general system of identification Figure 5.27  Typical terminal arrangements for a single-phase necessary. AS/NZS2374 sets out such a system for transformers power transformers. In brief, all terminals are given an identifying letter and a subscript number; capital letters are used for the higher voltage winding, and lower-case letters for the lower-voltage winding. Where more than one end of a winding is brought out to a terminal, the higher number is the line terminal unless a specific phase shift is required. An example for a single-phase transformer is shown in Figure 5.27. The standard specifies that the identification is permanently marked on, or adjacent to, the terminals. Invariably this means stamping the identification into the metal of the terminal or the case adjacent to the terminal. In addition to this, supply authorities might require further markings on the transformer to assist them in installation or to match their phase sequence. A2

a2

5.5.5  The consequences/effects of an incorrect connection Transformer connections should always be checked before loading. Serious damage can be caused by an improperlyconnected transformer, and operators risk injury or electric shock. When two unequal voltage sources are connected in parallel, the phasor difference between the voltages causes a circulating current to be set up. The current flow is limited only by the impedances of the windings and will flow despite all other conditions for parallel operation being met. Large quantities of heat are generated, and the circulating current effectively renders both sources of power useless.

Instantaneous polarities The two transformers shown in Figure 5.28 have their primary windings wound in the same direction around the iron core. When the instantaneous polarity of line A is positive (indicated by the dot), the mutual flux Φ in each transformer acts in the same direction. The secondary windings in Figure  5.28 are (a) W1 W2 shown wound in opposite directions to each other. I2 I1 The induced voltage V2 acts in an upward direction A in (a), while in (b) V2 acts downward. In both cases, V2 V1 V1′ the secondary flux Φ2 must oppose the mutual flux (Lenz’s Law). This condition is met by the induced voltage acting downward in (b) and producing an instantaneous current flow, as indicated by the arrows (b) W1 W2 in both figures. That is, when an instantaneously I2 I1 positive voltage is applied to the primary terminals A (indicated by dots), there will be an instantaneously V2 V1 V1′ positive voltage produced at the secondary terminals (also indicated by dots). In general terms, the positioning of dots on winding ends is used to indicate the similar instantaneous polarities. For single-phase transformers to operate in parallel, their voltages must Figure 5.28  Winding polarity 322

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Single- and three-phase transformers  Chapter 5

Supply

Supply

I1

I2

V2

V1

V2

I2

I1

I1

I2

V1

I1 V1

V2

V1

V2

I2

Load

Load

Figure 5.29  Parallel transformers correctly connected

Figure 5.30  Path for circulating current

be equal and their instantaneous polarities must also be identical. The correct connections for two transformers in parallel are shown in Figure 5.29. If terminals of the wrong polarity are connected together, a high circulating current is set up in both primary and secondary windings. Effectively, the two secondary windings are connected in series and then short-circuited. The path for the circulating current is shown in Figure 5.30 as highlighted yellow.

5.6  Special transformers 5.6.1  AS/NZS3000 requirements with respect to transformers Section 4.14 of AS/NZS3000 refers to the rules regarding the installation of transformers and states that they (excluding those listed as exempt) should be installed in accordance with clauses 4.14.2 through to 4.14.5. The section details the installation requirements for equipment connected to secondary circuits, control and protection, isolating transformers, other transformers, autotransformers and step-up transformers. Clause 7.4.7 details the verification of testing transformers.

5.6.2  Voltage transformers The voltage or potential transformer operates on the same principle as the power transformer, where the ratio of the primary and secondary voltages is proportional to the turns ratio of the primary and secondary windings (i.e. V2 ∞ V1). Voltage transformers are designed to have a standard output voltage when the full rated voltage is applied to the primary windings. For single-phase work, AS/NZS1243 specifies a secondary voltage of 110 V; where transformers are used in the star connection for control work in substations, the standard output voltage for each transformer is 63.5 V, giving a line-to-line voltage of 110 V.

L1

CT

V

W

A

Z

PT N

Figure 5.31  PT/CT power measurement

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Electrical Principles

The secondary voltage is connected to the appropriate loads such as voltmeters, wattmeters and protection relays. The VA ratings of potential transformers are quite P small as these instruments require little energy to operate. P S S One terminal of the secondary winding is often earthed as an added safety measure in the event of a breakdown in Secondary (110V) Secondary (5A) the insulation between primary and secondary windings. (a) Potential transformer (PT) (b) Current transformer (CT) The standard symbol for a potential transformer (or PT) is shown in Figure  5.32. A typical PT is shown in Figure  5.33. The four terminals of a PT are designated. Figure 5.32  Potential and current transformer symbols Care must be taken to see they are correctly connected and the two voltage systems appropriately isolated. The physical features are similar to those of a power transformer except that the primary has to be insulated for a much higher voltage and is often immersed in oil for extra protection. The important factor with potential transformers is the accuracy of the voltage ratio and the elimination of phase-angle errors. The energy levels being measured are generally large, and therefore losses in the transformer are inconsequential compared to the power levels. A phase angle of 0° is desirable (180° is also acceptable), particularly where a PT has to supply such instruments as wattmeters, which have more than one operating coil. As a general guide, a potential transformer usually operates at low flux densities in iron cores of relatively large cross-sectional areas. The copper conductors have few turns and are large in cross-section for the small current taken.

Potential transformer burden A PT is also assigned a load or burden rating. This gives an indication of the available full-load secondary current and also the load placed on the supply source. For example, a 200 VA potential transformer at 110 V would make available approximately 1.8 A of secondary current for meters and relays: ​110 V × 1.8 A = 200 VA​

Safe working procedures

Figure 5.33  Potential transformer Shutterstock/By Matee Nuserm

Potential transformers are designed to restrict the high voltage to a designated area and conduct a safe lower voltage to a monitoring point where it can be connected to instruments or relays. The secondary voltage should always be proportional to the primary voltage. One of the secondary terminals is usually earthed. Care must be taken in the choice of instruments and their handling to ensure that an additional earth is not introduced at some other point within the circuit. In some cases, a non-magnetic, electrostatic shield is installed between the primary and secondary windings during manufacture. This shield is earthed as a means of protection for the operator as well as removing electrostatic interference and noise. When connecting meters to a PT, a short-circuit across the terminals must be avoided, as with any high-impedance device.

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Single- and three-phase transformers  Chapter 5

5.6.3  Current transformers In a power transformer, the flux density in the core is high, the primary current depends largely on the secondary current and the voltage ratio is the main consideration. However, for the current transformer, the core flux density is very low, the secondary current is connected across a low-impedance load (and therefore depends directly on the primary current) and the current ratio is the main consideration. The primary winding of a current transformer is connected in series with the load and consists of one or a few turns of a heavy gauge conductor, often a copper busbar. The impedance of the primary winding is therefore so low that the primary current I1 is not affected by the secondary load but depends on the external load connected in the primary circuit. The secondary circuit consists of the current coils of ammeters, wattmeters and protective relays that are all lowimpedance loads. The secondary circuit is always closed, so the secondary current produces a flux, which opposes the primary flux, greatly limiting the flux density of the core and therefore any load on the primary. The current ratio is equal to the inverse of the turns ratio, and so there are more turns on the secondary winding. If the secondary becomes open-circuited, there will be no secondary flux to oppose the primary flux, and so the core flux density will increase. Owing to the large ratio of secondary to primary turns, and the excessive core flux, the induced voltage at the secondary terminals increases greatly, producing a safety hazard and the possibility of insulation breakdown. The greater core flux might also cause excessive heat losses and saturation in the core. Consequently, the secondary of a current transformer must never be open-circuited under any circumstances. A suitable short-circuiting link is normally provided for connection across the secondary terminals when the instruments are disconnected. Current transformers (CTs) are made in a number of forms, depending on requirements and current ratios. Some types have primary windings that have more than one turn, while others are variations of the one-turn primary stage. One variation of the single-turn primary type has a short straight conductor passing through a hole in the iron core that forms part of the transformer’s construction. Another type has an opening in the iron core and the transformer is slipped over the busbar or cable. Some current transformers have a secondary winding wound on a circular iron core, which is also slipped over the busbar adjacent to a circuit breaker or power transformer. The standard for current transformers (IEC 60044 (AS 60044)) specifies two values for current range—1 A and 5 A. The higher value is still used in many instances, but increasing use is being made of the lower value, especially in substation work where the instrumentation and control relays are some distance away from the transformers. At the lower value of current, the resistance and impedance of the cable is of relatively less importance. A current transformer suitable for use in a high-voltage substation is shown in Figure 5.34.

Current transformer burden Current transformers are designed to measure line currents without affecting the load in any way. Consequently, while a CT might be able to handle high or low currents, the burden it imposes must be as low as possible (e.g. 5 VA). The CT must have a load on the secondary at all times; therefore, the burden will exist at all times, causing a small voltage drop in the primary conductor at the point of the CT placement. Current transformers are used to handle high currents while providing a proportional current to normal instruments on a.c. The CT isolates the supply voltage from the operator, and at the same time smaller conductors can be taken from the CT to the measuring location. The secondary of a CT must never be open-circuited—to do so would allow high voltages at the terminals. With most CTs and associated instruments, a

Figure 5.34  Current transformer Source: ABB Australia

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Electrical Principles

shorting link is provided. Any connecting or disconnecting in CT circuits must follow a standard operating procedure that ensures the CT is not open-circuited at any stage. An additional factor that should be taken into account is that an open circuit, apart from the high secondary voltage problem, can also lead to magnetic saturation occurring within the core that can affect the accuracy of the CT for future use. Current transformers must have all the windings held firmly in place to withstand the magnetic forces created during overloads, current surges and fault conditions. The secondaries often have one side of the winding earthed for protection and, in some cases, a non-magnetic screen between the windings.

5.6.4  Instrument transformers It is unsafe to connect instruments and equipment to high-voltage and high-current circuits, so instrument transformers are used to reduce these voltages and currents to safer, more convenient values. The two types of instrument transformers used are potential and current transformers. Figure 5.31 shows how a voltmeter, an ammeter and a power meter are connected to high-voltage lines by means of voltage and current transformers.

Summary ∙ Transformers operate on the principle of mutual induction. Alternating current creates an alternating magnetic flux that cuts both windings and generates a self-induced voltage in the first or primary winding and a mutually induced voltage in the second winding. ∙ The secondary voltage can be greater or less than the applied voltage, depending on the number of turns on the two windings. ∙ The transformation ratios are: ​V​  ​​  ​N​  1​​  __ I​ ​  ​​  ___ ​​  1  ​ = ___ ​   ​ = ​  2  ​​   ​V​  2​​

 ​N​  2​​

 ​I​  1​​

∙ Transformer losses are due to copper and iron losses and affect the transformation ratios in practical situations. output  ∙ Transformer efficiency = ​​ _____________       ​​  output + losses (VNL − VFL)  ∙ Voltage regulation = ​​ ___________ ​     ​   ​​ × 100%  VFL [ ]

∙ Transformer cores can be shell type or core type for both single-phase and three-phase transformers. ∙ Cores are usually laminated with special grades of steel to reduce iron losses. Some smaller transformer cores may be made from powdered iron cores set in a medium to hold their shape. ∙ There is a growing trend towards C-cores that are pre-formed from special-grade steel and stress-relieved before use. ∙ Toroidal cores are a highly efficient alternative to C-cores. ∙ Coil winding arrangements depend on the use to which the transformer is put. Windings may be tightly or loosely coupled. ∙ Transformer cooling is essential on larger transformers. It may be air or oil cooling. There are many variations and combinations of cooling methods. Even the colour of the tank holding the transformer has an effect on cooling. ∙ Winding polarity knowledge is necessary in order to connect transformer windings for paralleling purposes. ∙ Three-phase transformer connections can cause phase shifts in secondary voltages. ∙ Factors affecting parallel operation of transformers are: voltages, frequencies, instantaneous polarities and phase relationships affected by connections. ∙ Commercial transformers have to conform to Australian Standards with regard to terminal plate layouts. ∙ Transmission transformers may have a tertiary winding to suppress third harmonics in the system. 326

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Single- and three-phase transformers  Chapter 5 ∙ In long-distance transmission lines, it might become necessary to change transformer ratios while on line to maintain voltage levels. ∙ Two methods for changing ratios are off-line and on-line tap changing. ∙ Special purpose transformers comprise: – potential and current transformers – autotransformers.

Questions Exercises 5.1 What is meant by the terms primary and secondary windings? 5.2 Explain the relationship between the voltages and number of turns of the two windings of a transformer. 5.3 Explain how a transformer regulates the amount of primary current required to supply a given secondary load. 5.4 What is meant by the term leakage flux and how is it kept to a minimum? 5.5 How are eddy current losses in a transformer effectively reduced? 5.6 What kind of steel has low hysteresis losses, making it suitable for electrical laminations? 5.7 What is a Variac? Explain an application where it might be used. 5.8 What is an isolation transformer? Explain an application where it might be used. 5.9 What type of transformer is suitable for a gaseous lamp ballast? Explain why it is used. 5.10 Explain what a flux shunt is and how it affects the operation of a transformer. 5.11 How does a welding transformer restrict current flow after the arc is struck? 5.12 What are the major losses in a transformer and how are they affected by the load? 5.13 List three tests that should be performed on a transformer prior to putting it into service. 5.14 Explain why the polarities of transformers must be known when the transformers are to be connected in parallel. 5.15 Using a diagram, show the method of connecting the instruments required to measure power in a high-voltage, highcurrent a.c. circuit. 5.16 Describe the construction of a current transformer. 5.17 Compare the operation of a current transformer with that of a potential transformer. 5.18 Why is it necessary for the secondary of a current transformer to be kept closed? 5.19 What is an autotransformer? List the advantages and disadvantages of autotransformers. 5.20 Explain an application where an autotransformer might be used. 5.21 What is the maximum percentage for voltage—over and under—given by Australian Standards for autotransformers. 5 .22 A 500 VA transformer supplied with a 32 V output is to be rewound to deliver 12 V. (a) Will it be necessary to rewind the primary winding? (b) How will the secondary need to be altered for the new voltage? (c) What effect will the rewinding have on the iron losses of the transformer assuming the core is correctly disassembled and reassembled? (d) What effect will the rewinding have on the copper losses of the transformer? 5.23 List two methods of changing transformer ratios. 327

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Electrical Principles

Calculations 5.24 The primary winding of a 4​ 00/24 V​transformer has 400 turns. How many turns are there on the secondary winding? 5.25 A 100 kVA ​11 000 V/230 V​transformer operates at 6 V per turn. Find the number of turns and current rating of each winding. 5.26 The ​230/110 V​transformer is connected to a 22 Ω resistive circuit. Calculate the primary current. 5.27 230 V is applied to the primary winding of a transformer having 100 turns. If the secondary has 900 turns, calculate the secondary voltage. 5 .28 Tests on a transformer rated at 19 kV to 480 V at 50 Hz establish: (a) open-circuit test—iron losses = 586 W (b) short-circuit test—copper losses = 600 W. If the transformer supplies a resistive load of 9.6 Ω, calculate the efficiency of the transformer. 5.29 An autotransformer is used to boost the voltage on a 7700 V feeder to 8000 V. If the load on the secondary is 72 kW at unity power factor, find: (a) the secondary or output current (b) the primary or input current (c) the current in the common section of the winding. Neglect all losses. 5.30 A ​230/115 V​single-phase transformer has 960 turns on its primary winding. Calculate the number of turns required on the secondary winding. 5.31 The load on the secondary of a ​230/32 V​single-phase transformer is 3 A. Calculate the primary current if the transformer efficiency is 75%. 5.32 A 230 V 50 Hz single-phase transformer has a core area of 25 cm2. If it is to work at a maximum flux density of 1.1 T, find the number of turns required for the primary winding. 5.33 The maximum flux of a 50 Hz transformer is 0.001 Wb. If the primary is wound with 1080 turns, find the applied primary voltage and then calculate the number of turns required for a 15 V secondary. 5.34 A voltmeter, ammeter and wattmeter are connected to a single-phase circuit, by means of the appropriate instrument transformers, and the following results are obtained: ∙ CT ratio  100:5 ∙ PT ratio   11 000:110 ∙ voltmeter reading   10 800 V ∙ ammeter reading   95 A ∙ wattmeter reading   872 kW. Calculate the actual voltage, current, volt-amperes and power in the secondary circuit. 5.35 A step-down autotransformer has 500 turns and is tapped at 300 turns. The primary current in thirty amperes, and the secondary voltage is 330 volts. Determine: (a) secondary current (b) primary voltage (c) the current in the common section of the winding. 5.36 A single-phase autotransformer is used to increase the voltage at the end of a long distribution line. The primary voltage is 220 volts and the secondary voltage is 250 volts when the secondary current is 22 amperes. (a) primary current (b) common current.

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Single- and three-phase transformers  Chapter 5 5 .37 A 5 kVA single-phase 50 hertz transformer has a 230 volt primary and a 120 volt secondary, calculate: (a) primary current (b) secondary current (c) transformer impedance. 5 .38 A 20 kVA single-phase transformer designed to operate from a 400 volt supply, calculate: (a) the base current (b) the base impedance for the transformer primary.

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Solve problems in single- and threephase low-voltage machines: Part 2 Alternating current rotating machines

6

CHAPTER OBJECTIVES • • • • • • • • • • • • • • • • •

describe the construction of three-phase induction motors explain how a rotating magnetic field is developed in a three-phase motor describe how torque is developed in a three-phase motor explain the relationship between speed, frequency and the number of poles describe how a three-phase motor is reversed list special purpose rotors available and explain the effect on torque explain the operation of wound-rotor motors list abnormal operating conditions for three-phase motors and their effect on performance describe maintenance and electrical testing requirements for three-phase motors describe how a rotating stator field is developed from a single phase describe how torque is developed in a single-phase motor list the types of single-phase induction motors compare operating characteristics of single-phase motors understand the relationship between speed, frequency and number of poles list applications for various single-phase induction motors explain the reversal of single-phase induction motors differentiate between single-phase motor circuits.

6.1   Operating principles of three-phase induction motors 6.1.1 Introduction The majority of electric motors used in industry are of the a.c. induction type, usually running on a three-phase supply. The induction motor gets its name from the fact that the currents flowing in the rotor are induced and not drawn directly from the supply. Three-phase induction motors are simple, efficient, rugged and have a high degree of reliability. They normally consist of a laminated stator with three identical windings distributed symmetrically around it. The stator and rotor are laminated as both carry alternating current. A typical three-phase induction motor is shown in Figure 6.1. 331

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Electrical Principles

6.1.2  Rotating magnetic fields

Figure 6.1  Typical three-phase induction motor

A three-phase induction motor depends for its operation on a rotating magnetic field being established by the a.c. windings. The three separate windings are installed in the stator at 120°E intervals to one another, and provide a fixed number of poles for each phase. This is shown diagrammatically in Figure 6.2(a) for one phase of a two-pole machine. Figure 6.2(b) shows the three phases in relation to one another, giving a total of six poles. Phase A is drawn as a solid line, phase B as a dotted line and phase C as a dashed line. This sequence applies to all of this explanation, including the current waveforms, the magnetic fields and the phasors.

CMG Engineering Group—a Regal Beloit Company

Assumption In the following explanation for the production of a rotating field, one assumption has been made as B1 a reference—that winding ends A, B and C, when connected to a positive source of voltage, make the C1 adjacent iron core a north magnetic pole. From this, it N follows that the opposite pole becomes a south magnetic S pole. These details are also shown in Figure 6.2(a). If the current flow is reversed, the magnetic poles are also C B reversed. With the three windings connected in star A1 A1 configuration by joining ends A1, B1, C1 together, and the ends A, B and C connected to a three-phase supply, (b) Three phases (a) One phase the phase currents IA, IB and IC are 120°E out of phase Figure 6.2  Polarities and connections in a two-pole, three-phase with one another. This is shown in Figure 6.3. motor As each current is alternating, each pair of poles sets up a magnetic flux that continually changes from lB lC lA one polarity to the other. Although the flux set up by phase A in Figure 6.2(b) alternates in the direction in the diagram, it does not rotate in any way. It simply varies in strength and direction in the vertical plane. Similarly, a pulsating flux is established by the other 0° 120° 240° 360° two phases, giving a total of three magnetic fluxes that combine into one resultant flux. This flux rotates at synchronous speed. At reference position 1 in Figure  6.3, the current IA is zero and no flux is produced by the winding A–A1. Current IB is negative and so will produce a 1 2 3 4 5 6 7 8 south pole at B and a north pole at B1. Current IC is Figure 6.3  Waveform diagram showing three-phase currents at 120°E positive so will produce a north pole at C and a south pole at C1. As currents IB and IC are equal, the two magnetic fields are equal in strength. The directions of these fields are shown in Figure 6.4(a). In the accompanying phasor diagram, the addition of these two fields is shown, giving a resultant instantaneous field ΦR. At position 2 in Figure 6.3, IA is positive, IB is still negative and IC is zero. This produces a north pole at A, a south pole at B and nothing at C. This is illustrated in Figure 6.4(b), together with the phasor diagram showing A

A

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Alternating current rotating machines  Chapter 6

A B1

ΦC

N

S

C1

ΦC ΦR

ΦR C

ΦB

N

S

ΦB

B

A1 (a) Position 1

ΦB

ΦC ΦA

ΦA ΦR

A

ΦR A

N

B1

N

C1

N

B1

N

C1

ΦC C

ΦB

ΦA

ΦR

S

B

S

A1 (b) Position 2

C

S

ΦR

ΦA

B

S

A1 (c) Position 3

Figure 6.4  Resultant flux produced at positions indicated from Figure 6.3

the addition of the phasors and the resultant instantaneous magnetic field. Since all coils have an equal number of turns, the relative strengths of the magnetic fields can be gauged by measuring the vertical heights of the current waveforms at the positions indicated by the reference number. In this instance, the direction of the resultant magnetic field has shifted 60°E clockwise from that in position 1. If drawn to scale, it can also be shown that the length of the resultant has remained constant, indicating that the field strength has remained constant. At position 3 (in Figure 6.3), IA is positive, producing a north pole at A and a south pole at A1; IB is zero and IC is negative, producing a south pole at C and a north pole at C1. These fields are drawn in Figure 6.4(c), together with their phasors. The resultant field has rotated a further 60°E in a clockwise direction. (There is a 60°E difference between all the numbered positions in Figure 6.3.) For each of the numbered positions, the resultant field rotates a further 60°E in a clockwise direction. For one complete cycle of current (360°E), the resultant magnetic field rotates 360°E.

6.1.3  Rate of rotation and factors affecting it Comparing Figures 6.3 and 6.4 shows that, for the time intervals of 60°E between positions 1, 2 and 3, the resultant field rotates an equal amount around the stator. For a complete cycle of a.c., a two-pole field rotates one complete revolution around the stator. The synchronous speed of the magnetic field in revolutions per minute can be determined from the frequency of the supply. 333

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Electrical Principles

EXAMPLE 6.1 A two-pole machine is connected to a 50 Hz supply. Find the speed at which the magnetic field rotates around the stator. 50 Hz = 50 cycles per second speed of rotation = 50 revolutions per second ​​              ​  ​   ​​ ​ ​ ​   = 50 × 60 revolutions per minute   = 3000 rpm With a four-pole machine, 360°E represents one-half of a full revolution of the stator field, so the speed of rotation of the field is halved. Similarly, the speed of field rotation for a six-pole machine is reduced to one-third of that of a two-pole machine. In each case, the speed is usually expressed in revolutions per minute, whereas the frequency is in hertz (cycles per second). The speed in revolutions per minute can be found from the following formula: 120f ​​n​  syn​​ =  ​ ____  ​​    p where nsyn = number of revolutions per minute f = frequency in Hz p = number of poles The speed n of the rotating magnetic field is called the ‘synchronous speed’ of the motor. The synchronous speeds of common sizes of motors at a frequency of 50 Hz are given in Table 6.1 below. Table 6.1   Speed of the rotating field in an induction motor for various numbers of poles Poles Synchronous speed (rpm)

2

4

6

3000

1500

1000

A

B1

6.1.4  Direction of rotation and reversal

R

8

10

12

750

600

500

C1

C

B A1

The direction of rotation of a rotating field depends on the phase sequence of the three currentsWflowing through the windings. In Figure 6.5(a), the three supply lines R, W and B are connected to terminals A, B and C of the motor. The resultant magnetic field rotates clockwise. B (a) RWB sequence R

R

A

A

B1

C1

B1

C1

C

B

C

B

A1

W

A1

B (a) RWB sequence

W

B (b) RBW sequence

R Figure 6.5  Phase sequence and field rotation

334 A B1

C1

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C

B

Alternating current rotating machines  Chapter 6

In Figure 6.5(b), the supply lines to phases B and C have been changed over and, using the procedure from the previous section, it can be shown that the rotation of the magnetic field is reversed. That is, the direction of rotation of the field can be controlled by interchanging any two supply lines to the motor. The part of Section 6.1.5 that deals with torque states that the rotation of a three-phase induction motor is in the same direction as that of the rotating field.

6.1.5  Induction and its effects When the stator windings of a three-phase induction motor are energised from a three-phase supply, a magnetic field is produced, rotating at synchronous speed. This rotating magnetic field crosses the air gap and cuts the rotor conductors, inducing a voltage in them (magnetic field, conductors and relative motion). When the rotor circuit is complete (through end rings in the case of the squirrel cage rotor or through external resistance in the case of the wound rotor), the induced voltages cause high currents to flow in the rotor conductors.

Torque Figure 6.6(a) shows a part of the stator and air gap of an induction motor with the stator flux rotating clockwise as indicated. When these lines of force cut the rotor conductors from left to right, the relative movement between the stator flux and the rotor conductor is from right to left. By applying Fleming’s right-hand rule (see Chapter 2), the direction of induced current flow in the conductor is towards the reader. Owing to the comparatively high rotor currents flowing, a large flux is established around the conductor (see Figure 6.6(b)). The stator and rotor fluxes react with each other as shown in Figure 6.6(c), forming a resultant field. This resultant field tends to straighten itself out and, in the process, causes a force to be exerted on the rotor conductor, trying to force it to the right and out of the stator magnetic field. A similar force is exerted on all the rotor conductors as the field rotates. If sufficient force is created, the rotor will start rotating in the same direction as the rotating magnetic field. Provided it is free to rotate, the rotor will accelerate until it approaches synchronous speed. This rotating force is called the ‘torque’ of the motor. It is the result of the interaction of the two fluxes. The stator flux remains fairly constant, but the rotor flux varies with the rotor current, which is determined by such factors as the impedance, the induced voltage and the relative speed of the rotor conductors.

Slip To produce torque, there must be a rotor flux caused by current flowing through the rotor conductors. If the rotor could run at synchronous speed, there would be no relative motion between the stator flux and rotor conductors. Consequently, there would be no induced voltage, no rotor current, no rotor flux and no torque; the rotor would slow down. An induction motor therefore cannot run at synchronous speed.

N

N

Rotor conductor Thrust

Rotor flux

(a) Stator flux

(b) Rotor flux

(c) Resultant field

Figure 6.6  Production of torque in an induction motor

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Electrical Principles

With the rotor running just below synchronous speed, relative motion exists and sufficient torque is developed to keep the rotor turning. The difference between the synchronous speed of the rotating field and the actual speed of the rotor is called the ‘slip speed’. It is commonly expressed as a percentage of the synchronous speed.

EXAMPLE 6.2 Determine the slip of a four-pole induction motor running at 1440 rpm when connected to a 50 Hz supply. 50 f  ​n​  syn​​ = 120​ __  ​  = 120 × ​ ___ ​   p  4   = 1500 rpm ​​               ​  =​  1500 − 1440 = 60 rpm  ​​ ​ ​ ​ ​ slip speed 1400  percentage slip = 1500 − ​ ___________       ​  1500  × 100   = 4% The formula for determining percentage slip is: ​n​  syn​​  − n  ​s% = ​ _______  ​     × 100​  ​n​  syn​​ where s% = percentage slip nsyn = synchronous speed n = rotor speed At standstill (i.e. when starting) the slip is 100%, but if the motor could run at synchronous speed, the slip would be zero.

Supply frequency

Rotor frequency

When the rotor of a two-pole motor is at standstill and the stator is connected to a 50 Hz supply, each rotor conductor is cut by a north pole and a south pole at a rate of 50 times per second. At standstill, the frequency Rotor frequency of the rotor voltage (rotor frequency) is the same as the frequency of the supply (stator frequency). As the rotor speeds up to half the synchronous Rotor stationary speed (1500 rpm), the rotor conductors are cut by only 0 Slip 100% one-half as many north and south poles per second as at standstill. So the rotor frequency is one-half the Figure 6.7  Relationship between rotor frequency and slip supply frequency (i.e. 25 Hz). If the rotor were to revolve at synchronous speed, the rotor frequency would be zero. The rotor frequency depends on the differences in the speeds of the stator flux and the rotor (i.e. the slip of the motor), as shown in Figure 6.7. The rotor frequency can be calculated using the following formula: s.f ​​f​  r​​  = ​ ____  ​​  100 where:

fr = rotor frequency in Hz s = slip percentage f = supply frequency in Hz

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Alternating current rotating machines  Chapter 6

EXAMPLE 6.3 Determine the rotor frequency of a two-pole, 50 Hz induction motor if the rotor speed is 2850 rpm. ​n​  syn​​  − n  s = _______ ​   ​     × 100  ​n​  syn​​ 2850   = 3000 − ​ __________       ​  = 5%  3000  × 100 ​​        ​  ​  ​  ​  ​​​ s.f ​f​  r​​ = ____ ​    ​  100 50    = 5 × ​ ____  ​  = 2.5 Hz 100 As the rotor frequency varies, so does the rotor inductive reactance. This affects the starting and running characteristics of the motor.

6.2  Three-phase induction motor construction 6.2.1 Stator Figure 6.8 shows stator laminations. The laminated stator core is made from stamped sheet steel with slots on the inner surface, and three identical windings are laid out in a series of overlapping coils. In motors of higher power ratings, the stator slots are of the open type to allow the insertion of the large pre-shaped and insulated coils; in lower-power motors, the slots are partially closed to reduce the air gap as much as possible. The stator core is fixed into the motor frame, which carries the bearings that support the rotor, protects the coils and provides a means for mounting the motor to the machinery it is to drive. The motor frame takes various forms, depending on the conditions under which the motor will operate. These forms range from open frame through to submerged pump motors.

6.2.2 Rotor Squirrel cage rotor The rotor of an induction motor consists of a shaft (or spindle) with bearings, laminated iron core and rotor conductors. The most common type of construction is one with rotor bars in the lamination slots rather than a winding. The rotor bars pass through the rotor via holes punched in the laminations when they are pressed. The ends of the rotor bars are short-circuited at each end by a solid conducting ring, which is often a copper ring that is brazed or fusion-welded to copper rotor bars. For small-to-medium motors, they may be cast in one piece from aluminium (usually including cast fins for

Figure 6.8  Laminated stator

CMG Engineering Group—a Regal Beloit Company

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Electrical Principles

creating air movement). The rotor windings, if shown without the laminations, would resemble a metal cage, giving rise to the frequently-used name ‘squirrel cage’ rotors (although the Standards refer to them simply as ‘cage’ rotors). Figure  6.9 shows a cast aluminium squirrel cage rotor with end fins. It also shows skewed conductors in the rotor, which means that the conductors are at an angle to the rotor axis. Skewed conductors cause a smoother power transfer to the rotor, resulting in less vibration and a steady acceleration during starting. Varying the physical design features of the bars affects motor performance. Embedding them deeper into the rotor, for example, increases the inductance and gives a lower starting current but creates a lower pull-out torque. This type of rotor is then restricted to loads requiring low starting torques, such as centrifugal pumps. A side section of a complete three-phase induction motor is shown in Figure 6.10.

Wound rotor The wound rotor is fitted with insulated windings, similar to the stator winding and having the same Figure 6.9  Squirrel cage rotor CMG Engineering Group—a Regal Beloit Company number of poles. The three phases are connected in star configuration with the ‘Y’ point connected on the rotor and the three phases terminated at one end of the rotor at three slip-rings. (See Figure 6.11 for an image of a typical wound rotor.) The slip-rings are connected by brushes to an external star-connected variable resistance, as in Figure 6.12. This rotor rheostat provides the means of increasing the resistance of the rotor circuit during starting, thereby producing a higher starting torque at a lower starting current. As the speed increases, the external resistance is gradually reduced, lowering the rotor circuit resistance as the rotor reactance decreases. Under operating conditions, the variations in rotor circuit resistance provide a means of controlling the speed of the motor over a small range. An increase in resistance results in a reduction in speed and torque, also producing a loss in efficiency due to the I2R losses in the rheostat. Brush holder yoke

Rotor Slip-rings Brush holder winding and brush

Increase speed Decrease speed

Rheostat

CMG Engineering Group—a Regal Beloit Company

Stator winding Grease fitting

M1 M2 M3

Figure 6.10  Side section of a three-phase induction motor

Stator iron

T1

T2

T3

Breaker L3 to 3L2 phase L1 supply

Figure 6.11  Typical wound rotor

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Alternating current rotating machines  Chapter 6

Three-phase supply

Stator

Slip-rings

Rotor

Rheostat

Figure 6.12  Wound rotor with starting resistance

The wound-rotor motor is more expensive than the squirrel cage motor because of its manufacturing cost. It also has a higher starting torque and lower starting current (but poorer running characteristics) than the squirrel cage motor, as well as higher maintenance needs.

6.2.3  Motor enclosures The conditions governing the actual installation of an induction motor are usually beyond the control of the motor manufacturer. As a result, the motor is manufactured in various enclosures. A motor driving a compressor for a refrigerated display cabinet, for example, may operate under such clean and dry conditions that the motor enclosure need only provide a mounting for the bearings and a means for fixing the motor in a horizontal plane. At the same time, the enclosure provides mechanical protection against accidental spillage and enables cooling air to circulate freely through the motor windings. Compare this situation with a water turbine pump used for irrigation. In most cases, the motor is mounted vertically at the bore head and is given no protection from the weather. It needs to be totally enclosed to prevent the entry of water, and cooling is by means of heat transfer through the motor housing. The air sealed within the motor housing is circulated by an internal fan, thus transferring the heat generated by the windings to the housing. This heat is then transferred to the atmosphere by a second fan circulating free air across the outside of the motor housing. AS/NZS 1359 provides detailed information on electric motor standards, including requirements for electrical rotating machines. Electrical rotating machinery is now classified by two letters followed by four numerals. This classification number is different for such categories as cooling, mounting and protection.

6.2.4  Terminal block arrangements Squirrel cage motors Most three-phase induction motors have both ends of the three windings brought out to a six-terminal block. The only exceptions are small, dedicated-purpose motors that can be started directly on line in either star or delta configuration at all times. These motors have only three terminals (not including the earth terminal). By custom (and some attempts at standardisation), the phase ends are brought out to terminals in one of two possible arrangements. Figure 6.13(a) shows the more usual arrangement, while Figure  6.13(b) illustrates an alternative system of connections.

U1

V1

W2

U2

W1

U1

V2

(a) Common arrangement

V1

V2

W1

W2 U2

(b) Alternative arrangement

Figure 6.13  Three-phase motor terminals

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Electrical Principles

U1 L1

V1 L2

W2

W1

L1

L3 U2

U1

V1 L2

W1 L3

V2 W2

U2

The idea is to standardise connecting arrangements for people installing the motor or reconnecting it after maintenance. To connect a motor in either star or delta configuration, winding ends are bridged (see Figure 6.14). The points to note are:

V2

1. Individual phase ends are not connected to terminal pairs but are offset (see Figure 6.14). 2.  Connecting a motor in star configuration means Figure 6.14  Bridging connections in a three-phase motor that the windings have only 58% of the line voltage terminal block applied to them. 3. In star configuration, one bridge couples all three corresponding ends of each winding. 4. The bridge can be placed across the beginnings of the phase windings instead of the ends as shown. The lines are connected to the opposite ends to the bridge. 5. There is no alternative option for the bridges when connecting a motor in delta configuration. Each bridge connects to line voltage. 6. While bridges or shorting strips are shown in Figure 6.14, it might be necessary to remove the bridges so that all six ends of the windings can be connected to a starter—for example, a star–delta starter. (a) Motor connected in star

(b) Motor connected in delta

Wound-rotor motors With wound-rotor motors, it is common to connect the stator windings internally in either star or delta configuration as required—usually delta. The terminal block will still have six terminals because the three appropriate ends of the rotor windings are connected in star configuration internally and the other ends brought out via slip-rings to the terminal block. It is usual to identify them in some way, such as separating them from the line terminals of the stator windings or using a different type of terminal connector. Care should be taken to observe that line voltages are not connected to the rotor terminals.

6.2.5  Electrical tests for three-phase motor windings The tests applicable to an electric motor are either electrical or visual—usually both. Electrical tests are possibly the easiest to carry out (assuming that the equipment is available) because they do not usually require the motor to be dismantled; the testing can be done at the terminal box. Subject to the results of the electrical test, it may then be necessary to dismantle the motor.

6.2.6  Continuity tests Low-voltage sources such as multimeters are suitable for continuity testing. The usual multimeter is a series ohmmeter type, and care must be exercised in taking any resistance readings as absolute readings, particularly at very low values. If a winding is supposed to read 1 Ω, L1 then a meter reading of, say, 0.7 Ω is inconclusive: the accuracy of the meter itself might be in question. All Open-circuit this shows is that there is some resistance and some form of electrical continuity between the two leads being checked. A C Without some knowledge of the motor circuit, it is impossible to establish whether the correct part of the circuit is actually being tested. For example, if a threeB phase motor connected in delta configuration is being L2 L3 tested, an ohmmeter would give a reading across any pair of terminals, even if one phase winding was open Figure 6.15  Delta-connected motor with one phase opencircuit. In Figure 6.15, phase winding A is open circuit, circuited 340

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Alternating current rotating machines  Chapter 6

yet a reading can be obtained between L1 and L2 (phase B), and also between L2 and L3 (phase C), and between L1 and L3 (phases B and C in series). If the motor is large, the winding resistance is low and it might be difficult for ohmmeters to detect the difference in readings. In such cases, it might be necessary to disconnect the delta bridges and check the phases individually. A similar situation occurs when testing single-phase motors. It is vital to know whether the two windings are in parallel, whether there is a capacitor in the circuit, whether the motor has a starting switch and whether it is operational.

6.2.7  Insulation-to-earth test An insulation-to-earth test must be made with instruments of the correct voltage. A 400 V circuit, for example, cannot be tested satisfactorily with a 3 V ohmmeter. Similarly, a small-town local supply with an exciter rated at 24 V should not be tested with an insulation tester of 500 V. Some prior knowledge of the circuit of the motor is necessary. Each phase or winding should be tested separately and the results compared. One phase with a reading considerably different from that of the other two could indicate a problem.

6.2.8  Insulation test between windings For an insulation test between windings, the windings should be disconnected both from each other and the supply source to make the test meaningful. A suitable test voltage should be used and the relative readings compared to see if there is variation. A low reading between two phases is an indication of a problem.

6.2.9  Visual inspection If a further check is required after electrical testing, the motor is usually dismantled for a visual inspection. With very large machines, it is possible to carry out a limited visual inspection by removing the covers and looking inside without dismantling the complete machine. In most cases, burnt-out motors have a characteristic smell that is quite easy to detect. Probably the most obvious sign is the smell of heat within the windings. Insulation can be charred and windings can consist of bare copper wire with all covering burnt off. The burning smell is not an infallible indication, however, as the fault can trip the supply before the burning becomes appreciable. Non-electrical tests indicating burnt insulation include pressing the winding with the hands and listening for a crackling noise (a winding in good condition should make no noise), rubbing the bindings with the fingers to see if they crumble and, on larger motors, tapping the windings lightly with a small hammer (a faulty coil group sometimes gives a flatter sound than the rest of the windings). Where windings have short-circuited to earth, small holes in the windings and associated copper globules can occasionally be seen. With lighter-coloured enamels and varnishes, faulty turns and coils are clearly visible as being much darker than other windings.

6.2.10  Specialised test equipment There are times when the checks described above do not give a definite answer about the condition of the windings. If a motor is faulty in operation but passes the above tests, further testing is necessary. One popular method involves using the windings as the secondary of a transformer with a piece of equipment called a ‘growler’—a name derived from the noise made when it is in operation. One type of growler is designed for testing armature windings and has a V-shaped gap in which to place the armature. When alternating current is applied to the growler, an alternating voltage is induced in the armature windings. The induced voltages on opposite sides of the armature are equal and opposing, so no circulating current flows. If there is a short-circuit in the windings, this balance is upset and a circulating current flows. The faulty coil can be detected by a light-gauge strip of steel held against the armature which vibrates when laid along the slot 341

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Electrical Principles

holding the faulty coil. One variation of this is where the V-shaped gap is rounded to sit inside the stator of a motor and a similar operating procedure is followed. Some models of growler have the ‘V’ on one side and the rounded section on the other. Another piece of test equipment, the Prufrex, is sometimes used with motor stators. It is plugged into an a.c. supply and moved around inside the stator. If a short-circuit exists in the stator windings, the circulating currents upset the magnetic field of the tester and a light flashes, indicating the location of the fault.

6.2.11  Dismantling three-phase induction motors When dismantling an electric motor, the main aim is to reassemble it in its original form after any inspection or repairs. To make that easier than relying on memory or experience, it is a common practice to mark the endshields and other pieces in some way. Probably the most common method of doing this is to use a centre punch and make adjacent punch marks on matching surfaces. (Punch marks should be avoided on machined surfaces.) Some technicians prefer to use a cold chisel to make one mark across two surfaces so they can reassemble the motor more accurately. In either case, only a light mark is needed; all that matters is that it can be used on reassembly. Large, deep marks are not recommended because of the possibility of damaging the casing. Making what are sometimes called ‘witness marks’ is good practice and is widely used by experienced technicians. A single centre-punch mark would suffice for both an endshield and a motor frame, for example. (These marks are usually placed at the top of the motor, where they can be easily seen.) The opposite end-shield could then be marked with two closely-spaced punch marks. A similar method could be used on the bearing covers. Whenever possible, an experienced operator will keep components of subassemblies separate from other subassemblies as they are removed. Taking photographs before and during disassembly can also provide an invaluable reference for reassembly. Putting all components in one container and then having to try to sort them out when they are needed for reassembly is bad practice. Withdrawing the rotor from the stator requires care, to avoid damaging either the rotor or the stator and its windings. A mechanical and electrical examination of the motor can then take place. Matching punch marks when rebuilding is a quick and accurate method of ensuring that the motor is assembled in its prescribed condition and manner. It also ensures that the motor shaft is protruding from the right end and the terminal block and housing is in the correct position. Bearings should be checked for wear and re-greased on assembly with just the right amount of correct-grade grease.

6.3  Three-phase induction motor characteristics 6.3.1  Squirrel cage motors When power is first applied to a stationary motor, the stator windings act as transformer primary windings, with the resultant magnetic field rotating at synchronous speed. The rotor then behaves as a shorted secondary winding, causing a high circulating current in the rotor bars and a high starting current in the stator windings. As the rotor accelerates in the direction of the rotating field, the difference between its speed and the rotating magnetic field becomes less, and the generated voltage causing the rotor circulating currents also becomes less. This in turn reduces the stator current. The typical relationship between the stator current and the rotor speed is shown in Figure 6.16(a). The initial circulating current in the rotor is affected by the frequency of the supply, the resistance of the rotor bars and the inductance of the rotor circuit—that is, the current-limiting factor is the impedance of the rotor circuit. With the standard type of power transformer, the frequency of the supply is the line frequency; but in this case the frequency starts at line frequency and steadily decreases as the motor speed increases. Consequently, the torque created can change as the speed changes. Figure 6.16(b) shows the typical relationships between speed and torque. 342

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Alternating current rotating machines  Chapter 6

Breakdown torque Locked rotor torque

Torque (%)

Current (%) Rated speed

Rated speed

Rated torque

100

Slip

Rated current

100

0

n

0

nsyn

(a) Current/speed curve

n

nsyn

(b) Torque/speed curve

Figure 6.16  Relationship between rotor frequency and slip

For small values of slip, the torque is assumed to be proportional to the slip. As the motor load increases, the torque increases and the speed decreases, until the torque reaches a maximum value called the ‘breakdown torque’. If the motor is loaded beyond this point, the torque and the speed both decrease and the motor quickly comes to a standstill. An overall figure for starting torque is in the region of 1.5 times the rated torque; the breakdown torque is usually about twice the rated torque. AS/NZS 1359.41 sets out minimum requirements for these torque values and provides a table for a range of motor sizes. The resistance of the rotor conductors remains constant at power-line frequencies for all practical purposes, while the inductive reactance decreases as the rotor speed increases. As a guide, torque reaches a maximum when the rotor resistance in ohms is equal to the rotor reactance in ohms. Since the resistance is fixed, the breakdown torque can be altered only in relationship to the motor speed by altering the inductance of the rotor. This in turn affects the starting torque. AS/NZS 1359.41 allows for only two basic types of rotor—normal and high torque. Any other types necessarily require prior arrangement with the manufacturer. For the high-torque motor, the required breakdown torque remains around twice the rated torque, while the starting torque is increased to approximately 2.5 times the rated torque.

6.3.2  The squirrel cage motor operating characteristics conditions necessary for an induction motor to produce maximum torque Reference has been made to the fact that the rotor bars in a squirrel cage rotor can be designed and manufactured to suit different operating conditions. In general, for any one stator, only the impedance of the rotor can affect the current flowing in the rotor bars. Impedance can in turn be broken down into resistance and inductive reactance. Altering either affects the current flow. Resistance can be altered by changing the crosssectional area of the bars, while the inductive reactance can be altered by varying the depth and shape of the bars in the iron core of the rotor. Figure 6.17 shows typically-shaped rotor bars where the starting current is around six to seven times the rated

300

Torque %

Rated speed

200

100

Rated torque

0 Speed

nsyn

Figure 6.17  Low starting torque rotor

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Electrical Principles

Air gap

300

300

Rated speed Torque %

200

100

Torque %

Rated torque

200

100

Rated torque

0

0

Speed Speed

Figure 6.18  Standard rotor bars

Rated speed

nsyn

nsyn

Figure 6.19  Double cage rotor for high starting torques

current and the motor has a starting torque of approximately 150% of the rated running torque. Its use is restricted to very low starting torque requirements. Figure 6.18 shows rotor bars of greater cross-section, where part is embedded deeper into the rotor magnetic circuit. Starting torque is still about 150% of running torque, but the starting current is reduced to about five times the running current. It is suitable for use with equipment of low starting inertia such as fans, blowers and some types of machinery. Figure 6.19 gives one example of a rotor with two sets of rotor bars. The inner set has half as many bars as the outer set and includes an optional air gap. Depending on performance requirements, there may be different-shaped bars, no air gap or a full set of bars in the cage. Starting torque is high—here it is 225% of rated torque—and starting current is about five times the 300 rated running current. Applications are in air compressors, Rated crushers, refrigerator compressor motors or reciprocating speed 200 force pumps. Torque % A typical example of high-resistance rotor bars with low Rated torque 100 starting current requirements is shown in Figure 6.20. With this construction, the starting torque can be increased to 0 about 275% with fairly low starting currents. This comes at nsyn Speed the cost of a lower-rated speed (i.e. increased slip). Typical uses are flywheel-mounted machinery such as presses and punches. This type of construction is excellent with hoists, Figure 6.20  High-resistance rotor bars where the maximum load occurs at the start of the lift. The above details apply particularly to copper rotor bars. If aluminium is used for the rotor bars, their crosssectional area must be increased to allow for the metal’s higher resistivity. The shape may also be changed to incorporate desired starting and running characteristics. Figure  6.21 shows a teardrop-shaped cast aluminium bar. In practice, the shape may also be inverted to alter the characteristics to suit a particular purpose. Figure 6.21  Cast aluminium rotor bars 344

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Alternating current rotating machines  Chapter 6

6.3.3  Wound-rotor motors The introduction of resistance into the rotor circuit of an induction motor produces three effects: 1. The rotor current is reduced, resulting in less stator current. 2. The starting torque is increased because rotor and stator magnetic fields are more in phase with each other. 3. The slip speed is increased.

(d) Torque(%) (b)

(c)

Rated speed

(a) 100

Rated torque

n nsyn 0 An adjustable resistor is used external to the rotor, which is wound with comparatively low resistance Figure 6.22  Operating characteristics for a wound-rotor motor windings. The value of the external resistance can be adjusted as required and, as the motor accelerates, the value is gradually reduced until all the resistance is out of the rotor circuit and the motor behaves as an ordinary induction motor. The torque-speed characteristic of a typical three-stage wound-rotor motor is shown in Figure  6.22. When all the resistance is in the rotor circuit, the starting current is low and the starting torque is high, as shown by curve (a). If this resistance is left in, the full-load torque would occur at approximately 25% slip, resulting in extremely poor speed regulation. If one stage of the resistance in the rotor circuit is shorted out, the operating characteristics are modified as shown by curve (b). If all the external resistance in the rotor circuit is shorted out, the operating characteristic is shown by curve (c). The normal starting procedure is to start the motor with all the resistance in the rotor circuit. As the motor speeds up, the resistance is reduced. The motor increases in speed but maintains a high torque. During the starting procedure, the torque-speed curve is as shown by the thicker curve (d). By comparing Figures 6.17 and 6.22, it can be seen that full-load torque occurs at a greater slip in a wound-rotor motor than a squirrel cage motor. This is due to the extra resistance of the windings in the wound rotor. The main use for wound-rotor motors is the starting of high-inertia loads that may take several minutes to attain operating speed. The high starting torque and reduced starting current of this type of motor ensure that the motor windings are not subjected to excessive starting currents for any length of time. Applications for wound-rotor motors invariably involve the need to get pairs of large flywheels up to speed. Once they are, they can absorb the impact shock of sudden loads and so enable the machinery to continue operating. Applications include large air compressors, metal presses and stone-crusher heads that are used in quarries to reduce excavated material to suitable sizes before grading.

6.3.4  Operational parameters for induction motors On no load, the stator current of any induction motor is largely a magnetising current, with a small energy component required to supply the no-load losses. Accordingly, the power factor of an induction motor on no load is very low. The no-load current is relatively high when compared with a transformer because of the high reluctance of the magnetic circuit resulting from the air gap between the stator and rotor. The stator flux remains fairly constant from no load to full load, so the magnetising current is also fairly constant. In Figure 6.23(a) the no-load stator current I0 lags the supply voltage by Φ degrees. As a load is applied to the motor, a load current I​ ​​ 1′​ ​​is required to accommodate it. This load current I​ ​​ 1′​ ​​ lags the supply voltage slightly, owing to the effect of the stator and rotor reactance. The two current components I0 and I​ ​​ 1′​ ​​ combine to give the total stator current I1 at that load. The phase-angle decreases from Φ to Φ1, and the power factor of the induction motor increases as the load on the motor increases. Figure  6.24 gives representative characteristic shapes for some parameters of a three-phase induction motor. It shows the speed decreasing and the slip increasing as the load on the motor is increased. It also shows the line current increasing and the power factor improving simultaneously. 345

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Electrical Principles

V Φ 100% ed

Spe

l0

cy

r we

Full load

Po

Effi cie n

(a) No-load conditions

tor

fac

V Φ1

l′1

Φ

nt

rre

Cu

Slip l0 (b) Loaded conditions

Figure 6.23  Current phasors for an induction motor

l1

Power output

Figure 6.24  Typical parameters for a three-phase induction motor

6.3.5  Abnormal operating conditions for three-phase motors The satisfactory operation of three-phase motors on a three-phase supply depends on the factors described below.

Three equal voltages at the correct phase displacement Under normal operating conditions, the phase displacement is a function of the generating equipment and stays relatively fixed. However, the line voltages can vary, depending on the individual loads connected at that time. For balanced loads, such as three-phase motors, unbalanced phase voltages lead to unbalanced currents flowing in the motor windings. Consequently, circulating currents are set up, heating is increased and uneven and torque is reduced.

Stator windings being correctly connected in either star or delta configuration If phase currents become unbalanced, windings generate increased heat and torque is greatly reduced. See Section 6.2.2 for more details.

Three line voltages being connected to the motor windings When any one supply line is unable to supply current to the winding to which it is connected, the condition known as ‘single phasing’ occurs. See Section 6.3.7 for more details.

The condition of all four windings in the motor The stator windings connected to the supply are prominent and therefore can be obvious areas of concern. Noisy operation and reduced torque of a three-phase motor can mean that the bars of the rotor might need attention. Many cages consist of aluminium cast into shape in the laminations, and little can be done in the way of maintenance; however, many of the larger motors have prefabricated bars and rings of copper, which are welded into place. It is possible to repair or replace items, whether they are broken or simply loose in the rotor. 346

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Alternating current rotating machines  Chapter 6

6.3.6  Phase reversal So far in this chapter, the operation of the induction motor has been described based on the assumption that the motor has three identical windings and three equal currents flowing in them, all spaced at 120°E to each other. If one phase is reversed (as shown in Figure 6.25(a) for a star connection), these conditions no longer hold true. Two of the three currents that flow are at 60°E to each other and the load system is unbalanced (Fig. 6.25(b)). The same condition applies to delta-connected loads. As a result of this incorrect connection, the motor loses most of its torque and is often unable to start against even a light load. If it is able to start at all, it usually rotates very slowly and has unequal values of current in the phase windings. The values of current approach those drawn during normal starting but remain high. The motor usually emits a ‘growling’ noise and has an associated vibration due to the sustained high-current values.

6.3.7  Single phasing Single phasing is a condition that occurs when one line of a three-phase supply is open-circuited and is not able to supply current to a three-phase load. The term is also used when one of the three-phase windings in a load is opencircuited. The condition for single phasing in a star-connected load is shown in Figure 6.26(a). It can be seen that a break in either the line or the phase winding reduces the circuit to a single current path. Figure 6.26(b) shows an open-circuited line for a delta-connected motor. There is one main current path, from L1 to L3 through phase A, and another path from L1 to L3 through phases B and C in series. Both currents are in parallel with each other, although not necessarily in phase with each other. In Figure 6.26(c), a delta-connected induction motor is shown with phase C open-circuited. There are two current paths—L1 through phase A to L3, and L2 through phase B to L3. In each of the cases shown in Figure 6.26, the rotating magnetic field is either destroyed or unbalanced and causes unsatisfactory operation of the motor. The motor rotates at slower speeds—if it is able to start at all—because of a much-reduced starting torque. It usually draws higher-than-normal currents in the parts of the circuit still operating, with values approaching starting current values in some circumstances. It can also emit a low-pitched ‘growling’ noise similar to that which occurs during a phase reversal. If single phasing occurs while the motor is operating at normal speeds, the normal humming sound often changes to a higher-pitched whine. For any of the conditions for single phasing outlined above, the three ratios between line and phase values are no longer valid.

C

−B

C

C1 A1

A A

B

Reversed phase B1

(a)

(b)

Figure 6.25  Reversal of one phase for a star-connected motor

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Electrical Principles

l l

L1

l L1

L1 A

X A

C C L3

X

A

C B

B B

L3

L3

X

X L2

L2 (a)

L2

(b)

(c)

Figure 6.26  Circuit conditions causing single phasing with a three-phase motor

6.3.8 Overloading As discussed in Section 6.3.1, standards are laid down for the operation and performance of induction motors, particularly for their starting and running torques. There are also stated limits for the amount of torque a motor can exert when it is unable to start or is stalled by the connected load. The limits are variable, depending on the size or rating of the motor. These requirements are built into the motor design and are beyond the control of anyone attending to the maintenance or installation of a motor. Overloading is a condition that is usually brought to the attention of a technician only when a motor is behaving in an abnormal manner. As a general guide, the motor may run at a slower speed and higher temperature than normal. The varnish used on the windings might start to smell, and in extreme cases smoke might start to issue from the windings. Once a motor is unable to meet the requirements of the applied load, it will come to a rapid stop and locked rotor conditions then apply (see ‘Breakdown torque’ in Figure 6.16(b)). Current in excess of normal full load will then be drawn, and the installed motor protection must rapidly disconnect the motor from the supply to prevent damage.

Summary 6.1–3 ∙ The stator core is made from laminations pressed into a frame. ∙ The rotor is laminated and pressed onto a shaft that is free to rotate in bearings. ∙ The rotor windings are usually single copper conductors shorted at the ends with copper rings. This construction is called a squirrel cage rotor. ∙ There are special types of rotor constructed to produce various amounts of torque. There are only two major types— standard and high-torque rotors, although some may be designed only for either star or delta starting. ∙ Wound rotors have three identical windings, usually connected in star configuration internally and the other ends brought out of the windings to slip-rings. ∙ Stator winding leads are brought out to terminal blocks and arranged in a standard manner for ease of connection in either star or delta configuration. ∙ Motor enclosures are made to Australian Standards requirements. They range from an open type to being completely sealed (see AS/NZS 1359). 348

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Alternating current rotating machines  Chapter 6 ∙ A three-phase motor has a rotating magnetic field, which gives the motor an inherent starting torque. The motor always rotates in the direction of the rotating field. ∙ Reversal of rotation of the field and the rotor is achieved by interchanging any two lines of the supply to the motor. ∙ The rate of rotation of the field depends on the frequency of the supply and the number of poles in each phase winding. ∙ The synchronous speed of an induction motor can never be achieved because the motor relies on a certain amount of slip to generate torque. Within the capacity of the motor, the greater the slip, the greater the torque. Once a maximum value is exceeded, the motor stalls and excess current flows. ∙ The rotating field cuts the conductors of the rotor, generating a voltage in the rotor conductors by induction. This causes currents to flow in the rotor bars and creates a magnetic field that reacts with the rotating field to produce the torque. ∙ Slip causes an alternating current to be generated in the rotor bars. ∙ Slip is the difference in speed between synchronous speed and actual speed. ∙ As a general guide, when the resistance of the rotor bars equals the inductive reactance of the rotor bars, maximum torque is created. ∙ Wound-rotor motors have a much higher starting torque than squirrel cage rotors. Reducing the external resistance in the rotor circuit allows the rotor to get up to speed gradually without excessive currents flowing. ∙ Wound-rotor motors have poorer speed regulation than squirrel cage motors. ∙ A three-phase motor needs to have all three windings correctly connected to operate properly. Reversal of one phase winding leads to flow of unequal phase currents and greater heat generation. ∙ A similar situation occurs when one phase winding has no current flowing in it. Unequal currents flow and greater heat is generated. Torque in both cases is greatly reduced. This also applies in the absence of one supply line. ∙ Overloading three-phase motors causes high temperatures to be created in the motor windings. This can damage the windings permanently. ∙ Electrical tests for single-phase and three-phase windings involve continuity and insulation tests both between windings and to earth. ∙ An additional test for an a.c. motor winding is for the detection of short-circuits between the turns or coils. Shortcircuits in this case lead to high circulating currents and heat generation, causing breakdowns. ∙ When dismantling a motor, care should be taken to ensure that it can be reassembled correctly in its original form. The use of punch marks is one method of ensuring this. Good technicians will try to keep components in separate units to avoid confusion on reassembly.

6.4  Single-phase motors—split phase 6.4.1 Introduction The induction motor is highly regarded because of its simplicity, ruggedness and reliability. The three-phase induction motors discussed earlier had inherent starting torque due to a rotating field; the single-phase induction motor, by contrast, initially has no rotating field and therefore no starting torque. In the three-phase motor, the supply consists of three identical currents being supplied to three identical windings in the motor. The resultant magnetic field rotates at a constant speed and strength. Similarly, if two identical currents at 90°E could be supplied to two identical windings displaced by 90°E in a two-phase motor, the magnetic field would rotate at a synchronous speed determined by the supply frequency and the number of poles in the windings. 349

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Electrical Principles

6.4.2  Single-phase induction motors A single-phase motor can easily be wound with two identical windings but, on connecting them to a single-phase supply, the individual winding currents may well be closely in phase with each other and not produce a rotating magnetic field. The two currents have to be displaced electrically from each other by some means to produce a rotating field. This can be achieved by having windings of different inductances and resistances. Sometimes a capacitor is also added in series with one winding to enhance the phase displacement. A single-phase motor is shown in Figure 6.27. Once the motor is rotating at sufficient speed, one of the windings can be disconnected and it will continue to rotate. Due to the more uneven magnetisation of the iron core, the motor develops a pronounced vibration that is a characteristic of the single-phase motor. This vibration is at twice the supply-line frequency and tends to make the motor noisier than a three-phase motor in operation. The motor also develops a small amount of negative torque, which is a function of slip speed. It results in a rather high no-load current at low power factor. When a load is applied, the current increases only marginally but the power factor improves in a similar fashion to that of the three-phase motor. The above considerations mean that special techniques have to be adopted to ensure the starting of the single-phase motor. Due to the various starting methods employed, there are several versions of the single-phase motor.

Figure 6.27  Single-phase motor

CMG Engineering Group—a Regal Beloit Company

Centrifugal switch

A

Run

Rotor

N

Start

(a) Run

90°E

t

St

ar

ar

t

St

Run

Run

t

St

ar

t

ar St Run

6.4.3  Split-phase motors

(b)

ΦR

V

ΦS ~30°

Φ ~30° IS

(c)

IR

Figure 6.28  Split-phase motor: (a) split-phase induction motor circuit (b) four-pole machine (c) phase relationships between start and run winding currents

The standard split-phase induction motor has two separate windings (start and run) connected across the supply during the starting process (see Figure 6.28(a)). For normal running, however, only the run winding is used. The run winding consists of a number of coils connected in series to form a set number of poles. A four-pole machine, for example, has four groups of coils, all in series and physically displaced around the stator to form four separate poles (see Figure 6.28(b)). The run winding is wound with a heavier-gauge wire to reduce its resistance. To increase the inductance of the run winding, the coils are embedded deep into the slots of the iron core and usually have more turns

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Alternating current rotating machines  Chapter 6

than the start winding. The current IR flowing through the run winding is highly reactive, and so it lags the applied voltage V by a considerable angle ΦR (see Figure 6.28(c)). The start winding also consists of a number of coils connected in series to form a set number of poles. If the machine has four poles in the run winding, it will also have four poles in the start winding. However, the start winding is physically displaced by 90°E around the stator core (see Figure 6.28(b)). The start winding of the standard split-phase motor is wound with finer-gauge wire, increasing the winding’s resistance. When compared with the run winding, the start winding has fewer turns, and the coils are placed nearer the surface of the slots in the stator core, reducing the inductance of the winding. The net result is that the current IS flowing in the start winding is more in phase with the voltage V than IR in the run winding. In Figure 6.28(c), IR lags V by ΦR and IS lags V by ΦS. 90°E Run This produces a phase displacement of Φ between Star t the two currents, resulting in a phase displacement between the respective fluxes of the two windings.

Starting For a two-pole machine, the windings are also physically displaced by 90°E (see Figure 6.29(a)). Assuming a 30° phase displacement between the two fluxes, at position a in Figure  6.3(b) the run flux ΦR is zero and the start flux ΦS is 50% of the maximum value in a positive direction. The resultant stator flux is shown at position a in Figure 6.29(c). At position b in Figure 6.29(b), ΦR is 50% of its maximum value and ΦS is 86.6% of its maximum value. These combine to form the resultant stator flux b in Figure  6.29(c). At position c in Figure 6.29(b), ΦR is 86.6% of its maximum value and ΦS is 100%. The resultant stator flux c is shown in Figure 6.29(c). By taking each position from a to l in Figure 6.29(b), it can be seen that the stator flux rotates one full revolution for one full cycle. The direction of rotation is the same direction as that of the resultant magnetic field. The stator flux rotates at a speed governed by the supply frequency and the number of poles in a winding. That is:

(a)

Run winding flux ΦR Start winding flux ΦS

Φ

l



​n = 3000 rpm​

c

d

e

f

g

h

i

j

k

l

a

j k i l h a

g

b

f = frequency p = number of poles n = speed in rpm

For a two-pole machine on a 50 Hz supply:

b

(b)

120f ​n = ____ ​   ​​     p where:

a

f e (c)

c d

Figure 6.29  Rotating field of a split-phase motor: (a) two-pole machine (b) start and run winding flux (c) resultant stator field

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Electrical Principles

For a four-pole machine: ​n = 1500 rpm​

If the direction of current flow through one winding is reversed, the resultant magnetic field rotates in the reverse direction. That is, the direction of rotation of the motor is reversed by changing the direction of current flow through one winding. This is done by exchanging the two end connections of any one winding. As seen in Figure 6.29(c), the rotating stator flux is not of uniform value, and an elliptical field pattern results. This produces considerable vibrations and humming noise during starting. The rotating stator field cuts the rotor bars and induces a voltage in them. As the rotor bars are shorted out, a current flows through them and produces a rotor flux. The stator flux and the rotor flux interact to produce a force on the rotor bars, causing the rotor to turn in the direction in which the stator flux is rotating. This rotating force is called the ‘starting torque’ and largely depends on the relative strengths of the start and run fluxes, as well as on the phase displacement between the currents flowing through both windings. The start and run windings are connected in parallel across the supply voltage. When the rotor has reached sufficient speed to provide a strong cross-flux, the start winding can be open-circuited. This is usually done by connecting a centrifugally operated switch in series with the start winding. The centrifugal switch is usually set to open when the rotor speed reaches approximately 75% of the rated speed of the motor. When the motor is switched off, the rotor slows down and the centrifugal mechanism operates, closing the switch contacts again in readiness for the next starting operation. As the start winding is only connected during the starting procedure, it is designed for a very short duty cycle. If the centrifugal switch fails to operate, the start winding will quickly overheat and burn out.

Running When the rotor speed of the standard split-phase motor reaches approximately 75% of the synchronous speed, the centrifugal switch open-circuits the start winding and only the run winding is connected to the supply. For a two-pole motor, when the stator current flows in one direction for one half-cycle, a magnetic field is produced in the direction C–A, as in Figure 6.30(a). During the next half-cycle, when the stator current is reversed, the magnetic field also reverses and is in the direction A–C, as in Figure 6.30(b). This stator field (which is produced by the run windings) varies in strength and direction according to the supply, but it does not rotate. It is a stationary pulsating field. This is why some form of starting (i.e. start winding) is required for split-phase motors. A

A

+

+ +

+

+

+

+ +

+

+

+ +

C

C

(a) First half-cycle

(b) Second half-cycle

Figure 6.30  Pulsating stator field

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Alternating current rotating machines  Chapter 6

A

A

+ +

D

+ + +

+ +

+

+ + +

+

+

+

+

+ +

C (a) Stator flux

B

D

+ +

+ +

+

+ + +

+

+

B

+

C (b) Rotor flux

Figure 6.31  Magnetic fields in a split-phase motor

When the stator winding is connected to the a.c. supply and the rotor is turning, the rotor bars cut the stator flux, causing an EMF to be generated in them. In Figure 6.31(a) the rotor is revolving clockwise and the stator field is acting in the direction C–A. By Fleming’s right-hand rule, the generated EMF in the rotor acts in the direction shown (out of the page) in all rotor bars above the axis D–B (indicated by the dots), and into the page in all rotor bars below the axis D–B (indicated by +). The induced rotor voltages are in phase with the stator flux and cause a rotor current to flow. Because of the low resistance and high inductance of the rotor bars, these currents lag the induced rotor voltage by nearly 90°. Consequently, the rotor currents produce a rotor flux lagging almost 90° behind the stator flux and acting in the direction D–B (see Figure 6.31(b)). Because the rotor flux is at right angles to the stator flux, it is often referred to as the ‘cross-field’. The two fields effectively combine to form a rotating field, which tends to force the rotor bars in the direction in which the field rotates. For one full cycle of the a.c. supply, the resultant field rotates 360°E. For the two-pole machine described, this constitutes one full revolution. For a four-pole machine, it will rotate a half-revolution for each full cycle of the a.c. supply. Owing to the internal losses within the rotor, however, the rotor itself will not rotate at synchronous speed but at a slightly slower speed. Figure 6.32 shows a typical torque/speed characteristic curve for a split-phase motor. The break in the curve is caused by the switch operating to disconnect the starting winding. This is necessary to limit the losses in the motor and protect the starting winding. The torque curves between the running and starting sequences normally Switch speed do not coincide, so the speed and torque values have 400 to adjust when the switch operates. The values shown on the curve must be considered only as representative. 300 Rated They will vary from one make to another, and even speed within the same make (due to design changes). 200 Reversal of a split-phase motor is carried out Torque Rated torque % by swapping the connections of either the auxiliary 100 winding or the main winding—not both. Split-phase motors have only moderate starting 0 torque, so they are limited to uses such as washing nsyn Speed machines, blowers, buffing machines, grinders and machine tools. Figure 6.32  Split-phase motor speed/torque curve 353

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Electrical Principles

6.4.4  Abnormal operating conditions—voltage fluctuation Voltage fluctuation can be of two types—voltage rise or fall, where the voltages remain symmetrical or variations in individual phase voltages might occur (the latter is especially detrimental to the performance of three-phase motors). The torque produced is proportional to the square of the voltage. That is, if the voltage drops to 90% of its nominal value, the torque reduces to 81% of its rated value. Similarly, if the voltage rises to 110%, then the torque increases to 121% of its rated value. For example, a 10 kW motor with a 10% voltage variation should now be rated at 8.1 kW or 12.1 kW. Under normal operating conditions, a voltage variation of this magnitude should make only minor differences to the motor’s characteristics. With a voltage increase, for example, the increased torque reduces the slip only slightly, so a motor rotating at 1450 rpm on 50 Hz would increase its speed to approximately 1455 rpm. If advantage is taken of the increased torque, the operating temperature could be expected to increase. With voltage variations greater than 10%, the motor must be de-rated to prevent excessive temperature rise. Motors are normally given a full-time rating for a specified temperature rise, and under these conditions might have to be switched off after a duty period and be allowed to cool down. Starting and breakdown torque values are also affected. A voltage rise increases torque, while a voltage reduction decreases it. In the latter case, care must be taken to see that the motor does not stall while under load. For three-phase motors, a more serious problem occurs when only one phase shifts in value. The phase current is affected to a greater degree, which affects the rotating magnetic field in the motor. This results in reduced starting, running and breakdown torques, increased running noise and vibration, full-load speed reduction and a higher operating temperature.

6.4.5  Abnormal operating conditions—higher operating temperatures Common causes of overheating in motors are inadequate or restricted ventilation and overloading. Apart from accelerated deterioration of lubricants, possibly the most serious effect is on the insulation—at increased temperatures, there is a marked reduction in the life of insulation. For example, insulation designed to work at 90°C may have an expected life of 25 years. If the operating temperature is doubled to 180°C, the life expectancy is reduced to about 1.25 years. The result is increased efficiency of the cooling system and a decrease in the load applied to the motor.

6.4.6  Abnormal operating conditions—frequency variation Motor speed can be regulated by the frequency of the supply. Allowances are made when selecting a motor for this purpose, but a variation in supply frequency under other circumstances can affect motor operation. The obvious effect is a change in speed, but there are also changes in power factor, efficiency and torque. A higher frequency causes an increase in power factor, a slight increase in efficiency and a decrease in torque. With a decreased frequency, the opposite occurs. A variation in the frequency of supply usually occurs when there are comparatively few large loads connected to a smaller supply.

6.4.7  Abnormal operating conditions—overloading Manufacturers build into their motors the capability to handle short-duration overloads, as specified in AS/NZS 1359.41. In general terms, the Standard requires the motor to be able to withstand 1.5 times full load for a period of 15 seconds without appreciable change in speed or excessive heating. For a motor to operate under these conditions, it must also have a breakdown torque greater than the overload test figure. The heating effect in a machine winding is related to the square of the current and the time it is flowing, so any excess current must result in a temperature rise. With short-duration overloads, the amount of heat generated is small and can be expected to be dissipated by the normal cooling process. Long periods of overload, however, can 354

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Alternating current rotating machines  Chapter 6

lead to excessive increases in temperature, which in turn leads to a shortened motor life. Other effects are a slight decrease in speed, decreased efficiency, decreased power factor and an increased possibility of stalling because the working torque is closer to the breakdown torque. When the motor stalls, it draws starting current at full line voltage until its protection system operates. Large amounts of heat can be generated in short periods of time under these conditions. Special types of motors are given restricted duty cycles. In effect, they are overloaded for short periods of time, after which they must be switched off and allowed to cool down to room temperature. If this type of motor is required to run on a continuous duty cycle, it must be de-rated to a lower power value.

6.4.8  Abnormal operating conditions—frequent starting Motors in general are mechanically strong enough to handle normal loads with a fair safety factor. However, the number of times a motor is started cannot be provided for by the manufacturer unless this is specifically requested at time of purchase or manufacture. When a motor is started, there is a high current flow that decreases as the motor accelerates up to its operational speed. While this current is flowing, heat is being generated within the windings at a rate in excess of the usual heat dissipation rate. Under normal conditions, this excess heat is removed by the cooling system while the motor is in operation. With repetitive starting, however, the heat generated does not have sufficient time to be removed and the temperature of the motor rises. The circumstances are similar for repeated reversing and plug braking. Starting current values repeatedly stress the windings, whether they are being used for starting, reversing or braking. Unless the coils are firmly braced, they rub against one another, eventually rubbing through the insulation and causing short-circuits within the windings of the motor.

6.4.9  Abnormal operating conditions—other factors Other factors can cause—or constitute—abnormal operating conditions. These include exposure to corrosive fumes, explosive vapours, dust, steam, salt air, high humidity and operation in ambient temperatures of below approximately 10°C or above 40°C, or operation at altitudes in excess of 1000 metres. Generally, all these factors can subject a motor to damage of some kind; initially, though, the damage caused by them is due to the selection of the wrong type of stator housing at the time of purchase. Even motors selected for operation at elevated altitudes are subject to the same restrictions and must be rated by the manufacturer at the time of purchase for the conditions under which they will work. Probably the most common abnormal operating condition for single-phase motors is encountered with centrifugal switch failure, which usually shows itself in the following two conditions.

1. Starting switch contacts remain closed after motor starts A starting switch that remains closed effectively prevents the isolation of the starting winding from the power after the starting process has been achieved. Since most, if not all, starting windings are designed with a limited duty cycle, there is very little tolerance in terms of the amount of time they can remain energised. After a period of about 20 to 30 seconds, they overheat and can be permanently damaged.

2. Starting switch contacts open-circuit A fault of this nature usually occurs when the switch becomes jammed in its running position. The next time the motor is required to start, the starting windings cannot function. The motor is unable to start its rotation and remains stalled, with full line voltage applied. A high starting current is maintained and is not able to reduce to a normal running value. The effect is that the excessive current continues and overheats the running winding, leading to possible burnout. In both of these conditions, there is also the real possibility that the heat generated in one winding can be transferred to the other, causing damage to that, too. Without suitable motor protection, only prompt action on the part of the operator will prevent further damage. 355

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Electrical Principles

6.5  Single-phase motors—capacitor and shaded pole types 6.5.1  Capacitor-start motor Design limitations restrict the split-phase motor to a maximum of about 30°E between the starting and running winding currents. To increase this angle and produce improved starting characteristics, a capacitor is connected in series with the starting winding (see Figure 6.33(a)). A capacitor-start motor is identical to a split-phase motor, with the addition of a capacitor which is usually mounted on top of the motor (see Figure 6.33(b)). If the correct size capacitor is selected, the two currents will be at 90°E to each other and improved starting torque will be obtained. On start, any value capacitor will increase the angle, but values that enable the starting winding to approach resonance must be avoided. For this reason, it is advisable to use a capacitor much larger than necessary to ensure that resonance does not occur. The phasors in Figure 6.33(c) indicate the ideal phase displacement of 90°E. This angle of phase displacement between IR and IS provides a more uniform strength of stator flux during starting—a comparison of Figures 6.33(c) and (d) is useful here. Owing to this more even field strength, the starting torque is higher than for the equivalent size split-phase motor. Figure 6.34 shows the speed/torque curve for a capacitor-start motor (it is drawn to the same scale as Figure 6.32 to facilitate comparison). It demonstrates a large increase in starting torque due to the addition of the capacitor, while the torque is the same as for the split-phase motor after the switch has operated. In a similar fashion to the split-phase motor, the switch operates at approximately 75% of full-load speed. The actual starting windings for the two types of motor may consist of different data. The reversal of rotation is achieved by the same principles that apply to the splitphase motor. That is, the motor can be reversed by changing over the two leads of any one winding (but not of both). Capacitor-start motors are used in general-purpose, heavy-duty applications requiring high locked-rotor starting torque, such as that used in starting refrigerators and air compressors.

6.5.2  Capacitor-start/capacitor-run motor This type of motor has both windings permanently connected across the supply, and these are referred to as the ‘main’ and ‘auxiliary’ windings. During starting, additional capacitance is connected in series with the auxiliary winding to provide the necessary phase displacement between the winding currents for maximum torque. The starting capacitor is therefore connected in parallel with the running capacitor. When the rotor speed reaches about 75% of the rated speed, the centrifugal switch disconnects the starting capacitor from the circuit (see Figure 6.35(a)).

Centrifugal switch

A

Start capacitor

Run

Rotor

N Start

Figure 6.33(a)  Capacitor-start, induction-run motor circuit

Figure 6.33(b)  Capacitor-start, induction-run motor

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Alternating current rotating machines  Chapter 6

j

IS

i

K

h

l

V g

~90° IT

a

b

f c

e d

(b) Relative field strengh

IR

Figure 6.33(d)  Resultant stator field IR

Switch speed 400

IS

300

Torque %

90°E

Rate speed

200 Rated torque 100

a

b

c

d

e

f

g

h

i

j

k

Figure 6.33(c)  Phasor and waveform diagram

a

0 nsyn

Speed

Figure 6.34  Capacitor-start motor speed/torque curve

Figure 6.35(b) shows a capacitor-start/capacitor-run motor. During operating conditions, the running capacitor ensures the correct phase displacement between the two currents in the windings, thus providing a constant-strength rotating magnetic field. The starting capacitor can be rated for intermittent duty, but the running capacitor must be of a construction suitable for continuous rating, such as the paper-spaced oil-filled type. The two-capacitor motor provides

Centrifugal switch

A

Run capacitor

Run

Rotor

Start capacitor

N

Auxiliary

Figure 6.35(a)  Capacitor-start/capacitor-run motor circuit

Figure 6.35(b)  Capacitor-start/capacitor-run motor CMG Engineering Group—a Regal Beloit Company

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Electrical Principles

substantially the same running torque as the capacitor-start, induction-run type, but has beneficial effects. Adding the second capacitor:

1. 2. 3. 4.

increases the breakdown torque improves full-load efficiency and power factor reduces operational noise and vibration increases locked-rotor torque.

Again, the direction of rotation can be reversed by changing over the two leads of any one winding, but not of both. This changes the direction of rotation of the magnetic field in the stator. The capacitor-start/capacitor-run motor is suitable for heavy-duty loads where quietness is a consideration and substantial starting torque is necessary (wall-mounted air-conditioning units where high head pressures are encountered in hot weather, for example).

6.5.3  Permanent split capacitor (PSC) motor The permanent split capacitor (PSC) motor also has both windings permanently connected across the supply, with a capacitor in series with one of them (see Figure 6.36). For this type of motor, both windings are identical in wire size and number of turns, and they are also referred to as the main and auxiliary windings. Because the capacitor is in series with one winding, the current in that winding leads the current in the other, providing the phase displacement necessary to produce a rotating stator field. However, the phase displacement between the two fluxes is relatively small and so the starting torque is low. By changing the line connection to the ‘reverse’ position shown in Figure 6.36, the capacitor is then in series with the main winding instead of the auxiliary winding. The current in the main winding leads that in the auxiliary winding and the rotor runs in the reverse direction. The permanent split capacitor motor is suitable for light applications with low starting torque (fans and blowers, for example) which might need to be reversed frequently. It is also suitable for remote control of induction regulators and dampers for regulating air flow in air-conditioning systems. The permanent split capacitor motor is suitable for unit heaters and fans because its speed can be varied fairly easily with series inductances.

6.5.4  Shaded pole motor

Main

The shaded pole motor has a cage rotor with salient poles in the stator. On one side of each pole a slot is cut and a shading ring is embedded into it (see Figures 6.37(a) and (b)). The shading rings are made of copper bar formed into a closed loop, providing a low-resistance path through the ring. The supply current produces an alternating flux in each pole. This alternating flux cuts the shading ring, inducing an EMF in it. Because of the low resistance path, the current flowing through the ring is relatively high. Also, according to Lenz’s Law, the induced current in the shading ring will produce a flux that will tend to oppose the change of the main flux. When the supply current rises rapidly from A to B (as Reverse A in Figure 6.38(d)), an induced voltage is established in the Forward shading ring. The current in the ring produces a flux that Rotor opposes the build-up of the main flux. As a result, the main flux is concentrated in the unshaded section of the pole (see Figure 6.38(a)). When the current changes from B to C, there is little change in value of current and very little voltage is induced in the shading ring. Consequently, practically no current or N flux is produced in the shaded ring. The main flux is at Auxiliary this time nearly always at maximum value and is uniformly distributed over the whole pole face (see Figure 6.38(b)). Figure 6.36  Permanent split capacitor motor circuit 358

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Alternating current rotating machines  Chapter 6

A

Shading ring Rotor

Pole

N

Figure 6.37(a)  Shaded pole motor circuit

Figure 6.37(b)  Salient poles, windings and shaded ring

C

C

C

B

C

l

A (a)

(b)

(c)

Time

D

(d)

Figure 6.38  Movement of field in a shaded pole motor

When the supply current drops rapidly from C to D, an induced voltage is established in the shading ring. The current in the shading ring produces a flux that opposes the collapse of the main flux. The concentration of flux therefore occurs in the shaded action of the pole (see Figure 6.38(c)). The magnetic axis shifts across the pole face from the unshaded part to the shaded part. This shifting flux is similar to a rotating field and produces a small torque, causing the rotor to rotate in the direction of the flux, towards the shaded section of the pole. The starting torque of a shaded pole motor is very low, as indicated in Figure 6.39, and the motor runs with a slip speed slightly higher than the single-phase motors described above. It is simple in construction, low in cost and reliable. There are no switches, slip-rings, brushes or capacitors that might require maintenance. The motor efficiency is down, and this tends to restrict its use to low power ratings. The direction of rotation has to be reversed by altering the direction of the rotating magnetic field across the pole face. This is done by shifting the shading ring to 300 the other side of the pole face. Some poles are fitted with slots on both sides for this purpose, but with others the Rated Torque 200 speed only method is to remove the stator from its housing and % Rated torque replace it the other way around in the frame. 100 Because its speed can be varied within a limited range by a series resistor or inductor, the shaded pole motor is nsyn suitable for fans and blowers, advertising signs, damper Speed controllers, hair dryers and other applications where the starting torque requirements are minimal. Figure 6.39  Shaded pole motor speed/torque curve 359

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Electrical Principles

6.6  Single-phase motors—universal motor 6.6.1  Operating principles of a series universal motor The series motor is often called a ‘universal’ motor because it can operate effectively on d.c. and a.c. up to powerline frequencies. Like the normal d.c. series motor, it has a highly variable speed characteristic, with speeds up to 15 000 rpm in domestic appliances. Under some circumstances, governors have to be used to restrict speeds to safe values.

6.6.2 Construction The armature construction is similar to that of a d.c. armature, with laminations, commutator and windings. The armature windings are connected in series with the two field coils by means of carbon brushes running on the commutator (see Figure 6.40(a) and (b)). Field pole construction consists of lamination stampings riveted together to form salient poles. The field coils are concentrated-type windings fitted closely around the salient poles.

A Series field

Brush

N

Figure 6.40(a)  Universal/series motor

Armature

Brush

Series field

Figure 6.40(b)  Typical series universal motor

6.6.3 Operation There is a common current flowing through both windings so the two magnetic fluxes produced are in phase with each other. Interaction of the fluxes produces torque to turn the armature. As the a.c. supply alternates, the fluxes change in unison, remaining in phase. When the line current flows from A to B in Figure 6.41(a), north and south poles are produced as shown. Assuming that the armature current is in the direction indicated by the dots and crosses, the flux produced around the armature conductors interacts with the field flux, producing an anticlockwise rotation. When the line current flows from B to A on the alternate half-cycle, the polarities of the main fields are reversed (see Figure  6.41(b)). The current through the armature also reverses, reversing the armature flux. The resultant torque is still in the anticlockwise direction, so a steady rotation in one direction is maintained. Rotation is reversed by changing the direction of current flow through the armature with respect to the field; that is, changing over the leads to the armature or the fields—but not both (see Figure  6.42). The speed/load characteristics for the series universal motor are shown in Figure 6.43. When the load is heavy, the speed is low; at light loads, the speed is very high. With the very small series motor in domestic use, the internal losses (such as friction and windage) are large enough to limit the speed to a safe value. The motor runs at a relatively high speed and has good starting and running torque characteristics, considering its size. 360

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Alternating current rotating machines  Chapter 6

l

l A

A

N

S

S

N

B

B (b) Second half-cycle

(a) First half-cycle

Figure 6.41  Torque production in a universal motor

A

A

(a)

(b) Speed

A

(b)

Figure 6.42  Reversing the direction of rotation of a universal motor

Load

Figure 6.43  Speed/load characteristics of a universal motors

6.6.4 Application The series motor is popular in portable appliances such as saws and drills, sewing machines, business machines, food mixers, small washing machines and vacuum cleaners. 361

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Electrical Principles Table 6.2  A summary of single-phase motors Motor type

Reversal

Applications

Torque

Split phase

Interchange connections of one winding

Washing machines Blowers Bench grinders

Moderate

Capacitor-start

Interchange connections of one winding

Pumps and small compressors

Moderate increase

Capacitor-start/ capacitor-run

Interchange connections of one winding

Air-conditioning units

Substantial increase

Permanently split

Interchange connections of one winding

Light loads subject to regular reversals

Very low

Shaded pole

Move shading rings to opposite side of pole or reverse stator in body

Fans

Low

Series

Interchange connections of either field or armature

Domestic appliances Hand tools

Low

Table 6.3  Comparative advantages and disadvantages of single-phase and three-phase motors Advantages of three-phase motors

Advantages of single-phase motors

1. For the same power output, a three-phase motor is smaller and lighter. 2. More efficient use of the iron core. 3. Higher efficiency—less input power for the same output power. 4. For the same output power, line currents are smaller. 5. Suitable for powerline frequencies in excess of several hundred hertz. 6. Less mechanical vibration, owing to magnetic fields of more constant strength. 7. Inherently self-starting, owing to naturally rotating magnetic field. 8. No starting mechanism or switches required. 9. No additional wiring of extra conductors for fully sealed motors and reduced complications of difficult installations such as submersible pumps. 10. Direction can be reversed externally by interchanging supply lines. 11. Starting currents more easily controlled without great loss of starting torque.

1. Only two windings in use, one of which can be of lighter construction. 2. More amenable to automatic machine winding— reduced construction costs in many cases. 3. Only one active and one neutral conductor needed in most cases.

Disadvantages of three-phase motors

Disadvantages of single-phase motors

1. Three identical windings are needed. 2. Three active conductors are needed. 3. Not conducive to machine winding—more labour intensive.

1. Higher line currents for the same power. 2. Energy distributors may limit starting currents of large motors. 3. Single-phase motor reversal is usually done internally.

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Alternating current rotating machines  Chapter 6

Summary 6.4–6 ∙ Single-phase squirrel cage motors have no rotating field or starting torque. ∙ A rotating field is created by having two separate windings with the currents displaced electrically. ∙ The phase displacement between the currents in the two windings produces a phase displacement between the two fluxes produced. ∙ The phase displacement can be enhanced with the addition of a capacitor in series with one winding. ∙ The spilt-phase motor has two windings—a ‘run’ winding and a ‘start’ winding. ∙ The run winding has low resistance and high inductance while the start winding has higher resistance and lower inductance. ∙ The current in the run winding lags the current in the start winding by a considerable angle. f ∙ The rotational speed of the stator flux can be determined using the formula n = 120​​ __  ​​ . p ∙ Reversal of motor rotation is achieved by reversing one of the windings. This reverses the direction of the rotating field. ∙ Once up to speed, the rotor produces a ‘cross-field’; the motor is able to keep rotating and the second winding can then be disconnected. ∙ The start winding in a split-phase motor is disconnected, using a centrifugal switch, at about 75% rated speed. ∙ The field from the run winding and the field from the rotor combine to form a rotating field. ∙ The capacitor-start motor has improved starting torque when compared with a standard split-phase motor. ∙ The capacitor-start motor is used in general heavy-duty applications such as refrigeration and air compressors. ∙ The capacitor-start/capacitor-run motor has two capacitors in series with the starting winding. At 75% full speed, one is disconnected. ∙ The capacitor-start/capacitor-run motor has a number of advantages. Adding the extra capacitor: – increases the locked-rotor and breakdown torques – improves full-load efficiency and power factor – reduces operational noise and vibration. ∙ The capacitor-start/capacitor-run motor is suitable for heavy loads where high starting torque and quietness are required. ∙ The permanently split motor has both windings permanently connected to the supply. Both windings are identical. ∙ The permanently split motor is suitable for low-torque, light applications such as small fans. ∙ The permanently split motor is also suitable for remote control of air-dampers and regulators. ∙ The shaded pole motor has a cage rotor with salient poles on the stator. ∙ A shifting-flux across the pole face produces a starting torque in a shaded pole motor. ∙ To reverse the direction of rotation of a shaded pole motor, it is necessary to remove the stator from its housing and replace it the other way around in the frame. ∙ The speed of a shaded pole motor can be varied over a limited range by using series resistors or inductors. ∙ The shaded pole motor can only be used where the starting torque requirements are minimal. ∙ The series or universal motor can run on either a.c. or d.c. ∙ The universal motor has field windings and an armature similar to that of a d.c. motor. ∙ A common current flows through the field windings and the armature, producing fluxes that interact to cause rotation of the armature. 363

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Electrical Principles ∙ When operating on a.c., both the fluxes reverse at the same time, so the resultant torque remains in the same direction. ∙ The universal motor has a highly variable speed/load characteristic and needs a governor to restrict the speed to a safe level at low loads. ∙ The universal motor has good starting and running torque and is used in applications such as portable appliances— drills, saws, vacuum cleaners, etc. ∙ The torque produced by a single-phase motor is proportional to the square of the supply voltage T ∝ V2. ∙ A supply voltage that is below the rated value will produce substantially lower torque—(90%)2 V = 81% T.

6.7  Motor protection 6.7.1 Introduction An electric motor will normally run unattended for many years. During its operational life, there will be occasions when an overload will be placed on it or a fault will occur in it (or in the control gear or the supply circuit). The motor and its associated circuit must have devices to protect them should such a problem occur. Protection is normally supplied by the circuitry associated with any starter; in addition to monitoring an electric motor for such functions as controlled acceleration, reversing, braking or speed control, a starter should also provide the motor with some form of protection. Line voltages and motor currents need to be monitored and, when required, the motor should be isolated from the supply. Protective devices take many forms, but most are designed to operate within the control circuit of the motor starter. In this way, a fault occurring in one phase can be used to trip a contactor to isolate all three phases and disconnect the motor from the supply. All electrical circuits must be protected against the effects of both overload currents and fault currents. Before discussing their effects, it is important to note the difference between an overload current and a fault current. An overload current flows when the motor is used incorrectly—that is, if it has been overloaded and draws more than its rated current. If the motor draws more that the rated circuit current, then both the motor and the circuit are overloaded. There is nothing wrong with the motor or the circuit—the problem is how the machine is being operated. In Figure 6.44, if too much product were placed on the conveyor, the motor would slow down due to overload. The motor will draw excess current because of operator error; this is an overload current. When an overload current flows in the circuit, the circuit protection device needs to operate before damage can occur to the cable or the motor. The values of current-carrying capacity allocated to cables are generally determined so that the cable insulation does not sustain damage due to temperature rise during normal operation. A fault current occurs when there is a short-circuit between live conductors only or between live conductors and earth. This current can be very large and can cause considerable damage if the correct circuit protection has not been used. For a motor circuit, a short-circuit current would only be present if a serious fault developed in the motor, control gear or associated supply circuit.

6.7.2  Motor protection

Figure 6.44  A typical conveyor system

One common cause of motor failure is temperatures rising above design values. This can be due to an electrical fault such as single phasing or to mechanical overloading by the driven machine. The overload might be a relatively small one for a sustained period, or it might be a large and sudden overload such as occurs when a machine locks up because of a mechanical fault.

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6.7.3  Short-duration overload Standard motor design allows for a short-duration overload by having a normal running temperature that is well within the capability of the temperature rating of the motor insulation. When an overload current flows in the motor windings, the heat generated by the current is proportional to the square of the current (H ∝ I2). If a motor rated 10 A has an overload of 20 A, it will cause (102 = 100, 202 = 400) four times the amount of heat to be generated in the motor. This is a serious situation if the overload is sustained for more than a few seconds. To compound the problem, an overloaded induction motor will slow down with the load and the shaft-mounted fan will supply less cooling air, just when proper cooling is most required.

6.7.4  Sustained overload If a motor has a sustained overload, there will be a high temperature rise within it. If the temperature becomes higher than the rated temperature of the insulation, the motor will most likely sustain a serious insulation failure.

6.7.5  Locked rotor When the rotor of an induction motor is locked (meaning that the motor has stalled on an overload), the motor will draw excessive current. The value of the locked rotor current is the same as the DOL (direct online) starting current, and this is usually about seven times the rated current. The heat generated by a 10 A motor with a locked rotor will be approximately 49 times the heat produced at full load (102  =  100,  702  =  4900). At the same time, the shaft-mounted fan is not supplying any cooling air at all. This is serious, and if the correct protection has not been provided, the motor can sustain a significant insulation failure.

6.7.6  Under-voltage protection Two kinds of under-voltage protection are available for motors controlled by contactors. The first is called ‘no-volt protection’ because once the voltage is reduced below the holdingin voltage level of the coils, the contactors drop out. When power is restored, the motor has to be taken through the starting sequence again until it is up to speed. The second type is an additional part of a control circuit and keeps the contactors in a holding position for momentary dips in voltage. If the power is restored before the motor can coast down appreciably in speed, full power is immediately restored to the motor. One such circuit is illustrated in Figure 6.45 (only the control circuit is shown). When the start button is pressed, relay coil K1/1 closes immediately. This closes contact K1.1. (As the symbol indicates, the relay can close instantly but delays on opening.) The circuit is completed for relay K3/4, and it closes and connects the motor through contacts K3.1, K3.2 and K3.3 to the three

L1

L2

K2.1 Stop K3.4

K1.1

Start

K1/1

K2/1

K3/4

Figure 6.45  Control circuit for under-voltage protection

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Electrical Principles

supply lines. Contact K3.4 latches across the start button, so holding the circuit in a completed condition. The normally closed contact K2.1 is connected in series with K3/4. To stop the motor, pressing the stop button releases relay K1/1 and also completes the circuit to relay K2/1 via a mechanically attached switch simultaneously. Contact K2.1 opens, releases the main contactor K3/4 and so isolates the motor from the supply. During a sudden dip in voltage, the delaying action of K1/1 and its accompanying contact K1.1 ensures that the circuit to the main contactor remains complete. If the power dip is short, the motor can restart automatically without an operator being required to initiate a starting sequence. If the power dip is greater than the delay time of the contactor, the starting sequence has to be initiated. In the interests of safe working, many machines do not lend themselves to this type of circuitry as an automatic restart might be dangerous to the operator.

6.7.7  Over-voltage protection For alternating current motors connected to a distribution system, over-voltage is rare. It is more common with long-distance high-voltage transmission lines where lightning strikes are likely to occur. It is a more prevalent problem with variable-speed mobile generating plants such as those in aeroplanes and automobiles. As it is undesirable to have an electrical installation operating with a low power factor, consumers are encouraged to keep loads at high power factors. Sometimes, consumers adopt the uneconomical practice of connecting capacitors in parallel with individual induction motors to correct the power factor. This can lead to over-voltage transients occurring when a motor is switched off. The size of the capacitors should be sufficient only to correct the power factor of each load, and preferably ensure that it still has a lagging power factor. Capacitors connected across an induction motor can cause self-excitation as the motor continues to spin. In some circumstances, this generated voltage can be as high as double line voltage. In normal circumstances, this overvoltage lasts only for a short period and most equipment can cope with the voltage surge. There are occasions when a motor application requires the fitting of surge suppression devices. One example is the submersible bore pump. In its operating location, it is a very good earthing point and, as many bores are fed from overhead lines at a distance from a source of supply, the installation is vulnerable to lightning strikes. In an attempt to protect the motor against what may well be a 500 kV over-voltage surge, suppressors are fitted. Motor protection is rather uncertain in such circumstances.

6.7.8  Repetitive starting The starting current of an induction motor can be up to seven times the full load current. The heat generated during a normal start can be handled by the motor due the starting current only being present for a brief time. When the motor is up to speed, the shaft-mounted fan will remove any excess heat. The total heat produced by the current can be determined using Joule’s law. H = I 2Rt where:



H = heat in joules I = current in amperes R = winding resistance in ohms t = time in seconds

The amount of time the high current flows for is the important factor. From the formula, it can be seen that the heat produced is directly proportional to the time in seconds. In the case of repetitive starts, the amount of heat produced will keep building up due to the extended time factor and the fan not running at full speed long enough the remove the excess heat. 366

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6.7.9  Special requirements for motor protection in high-humidity or moist environments, high-temperature areas and corrosive atmospheres The temperature rating of a motor indicates the maximum temperature that the windings can withstand before permanent damage is done to them. Motors with Class ‘B’ insulation have a maximum operating temperature of 130°C, so they operate satisfactorily at temperatures up to that. If the winding temperature exceeds that value, some deterioration of the windings will occur. As a general rule, for every 10°C of temperature rise above the rated value, the insulation life is halved.

Temperature rise Temperature rise of a motor is the difference between the ambient temperature and the motor’s winding temperature. The winding temperature is calculated by the resistance method. If the ambient temperature is 30°C and the rated maximum temperature of the motor is 105°C (Class ‘A’ insulation), the maximum permitted temperature rise is 65°C. ​105 − 40 = 65​ However, if the ambient temperature is 40°C, then the maximum permitted temperature rise is only 55°C. The motor may be handling the load when the ambient temperature is low but may suffer over-temperature problems when the ambient temperature is high.

Hot-spot allowance The above calculation assumes that the winding has the same temperature throughout. However, if the temperature has been determined using the resistance method, then it will be the average value. To offset any hot spots in the winding, an allowance is made for safety. A value of 10°C is normally used. So, for the above situation with a 40°C ambient, the maximum permitted temperature rise would be 55 − 10 = 45° C.

Calculating winding temperature Calculations to determine the temperature of a motor winding are based on measuring the cold winding resistance and the hot winding resistance, as well as the extrapolated temperature for zero resistance. An extrapolated value can be used because the resistance of copper, and of aluminium, windings increases in a linear manner with temperature. The extrapolated temperature for zero resistance of copper windings is −234.5°C.

EXAMPLE 6.4 A motor has a winding resistance of 16.5  Ω at 25°C. After running at full load for two hours, the resistance is measured as 20 Ω. What is the temperature of the windings? ​R​  1​​[234.5 + ​t​  2​​  ] ​​R​  2​​ = ___________ ​        ​​ 234.5 + ​t​  1​​ by transposition: ​R​  ​​  ​t​  2​​ = ​ ___ ​  2  ​   ​× (234.5 + ​t​  1​​) −  234.5 ( ​R​  1​​)

20   ​​              ​  =​  ​ _____ ​  − 234.5 ​ ​​​ ​    ​  ​ × (234.5 + 25) (16.5)   = 1.21 × 259.5 − 234.5   = 80° C

EXAMPLE 6.5 A motor has a winding resistance of 16.5 Ω at an ambient temperature of 25°C. After running at full load for two hours, the resistance is measured as 20 Ω. Determine the temperature rise in the windings. (continued) 367

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Electrical Principles

The resistance formula used above can be modified to give: (​R​  ​​  − ​R​  1​​) Temperature rise = ________ ​  2  ​      × (234.5 + ​t​  1​​  ) ​R​  1​​ (20 − 16.5)   = _________ ​   ​     × (234.5 + 25) ​​            ​  ​   ​​ ​ ​ ​ 16.5 3.5 × 259.5   = __________ ​   ​     16.5   = 55°C An allowance of 10°C is then added to this value to give a value of 65°C. If the maximum permitted temperature of the motor is 105°C, then the motor is operating within its safe temperature range. Motor temperature = temperature rise + ambient       ​  ​  =​  65 + 25  ​​ ​ ​  ​​     

= 90° C

6.7.10  High humidity Motors that operate in areas where the humidity and temperature are high are subjected to moist conditions, which can produce condensation on their inner surfaces. In humid areas, where the operating temperature of a machine has a large differential to the off state and ambient temperature, the motor is particularly susceptible to condensation. For example, a machine can sometimes go from 20°C to 40°C, with relative humidity often reaching 100%. Condensation will occur on a motor surface when the frame temperature of the motor is lower than the dew-point temperature of the ambient air. Any condensation can cause the condition of the windings and inner surfaces to deteriorate over time. This problem is compounded if the motor is installed in an area where there is little or no natural ventilation. To protect the motor and windings against these conditions, motors can be given an extra coating on their inner surfaces and on the windings. The stator windings are impregnated with a special electrical varnish that is designed to prevent any moisture from reaching the windings. The metal surfaces are also given a special coat of a rustpreventative paint.

6.7.11  Environmental protection Enclosures Induction motors are available in many different enclosures, depending on the task allocated to them. Some of the types of enclosures are:

1. open 2. totally enclosed 3. duct or force ventilated 4. drip proof 5. flame proof 6. weatherproof 7. submersible 8. explosion proof.

AS/NZS 1359.21 lists more than a dozen methods for cooling induction motors. Adding to this a variety of different mounting types, such as horizontal or vertical, tends to make the list rather long. The type of motor enclosure chosen depends on the conditions under which it has to function. The enclosures listed below are the main general groups, but there can be many sub-groups of each. 368

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Open motors The ends of the machine are open, allowing free ventilation through and around the windings. Air is circulated through the motor by a fan attached to the motor shaft. The motor needs to be installed in a clean and dry atmosphere.

Protected motors With the protected motor enclosure, the windings and live parts are protected mechanically but a free flow of air is still drawn through the motor by a fan attached to the motor shaft. The protection is often obtained by fastening wire mesh or perforated metal over enclosure openings.

Drip-proof motors Drip proofing is an advance on the protected type of enclosure. The openings are further protected by a hood, preventing foreign materials and moisture from falling vertically onto the motor and entering it. The hood may be incorporated into the enclosure during manufacture of the motor.

Duct or force ventilated With forced ventilation, a fan forces air through the motor at a constant rate. A motor with forced ventilation is shown in Figure  6.46. This is essential where the motor is connected to a variable speed drive and is required to run at reduced speed with a load. In these conditions, the motor’s own fan will not be spinning fast enough to deliver the required amount of cooling. The motor might not be in a suitable atmosphere to allow clean air to flow through it—for example, corrosive atmospheres, high temperatures, high humidity and similar conditions. For ventilation, cool and clean air must be drawn in from outside the installation. There are two major types of ventilation in this case. In one type, air is drawn from outside through a duct and can be expelled inside the installation, or it may have to be ducted to the outside atmosphere again. In the second type, a blower is installed outside and air is forced through a duct to the motor. It may be expelled directly, or it can be ducted outside into the atmosphere again. This is a method of cooling usually adopted for very large motors.

Figure 6.46  A three-phase motor with fan-forced cooling

Totally enclosed In the totally-enclosed type (see Figure 6.47), there is no contact between the air inside the machine and the air outside. The fan attached to the shaft is external to the motor proper and enclosed within its own housing. The motor housing is usually ribbed, and the air driven by the fan flows along the ribs and removes the internal heat by conduction through the housing. The heat is removed from the motor at a slower rate than by direct cooling, but the increased surface area created by the finning process assists. Modifications to this method of enclosing a motor enable it to be classified as waterproof, weatherproof or submersible.

Figure 6.47  Totally enclosed fan-cooled motor

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Electrical Principles

Flame proof

Three-phase induction motor kW ˜° Type Ex‘d’ Volts ˙ˆ˝ Duty CONT COS O °.˛˝ Amps ˆ° RPM ˆ˙˙° HARREGO MOTOR COMPANY

Figure 6.48  Typical flange-mounted flame-proof motor

The flame-proof type (see Figure  6.48) is a totally enclosed motor with additional precautions to seal the bearings and assembly contact surfaces. Electrical connections are made through a special sealed gland. The motor housing is made strong enough to withstand any internal explosion and still prevent sparks escaping to the external atmosphere. The motor is used when there are flammable gases and the risk of explosion if sparks enter this atmosphere. The enclosure must comply with stringent regulations before being classified as flame proof.

6.7.12  Protection devices AS/NZS 3000 requires that circuits supplying motors should be protected against overload and fault currents. In addition, any unattended motor is required to be protected against:

∙ overloads ∙ fault currents ∙ under-voltage ∙ over-temperature.

There is also a requirement that all motors should have a control device for stopping and starting, as well as an isolator. All of the above requirements are usually met by installing fuses or circuit breakers in the switchboard, a motor starter with controls at a convenient location and an isolator near the motor. Modern proprietary motor starters are available with some, or all, of the above features built into the one unit.

6.7.13 Fuses The fuse is possibly the simplest form of circuit protection. It consists of a fuse element designed to melt and prevent further current flow. The major disadvantage of a blown fuse is that the active component has to be replaced. The primary purpose of a fuse is to protect a circuit rather than any load. Under short-circuit conditions, the reaction time of a high rupturing capacity (HRC) fuse in isolating a circuit is probably the fastest of all protection systems. A fuse element has to have a current rating that is high enough to allow a motor to draw starting currents yet low enough to give some protection against overloads. Because of these opposing factors, a fuse cannot provide complete protection for both the circuit and the load. Figure 6.49 shows a set of three typical HRC fuses used for motor circuit protection. They have a plastic carrier and base and are designed to be used with enclosed fuse links. HRC fuses are extremely consistent and reliable in terms of tripping values. The element of a HRC fuse is enclosed in an insulating tube filled with powdered quartz to quench any arc that might develop. Figure 6.50 shows a cutaway drawing of an enclosed-type fuse link. This type has lugs to allow the fuse link to be held in place with machine-threaded screws. HRC fuses up to 63 A are often manufactured with plug-in fuse links. The silver element has restrictions cut into its section to give a Figure 6.49  HRC fuses for three-phase motor circuit very fast response to fault currents. If a fault current flows through 370

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the fuse, the restricted sections of the fuse element heat up very quickly by the Joule’s law effect (H  =  I2Rt). This gives the HRC fuse a very fast response time to fault currents. The fuse element of a HRC fuse has a eutectic bead to give a good response to prolonged overload currents. If a prolonged overload current flows, the eutectic bead Figure 6.50  Cutaway of an enclosed-type fuse link will reach a point where it can no longer dissipate the heat and will melt. By careful selection of the mass of the eutectic bead, manufacturers can tailor the operation of the fuse to any time/overload-current characteristic required. To ensure the safe operation of equipment, it is essential that only the correct size is used when replacing HRC fuses. Replacement cartridges of the correct size should be kept on hand for all HRC fuses. When used to protect induction motor circuits, HRC fuses that are rated ‘M’ for motor starting should be used. These are capable of providing protection while not tripping on motor-starting currents.

6.7.14  Circuit breakers When circuit breakers are used for motor protection, the correct type must be selected. Figure 6.51 shows a typical time/current characteristic of a type ‘C’ and ‘D’ circuit breaker. It can be seen from the characteristics that a standard ‘C’-type circuit breaker has the magnetic trip portion set at approximately 7.5 times the nominal current rating of the breaker. This value may not be enough to allow for the starting current of the motor, and could result in nuisance tripping. A ‘D’-type circuit breaker has the magnetic trip set to about 12.5 times the nominal circuit breaker rating. Tripping times that lie within the thermal characteristics are identical, as both types will trip at the same time for a steady overload. The circuit breaker shown in Figure 6.52 combines the features of a motor circuit breaker and an isolator in the one unit.

10 000 1 hour 1000

Tripping time

100

10

1

0.1

‘C’ type

‘D’ type

0.01

0.001

1

2

4

6 8 10

20

40 60 100

Multiple of circuit breaker rating

Figure 6.51  Typical time/current characteristic for ‘C’- and ‘D’-type circuit breakers

Figure 6.52  Combined motor circuit breaker and isolator Reproduced with permission of NHP Electrical Engineering Products Pty Ltd

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Electrical Principles

6.7.15  Over-current relays Magnetically activated over-current relays

Electromagnet To load circuit

Armature

To trip circuit

Stop

Figure 6.53  Simple electromagnetic overload trip

Instant tripping relays are operated by the direct action of the motor current on an armature. The principle is illustrated in Figure  6.53. The relay consists of a series coil wound on a magnetic core. The coil is connected in one motor line and the armature is attracted to the main body of the core when the motor current exceeds a predetermined value. The mechanical movement of the armature can be arranged to either close or open an electrical circuit as desired.

6.7.16  Magnetic trip circuit breakers with dashpots One construction method for an over-current relay is that of a coil wound on a cylinder. The coil is connected in series with the motor so it carries the same current as the motor. A plunger positioned so that it can be attracted into the coil activates the tripping process when the motor current exceeds the preset value. The direct-acting over-current relay has one serious disadvantage for protecting electric motors: starting currents far exceed normal full-load running currents and the relay would trip out each time an attempt was made to start the motor.

Delayed tripping Time-delayed tripping is achieved by attaching a small oil dashpot to the plunger (see Figure 6.54). The piston has a small hole drilled in it, and when excess currents attempt to pull the plunger into the solenoid, the action of the oil moving through the small hole delays the tripping action sufficiently to prevent operation while the starting sequence is occurring. When correctly adjusted, the relay will not trip on starting current but will trip on even small sustained overloads.

6.7.17  Thermal overloads Many types of thermal overload relays are available for motor protection. Some operate on different principles from others, but all are designed to open a contact when a temperature-sensitive element—such as a bimetal strip—receives sufficient heat to activate it. Because the contact is usually connected in the control circuit of the starter, the opening of the contact allows the main contactors to drop out and switch off the supply to the motor. The operating principle of most thermal overload elements relies on a bimetal strip (see Figure 6.55). Correctly designed thermal elements produce an amount of heat related to the amount of motor current. The quantity of heat stored, and hence the temperature of the bimetal strip, relates to the amount of bending of the strip. After shortduration overloads, the heat can dissipate and the temperature of the strip is reduced. If small overloads continue for any length of time, the amount of heat generated will activate the relay. With starting currents, insufficient heat energy is developed in the strip for it to bend enough in the time taken for the motor to run up to speed and the current to reduce to the normal running value. Ideally, there should be a thermal detecting element in each line of a three-phase motor, but the trend is to use only two. In economic terms, the extra cost involved is small compared with that involved in replacing a partially burned-out motor. Thermal overload elements are placed in the main supply lines leading to the motor, while the associated control contacts are connected in series with the control circuit. This is to ensure that if only one overload operates, it disconnects the motor from the supply. 372

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Trip contacts

To trip circuit Invar

A1 Solenoid carrying load current

Brass or nickel alloy

Bends when heated

A2 Load current

Solenoid plunger

Heating coil

Oil Piston

Fixing

Bypass hole

Figure 6.54  Magnetic overload with oil dashpot for time-lag

Figure 6.55  Operating principle of a bimetal strip

6.7.18  Combined thermal-magnetic over-current relays In the thermal-magnetic version of the over-current relay, the advantage of the inbuilt delay of the thermal type is combined with the instantaneous tripping characteristic of the magnetic current overload relay. The combination of the two methods is considered ideal motor protection, for the following reasons: ∙ For very high currents, the magnetic section of the relay acts almost instantaneously. ∙ For small overloads, the heat accumulated in the thermal section causes delayed tripping according to the rate of heat generation. Depending on design and application, the combined unit might not have oil dashpots to delay the magnetic relay action. Instead, it is set at a current rating in excess of motor starting requirements, and the thermal element rating is retained at the lower value. The combined unit shown in Figure 6.56 has three separate devices connected in series to fulfil a number of requirements. The components have been designed to operate together. The top part is a magnetically operated circuit breaker and isolator, the middle part is a contactor and the lower part is a thermal overload sensing unit. Figure 6.57 shows a small DOL starter. The contactor and overload unit can be seen mounted inside the starter, while the stop and start button are on the cover. This type has an IP65 rating.

Figure 6.56  Motor circuit breaker with contactor and overload unit

Reproduced with permission of NHP Electrical Engineering Products Pty Ltd

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6.7.19  Microtherm devices Temperature-dependent resistor protection

Resistance (Ω)

A resistor with a positive temperature coefficient (PTC) has the characteristic of increasing its resistance only gradually until a critical temperature is reached. Above this point, its resistance increases rapidly. (A popular trade name for this type of resistor is thermistor—but there are others.) This critical temperature can be varied by altering the composition of the material from which the resistor is made. The determination of a critical temperature for a PTC resistor can also determine its use (see Figure 6.58). For example, many electric motors are designed to have a maximum operating temperature of 60°C. At this temperature, the heat generated by motor losses is approximately equal to the heat being Figure 6.57  Small DOL starter with cover removed lost by the motor. Effectively, this means that the Reproduced with permission of NHP Electrical Engineering Products Pty Ltd temperature of the motor then remains constant. PTC resistors are made in many different shapes so they can fit the requirement of particular jobs. When suitably insulated and placed inside the windings of a motor, the internal temperature of the windings can be monitored. If the critical temperature is, say, 65°C, then the PTC’s resistance would increase rapidly above this temperature and could be an indication that there is something wrong with either the motor or its load. Under normal conditions, temperature-dependent resistors are only capable of handling small values of current and must be used in conjunction with other equipment. Figure  6.59 illustrates one method of monitoring the temperature of motor windings. During the winding process, a PTC resistor is inserted into each phase winding of the motor and all are connected in series with the coil of a small relay. This relay controls a pair of contacts in the control circuit of the motor starter. An isolating transformer and a bridge rectifier supply this circuit with direct current. When the start button is pressed, the transformer supplies power to the PTC resistor circuit and, provided their collective resistance is below the critical temperature value, enough current will flow to activate the relay coil and close the contact connected in series with the main contactor coil. Normal DOL (direct online) starting procedure follows, with normal contactor action. If the temperature of any one 10 kΩ of the three PTC resistors rises above the critical value, the Symbol resistance of the circuit increases, the current flow through the relay coil decreases and the relay drops out. This action causes the main contactor to drop out and isolate the motor. + t°C The complete control circuitry for a thermistor relay is usually housed in the one unit (see Figure 6.60). As with other thermally-activated devices, there is an inherent delay in a PTC resistor cooling down and resetting itself. A thermal overload is normally made as small as possible to reduce its thermal capacity, but this has no effect 4Ω on the thermistor when it is buried within the windings 15 60 because they regulate the rate of cooling. Temperature (t°C) For a locked rotor situation, PTC resistors are an inadequate form of motor protection and external thermal and magnetic Figure 6.58  Typical PTC thermistor characteristic 374

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overload protection should still be provided. The time taken for motor windings to heat up when the rotor is locked in a standstill position is comparatively long; irreversible damage can be done to the motor windings before the PTC resistor exceeds its critical temperature and disconnection occurs.

K1.1

K1.2 K1.3

6.7.20  Single-phasing protection A three-phase motor operating under ideal conditions will draw three equal phase currents. This suggests that K1.4 the three line voltages are also equal, a situation that rarely exists in practice. A small variation in voltage of, say, 2% can cause a current variation of around 10% to K2.1 15%. The function of an overload relay, whether K2/1 K1/4 magnetically or thermally activated, is to disconnect the motor from the supply lines under specified conditions of current flow and within a set period of time. Figure 6.59  Using PTC resistors to protect motor windings Overload relays cannot protect a motor against internal faults—that is not their intended function; controllers are intended to handle the starting currents of induction motors. Fault currents may be many times this value, so fuses or circuit breakers should be installed ahead of the controller. The only protection readily available for a threephase motor is the provision of thermal overload heating +t° elements in each phase. An internal fault in the motor shows externally as greatly unbalanced line currents. Thermal or magnetic overloads can then disconnect the Trip Supply motor from the supply. If an external fault occurs, such as a line to the motor becoming open-circuited when the motor is running, the motor is also said to be ‘single phasing’, and the two remaining line currents increase by approximately 73% each. One of the phase windings then carries about twice as Figure 6.60  Typical thermistor relay much current as the other two and motor damage can occur. For smaller motors, the cost of installing phase-failure relays might be prohibitive, but for larger motors it can be worthwhile as additional protection. Voltage-sensitive relays are connected across each phase, with operating contacts connected in the motor’s control circuit to ensure that the motor is disconnected from the supply in the event of any phase voltage deviating beyond specified limits.

6.7.21  Reverse-phase sequence protection Some machines can be damaged if inadvertently driven in the wrong direction by the drive motor. This can occur when the phase sequence of the supply has been changed. A phase-sensitive relay is supplied by voltages from each phase and isolates the motor from the supply if the phase sequence is incorrect. The relay itself may be partially mechanical and operate a vane, which in turn operates contacts in the main control circuit; or it may be an electronic device. 375

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6.7.22  Electronic overloads The modern equivalent of the thermal overload unit is the electronic overload. These units, which are a similar size to the traditional bimetallic strip-operated units, have small current transformers inbuilt to sense the value of the current. An electronic overload unit is shown in Figure  6.61. The advantage of the electronic unit is that, in addition to having the normal settings with trip and alarm contacts, it has added features such as single-phasing protection. The current setting can be adjusted for different motor runup times by the use of DIL switches. Additional clip-on modules can be added to give further features such as remote-tripping, device-net, PTC thermistor relays and ethernet connections.

SIRIUS TRIP RESET CLASS

M

A3–

A RESET

A4+

95

TEST

96

97

98

6.7.23  Direct current motor protection A2

In general, d.c. motors require the same sort of protection as a.c. motors. Thermal and magnetic overload protection is Figure 6.61  An electronic overload relay equally applicable to both, and fuses are an essential part of both d.c. and a.c. circuits. There are, however, some items of protection that apply specifically to d.c. motors. These are outlined in the following sections.

6.7.24  Field failure protection Extreme weakening or complete loss of a shunt field is unlikely—but it is nevertheless a possibility and precautions need to be taken in case it occurs. The complete or partial loss of the shunt field results in a sharp reduction of generated back EMF. This causes a big increase in armature current, often without a corresponding rise in torque. When a motor is coupled to a load, it might be unable to increase the speed of the load and high currents continue to flow, thus damaging the armature windings. If the motor can shed the load or is unloaded, high speeds occur. This can result in armature windings being thrown out of the slots by centrifugal force. Commutator segments can also be thrown out of their assembly. Where motors are coupled to loads subject to the forces of gravity, loss of motor control allows the load to fall out of control. Damage and injury can occur. To prevent these incidents, a field-failure relay is used. It consists of a pair of normally open contacts with the activating coil connected in series with the shunt field. The normally open contacts of the field-failure relay are connected in series with the main contactor. While field current flows, the relay is activated, the contacts are closed and power can be applied to the armature by the main contactor. In the event of a field failure, the relay contacts open, allowing the main contactor to drop out and isolate the motor. Figure 6.62 shows part of a control circuit with a field failure relay in circuit.

6.7.25  Field discharge protection When disconnecting the shunt fields of many d.c. motors from the supply, the induced voltages created as the magnetic field collapses can be high enough to break down the insulation of the windings. An electric circuit should be connected in parallel with the field to enable this converted energy to be dissipated without damage to the circuit. In Figure 6.62, two forms of protection are shown, although it is only necessary to use one of them. Where the polarity of the field supply is constant, the reverse-connected diode is sufficient protection for the field circuit. The diode has to have a voltage rating high enough to withstand line voltage in the non-conducting state. It also has to 376

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have a current rating high enough to avoid being damaged by the discharge currents. Where the polarity of the field supply is subject to reversal, the second type of protection is used. It consists of a special compound that has a high resistance at normal voltages. When the rated voltage is exceeded, the resistor reverts to a low resistance and allows the energy to dissipate. When the high voltage is removed, the unit changes back to a high resistance. The components are made under several trade names and are also used for lightning protection.

+

Push-button circuitry

K1.1

6.7.26  Over-voltage protection

V

K2/n

K1/1 Although included here as a protection method for d.c. motors, over-voltage protection is more applicable to d.c. generators. Generators that are subject to a wide range − of speeds when driven by a prime mover are capable of producing high voltages. The output voltage can be threeto-four times normal voltage while under the influence of Figure 6.62  Field failure relay connections full-strength magnetic fields. Automobiles, aircraft and similar engine-driven units have generators driven either by belts or directly by solid drives. They are an accessory and are quite separate from the primary drive intention. As the engines are necessarily subject to a wide range of speeds, the generators will also have a wide speed range. Since the generator is expected to produce a useful output at comparatively low speeds, it will need some form of voltage control when driven at high speeds. Many systems for regulating the output voltage have been used, but all rely on controlling the field current of the generator to control output voltage. Probably the most common form of voltage control is a quick-acting relay sensitive to voltages above a certain level. Older-style voltage regulators often had a voltage-controlled relay that inserted resistance in the field circuit when the relay was activated. In more modern units, voltage-sensitive semiconductor components were introduced. These conduct at specific voltages and reduce the current flowing through the field. Depending on circuit configuration, the unit can insert resistance into the circuit or divert the current around the field when voltage levels exceed a set value. The method is accurate and can also be combined with current-controlled sections. Many mobile units use alternators with rectifier units to produce direct current. A similar control method is used for over-voltage protection since the alternator field is excited with direct current.

Summary 6.7 ∙ An overload current flows when a motor is overloaded. ∙ A fault current flows when there is a low-impedance fault between phases or between any phase and earth. ∙ Different protection is required for the circuit and the motor. ∙ The most common cause of motor failure is over-temperature. ∙ A motor will normally be able to withstand a short-duration overload. ∙ When a motor sustains an overload, the protection must operate before damage to the motor occurs. ∙ When a motor has a locked rotor, very heavy overload currents will cause over-temperature damage if the protection does not operate quickly. ∙ Motors should be protected against both under-voltage and over-voltage. 377

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Electrical Principles ∙ Repetitive starting will cause a build-up of heat in a motor. ∙ The operating temperature of a motor can be determined using the motor-winding’s hot and cold resistance. ∙ Environmental protection can be provided by appropriate motor enclosures. ∙ A motor is physically protected by selecting the correct type of housing when choosing a motor for a particular purpose. Sealed types are available for special applications. ∙ Motor protection using fuses will protect the motor circuit, but not necessarily the motor. ∙ Magnetically operated relays controlled by motor current give protection to the motor but operate too quickly to prevent tripping on starting currents. ∙ Circuit breakers used to protect motor circuits should be type ‘D’ so they do not trip during starting. ∙ Combined circuit breakers/isolators are available for motor protection. ∙ Delayed tripping of magnetic-type overload relays is achieved with oil dashpots. ∙ Thermal overloads have a built-in delaying action but will also trip on small overloads after a delay. The delay enables motor starting. ∙ Some overloads have combined thermal and magnetic protection. On small overloads, the thermal section will trip after a short delay. For excessive currents, the magnetically operated overload will trip more quickly than the thermal type. ∙ Manufacturers can supply starter units in module form that include an isolator, magnetic circuit breaker, contactor and overload, all connected. ∙ DOL starters are available with contactors, overloads and push-buttons all mounted and ready to connect. ∙ Temperature-dependent resistors embedded in the motor windings allow monitoring of winding temperature. Above a critical temperature, PTCs enable the main contactor to isolate the motor. The motor needs time to cool down before the PTCs reset. ∙ Under-voltage protection has two forms—low voltage and no voltage. No-volt protection is inbuilt when using contactors. Low voltages are countered with slow-release relays. These do not release immediately for momentary dips in voltage. ∙ Single-phasing protection can be achieved with three thermal overloads—one in each phase. ∙ Electronic overloads are available that can provide all the normal protection features plus device-net and ethernet connections. ∙ Direct-current motor protection is similar to that of a.c. machines with some additional features. Loads need to be protected against over-voltages from faulty generating supplies or accessories. ∙ Direct-current motor shunt-field currents need to be monitored against field failure that results in excess armature currents and motor runaway. ∙ Shunt fields on larger motors need some form of discharge protection against the high induced voltages generated when the magnetic field collapses. ∙ If use is made of the torque produced by a higher supply voltage, overheating problems can occur. ∙ Common causes of overheating in motors are inadequate or restricted ventilation and overloading. ∙ An increase in temperature that is over the rated value will cause a reduction in the life of the insulation on the motor’s windings. ∙ A variation in the supply frequency to a motor will cause changes to speed, power factor, efficiency and torque. ∙ AS/NZS 1359.41 specifies the required capability of motors to handle short-duration overloads. ∙ The heating effect in a motor is related to the square of the current and the time it is flowing, so any excess current will result in a temperature rise. The amount of heat generated by short-duration overloads is small and can be dissipated by the normal cooling process, but long periods of overload can result in excessive temperature rises. ∙ When a motor stalls, it draws full starting current, so a large amount of heat is generated in a short period of time. ∙ With repetitive starting, the motor does not have enough time for the cooling system to dissipate the heat generated, so the temperature of the motor rises. ∙ Excessive heat is generated when a motor is repeatedly reversed or plug-braked. 378

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Alternating current rotating machines  Chapter 6 ∙ Motors are designed to withstand normal operating conditions. Therefore, abnormal conditions such as exposure to corrosive fumes, explosive vapours, dust, steam, salt air or high humidity need special consideration. ∙ A common fault with single-phase motors is a faulty centrifugal switch. These can seize in the open or closed position. ∙ If the centrifugal switch remains open, the motor will not produce a rotating field so it will not start. In this condition, the running winding will draw excessive current and, as cooling is not produced, the motor will most likely be permanently damaged. ∙ If the centrifugal switch remains closed, it will continue to draw current when running and most likely be permanently damaged by over-temperature.

6.8 Three-phase synchronous machines—operating principles and construction 6.8.1 Introduction When an alternator is driven at a constant speed, it produces an alternating voltage at a fixed frequency, depending on the number of poles in the machine. A machine designed to be connected to the supply and run at synchronous speed is called a ‘synchronous machine’. The description applies to both motors and generators. A synchronous condenser is a special application of a synchronous motor. While the synchronous motor has only one generally used name, the synchronous generator is also referred to as an ‘alternator’ or as an ‘a.c. generator’. The term ‘alternator’ has been used in previous chapters and will be used in this chapter, but it should be remembered that other terms are in use. In general, the principles of construction and operation for alternators and synchronous motors are similar. While alternators were once seldom seen outside power houses and whole communities were supplied from a central source, there is now an expanding market for smaller-sized alternators suitable for the provision of power for portable tools. With the high level of computer usage, there is a further need for standby generating plants to ensure a continuity of supply and prevent loss of data from computer memories. So much information is now being stored in computers that even brief interruptions to their power supplies can have serious consequences for the accuracy and extent of the information stored.

6.8.2  Three-phase alternator construction The three-phase synchronous machine has two main windings:

1. a three-phase a.c. winding 2. another winding carrying d.c.

In most cases, the rotor has the d.c. winding and the stator has the a.c. winding. An alternator with a rotating a.c. winding and a stationary d.c. winding, while suitable for smaller outputs, is not satisfactory for the larger outputs required at power stations. With these machines, the output can be in megawatts, a value too large to be handled with brushes and slip-rings. Because the terminal voltages range up to 33 kV, the only satisfactory construction is to have the a.c. windings stationary and to supply the rotor with d.c. This arrangement has the following advantages:

1. 2. 3. 4. 5. 6.

extra winding space available for the a.c. windings easier to insulate for higher voltages simple, strong rotor construction lower voltages and currents in the rotating windings high current windings have solid connections to the ‘outside’ circuit is better suited to the higher speeds (and smaller number of poles) of turbine drives. 379

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Electrical Principles

6.8.3 Stator

Figure 6.63  Stator for a three-phase induction motor

The stator of the three-phase synchronous machine consists of a slotted laminated core into which the stator winding is fitted. The stator winding consists of three separate windings physically displaced from each other by 120°E. Each phase winding has a number of coils connected in series to form a definite number of magnetic poles. A four-pole machine, for example, has four groups of coils per phase or four-pole phase groups. The ends of the three-phase windings are connected in either the star or delta configuration to the external circuit. The phase windings for a three-phase machine consist of three identical windings symmetrically distributed around the stator. A typical three-phase stator is shown in Figure 6.63.

6.8.4 Rotor The alternator rotor can be of two types—low speed and high speed.

Low speed (salient pole)

(a)

(b)

Figure 6.64  Main types of alternator rotors: (a) low speed (b) high speed

This type usually consists of a ‘spider’ similar to that used in d.c. machines, on which the field poles and the field coils are bolted (see Figure 6.64(a)). As the peripheral forces produced on the circumference of the rotor would be excessive at high speed, physical constraints limit the use of this type of rotor to low-speed machines.

High speed (cylindrical) The cylindrical rotor was developed to meet the needs of higher-speed prime movers. To counteract centrifugal forces, its diameter must be small compared with its length (see Figure 6.64(b)).

6.8.5  Parallel operation of alternators Most commercial power stations are designed to have a number of alternators operating in parallel, supplying a common load at constant voltage. As an alternator’s efficiency is at its maximum near its full-load capacity, it is more economical to have each machine delivering its approximate rated output. During the early hours of the morning, for example, when there is a light load, it might be necessary to have only one machine connected to the line, delivering its rated output. As the load varies during a 24-hour period, the number of machines connected in parallel is determined.

EXAMPLE 6.6 A three-phase 415 V 50 Hz alternator is rated at 150 kVA at 0.8 power factor. Calculate the: (a) power loading in kilowatts when fully loaded with power factor values of 0.8 and 0.6 (b) full load current of the alternator. 380

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(a) The machine is rated at 150 kVA and 0.8 power factor, so at this load: power output = 150 × 0.8 ​​    ​  ​   ​​​   = 120 kW At 0.6 power factor: power output = 150 × 0.6 ​​    ​  ​   ​​​   = 90 kW (b) In both cases, the current flowing will be the full-load current value, which should not be exceeded because of cooling problems within the windings. At 0.8 power factor: P = √3 V I cos Φ P ∴ I = __________ ​       ​ √3 V cos Φ ​​    ​       ​   ​​ ​​ ​ 120 000 ____________ ​ = ​       ​ √3 × 415 × 0.8 ​ = 208 A This is the full-load current rating for each phase winding of this particular alternator and it applies irrespective of the load power or power factor.

6.8.6 Synchronising Before a three-phase alternator can be connected in parallel with another three-phase supply, the following conditions must be fulfilled: 1. The output waveform of each supply must be identical. This is determined by the design features of the alternators. It is standard practice to generate a sinusoidal waveform supply. 2. The phase sequence or rotation of each supply must be the same. This ensures that the EMFs of each supply reach their maximum values in the same sequence—for example: R, W, B. The phase sequence is determined by the method of connection of the alternator phase windings to the terminals of the machine. This check is carried out during the commissioning process after the initial installation or following a major maintenance overhaul, and it is not necessary to do it each time the machine is connected in parallel with others. 3. The alternator and supply voltages must be the same. 4. The alternator and supply voltages must also be in phase. 5. The alternator and supply frequencies must be identical. The last three conditions can be adjusted by the operator. The voltage of the incoming alternator is adjusted by varying the field excitation, and the frequency is determined by the speed of the prime mover. To ensure that the alternator and supply voltages are in phase with each other before connecting them in parallel to the load, some method of indicating the phase relationship is required. Smaller-sized alternators can be synchronised with lamps, but for larger machines a more exact method is required.

6.8.7  Load sharing between alternators in parallel To examine the operation of alternators in parallel, it is helpful to consider three typical applications of an alternator. These are an alternator operating on its own, an alternator operating in parallel with an alternator of the same size and an alternator operating in parallel with a distribution grid. 381

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Electrical Principles

An alternator operating on its own Load

Alternator

Figure 6.65  An alternator operating alone

Load

Alternator 1

When an alternator is operating independently, the frequency and output voltage can be adjusted by adjusting the set points on the governor and the field current regulator (see Figure 6.65). Adjusting the governor’s set points adjusts the speed of the prime mover and, consequently, the frequency of the output. Adjusting the field current will change the output voltage. If the load connected to the alternator increases, the governor on the prime mover will open to increase the input power at the same frequency and the automatic voltage regulator will increase the field current to maintain a constant output voltage.

An alternator operating in parallel with an alternator of the same size

The main reasons for connecting two alternators in parallel are either to share any given load between them or to shift the load to the incoming machine Alternator 2 without causing an interruption to the supply. The incoming machine, when first synchronised, should Figure 6.66  An alternator operating in parallel with another have no load on it and might even be drawing power alternator of the same size from the supply lines. It is then necessary to adjust the controls of the incoming machine until it is delivering its appropriate share of the load to the supply lines. However, when two alternators of the same size are connected in parallel to a common system load, a change to the controls of one will affect the operation of the other (see Figure 6.66). As they are connected together and to the system load, the alternators will always have the same voltage and frequency. To increase the load taken by an alternator running in parallel, it is necessary to increase the set points on the governor. However, changing the governor set point on one alternator only will cause that machine to speed up and change the system frequency. To adjust the power sharing between the two alternators, the governor set point on one alternator is increased and, at the same time, the governor set point on the other alternator is decreased. The machine whose governor’s set point was increased will assume more of the load. To change the system frequency without changing the power sharing between the two alternators, the governor set points on both must be adjusted up or down simultaneously. Where a field-current adjustment controlled the output voltage of a single alternator, it will control the power factor of the load connected to each alternator when they are connected in parallel. If the field currents of both alternators are increased or decreased simultaneously, the system voltage will alter. To adjust the power factor of the load supplied by each alternator, increase the field current on one alternator and simultaneously decrease the field current on the other alternator. The power factor of the alternator whose field current was increased will lag by a greater angle.

An alternator operating in parallel with a distribution grid When an alternator is connected to a large transmission system, the operator of the alternator will have little effect on the voltage or frequency of the system. Consider the case of a single alternator connected to the Australian East Coast grid. The grid is so large that any adjustments to the controls of the alternator will not cause a change in the grid voltage or frequency. 382

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A large grid system is sometimes referred to as an ‘infinite bus’. This power system is so large that, no matter how much power is supplied to or taken from it, its voltage and frequency do not alter. So when an alternator is connected to a large grid, the frequency and terminal voltage of the alternator are controlled by that grid. This is demonstrated in Figure 6.67. To change the power supplied by a single alternator connected to the grid, the set point on the governor of the alternator is altered. In a similar manner, the field current regulator in the alternator controls the power factor of the load taken by that alternator.

Grid

Load

Alternator

Figure 6.67  An alternator operating in parallel with the grid

6.8.8  Hunting in alternators

Damper

The driving torque and speed of a piston engine are winding not absolutely constant during a complete revolution but vary according to the position and speed of the pistons. This causes minute variations in the speed of the alternator shaft. The speed variations are small but cause momentary increases and decreases above and below the average rotational speed. The effect is called ‘hunting’ and leads to small voltage Salient variations, which can include harmonics that will pole distort the waveform. It is partially neutralised by the inertia of the rotating parts. Remedies for hunting involve the use of quite heavy flywheels and special windings in the pole faces. These are called ‘amortisseur’ or ‘damper’ windings (see Figure 6.68). The voltage pulses created by hunting can cause circulating currents to flow between alternators connected in parallel, resulting in an increase in Figure 6.68  Amortisseur windings for an alternator the mechanical oscillations of the rotating parts. Electrical losses are also increased. High-speed turbines are not affected to the same extent by hunting. The major causes of oscillation about a fixed point are the minor adjustments of the governors as load changes on the machine occur.

6.8.9  Three-phase synchronous motors A three-phase synchronous motor has no starting torque. It has to be brought up to speed (or as close to it as possible) by some other means so that it can pull itself into synchronism. Once up to speed, the rotor field can be excited with direct current and the rotor is, in effect, then dragged around at the same speed as the threephase stator field. Its speed is synchronised with that of the stator field. This is markedly different in principle from the induction motor, where the rotating field of the stator is pushing against the induced rotor field. That causes the rotor to rotate, but with some slip, whereas in the synchronous motor there cannot be slip, merely a ‘hanging back’ due to the load imposed on the machine. This is illustrated in Figure  6.69 and shows as a torque angle. If the load becomes too great for a synchronous motor, it immediately pulls out of synchronism and stops. 383

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Electrical Principles

Torque angle

Rotation of stator and rotor field poles at synchronous speed

α N

N Stator

S

S

Rotor

(a) No load

(b) Loaded

Figure 6.69  Relative position of stator and rotor magnetic fields

6.8.10 Construction Stator The stator has a three-phase winding and is of the same type as that in an alternator or induction motor. When this winding is energised with a.c., it produces a magnetic flux that rotates at the synchronous speed. It is the same speed at which the synchronous machine would have to be driven to generate an a.c. voltage at line frequency. The speed of the rotating magnetic field can be derived from the same formula used for alternators in Section 6.9.4: 120 f ​n = _____ ​   ​​     p

Rotor Although of similar construction to the alternator rotor, it is usually made with salient poles. When excited with d.c., it produces alternate north and south magnetic poles, which are attracted to those produced in the stator.

6.8.11  Operating principle A synchronous motor works on the principle of magnetic attraction between two magnetic fields of opposite polarity; one is the rotating magnetic field of the stator and the other is the magnetic field of the rotor. A synchronous motor has torque only at synchronous speed, so special steps have to be taken to get the motor up to speed and synchronised with the supply. The two magnetic fields are then rotating at the same speed and lock in with each other. 384

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VR

Vg V

Vg

VR

Vg α

I Φ (a) No load

(b) Light load

V

α

V Φ

I

(c) Heavier load

Figure 6.70  Effect of load on the line current with constant excitation

6.8.12  Effect of load on a synchronous motor When a synchronous motor runs on no load, the relative positions of stator and rotor poles coincide (see Figure 6.70(a)). When a load is applied, the rotor must still continue to rotate at synchronous speed but, owing to the retarding action of the load, the rotor pole lags behind the stator pole. Their relative positions are displaced by what is called the ‘torque’ or ‘load’ angle (see Figure 6.70(b)). The greater the load applied, the greater the torque angle. The magnetic coupling between each stator and rotor pole distorts according to the load applied. If the load on the motor becomes excessive, the magnetic coupling breaks and the rotor slows down until it stops. When the motor is rotating at synchronous speed, with a fixed d.c. excitation in the rotor windings, the rotor flux cuts the stator windings, inducing a voltage in each phase winding. By Lenz’s Law, this voltage opposes the applied voltage. The phase relationship between this induced voltage and the applied voltage depends on the relative positions of each stator and rotor pole, which in turn depend on the load applied to the motor. Using the example of an ideal synchronous motor with no losses, the operation on no load can be examined. Neglecting motor losses, on no load the torque angle is zero, and so the induced voltage Vg and the applied voltage V are equal and opposite. The resultant voltage VR across the windings is zero, and so the current drawn from the supply is also zero. This is illustrated by the phasors in Figure 6.70(a). (In a real motor, there will be a small no-load current to supply the losses.) When a light load is applied to the motor, the torque angle increases and the induced voltage Vg in the stator windings is now (180 − α)° E out of phase with the applied voltage V (see Figure 6.70(b)). These two voltages combine to produce an effective voltage VR across the stator windings, which is sufficient to draw a current I from the supply. Because of the relatively high inductance of the stator windings, the line current I in each winding lags each resultant voltage VR by nearly 90°E. This causes the line current I to lag the applied voltage by Φ. As the load is increased, so is the torque angle. This causes an increase in the resultant voltage VR across each stator winding (see Figure 6.70(c)). Due to the increase in the value of VR, the line current I increases and the phase angle Φ between the applied voltage V and the line current I also increases. Therefore for fixed excitation, any increase in the load on a synchronous motor will cause an increase in the line current, at a lower power factor.

6.8.13  Effect of varying field excitation If the load applied to a synchronous motor is constant, the power input to the motor is also constant. When the rotor field excitation is varied, the induced voltage in each stator winding is also altered. The phasor diagram in Figure 6.71(a) represents the conditions for a given load at unity power factor. The power input per phase is VI1. If the rotor field excitation is decreased, the induced voltage Vg decreases (see Figure 6.71(b)). This causes the line current I2 to lag the applied voltage V by Φ2. Since the load—and hence the power input—is constant, the power component of I2 must remain the same as I1 in Figure 6.71(a). The line current I2 must increase to accommodate the lagging power factor. Therefore, a reduction in the d.c. field excitation causes an increase in line current and a lagging power factor. If the d.c. excitation is increased, the induced voltage Vg increases (see Figure  6.71(c)). The line current I3 will therefore lead the applied voltage V by Φ3. It will also be greater than I1 in Figure 6.71(a) because the power 385

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Electrical Principles

Vg

VR

Damper winding I1

α

V

(a) Unity power factor

VR

Vg α

(b) Lagging power factor Vg

Salient pole

V

Φ2 I2

VR

I3 α

Φ3

(c) Leading power factor

Figure 6.71  Effect of varying the d.c. excitation

V

Figure 6.72  Salient pole with amortisseur windings

component is the same, owing to the load remaining constant. Therefore, an increase in d.c. excitation causes an increase in line current, and a leading power factor. It can be seen that if the excitation of a synchronous motor on a constant load is varied from a low to a higher value, then:

1. the stator current gradually decreases, reaches a minimum and then increases again 2. the power factor, which lags at first, gradually increases, becomes unity when the stator current is a minimum and then decreases again but becomes leading.

Care should be taken when adjusting the excitation of a synchronous motor. There are limits to which it can safely be taken. Over-excitation and under-excitation can cause a synchronous motor to become unstable. Once these limits have been exceeded, the power produced by the motor decreases and the danger of overloading becomes imminent as the machine exceeds its design limits. The most obvious situation is one of under-excitation where the magnetic bond between the rotating field and the rotor is so weakened that the load exceeds the pull-out torque of the motor and it drops out of synchronism. Overexcitation creates a situation where the line current and mechanical load exceed the full-load rating of the machine and the magnetic bond becomes so stiff that changes in load place undue mechanical stresses on the motor shaft.

6.8.14  Hunting in synchronous motors A change in the load on a synchronous motor causes a change in the value of the torque angle (see Figure 6.69). In general, the inertia of the rotor prevents an instant change to the new conditions, with the result that the rotor shifts past the point of equilibrium and then has to correct itself. While the rotor and the rotating field in the stator are still rotating at a synchronous average speed, the change in load on the rotor causes this periodic swing around the point of equilibrium. This hunting or surging causes an undesirable fluctuation in line current to the motor. The usual method for damping these surges is to use an amortisseur winding. It consists of copper bars embedded in the pole faces of the rotor and shorted out at each end (see Figure 6.72). Any surging causes an induced voltage in the copper bars. This results in a magnetic field being created and opposing the surging effect. Often the shorting-out bars are extended around the rotor, resulting in a squirrel cage-type rotor winding about the salient poles. While damping any tendency of the rotor to hunt, they can also assist the motor in starting by acting as sections of a squirrel cage winding. In effect, this winding enables the motor to be started as an induction motor. 386

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6.8.15  Applications of synchronous motors Power factor correction The characteristic of being able to adjust the power factor of a synchronous motor while it is running can be put to beneficial use in industry as a means of correcting the power factor of the loads supplied from the plant’s mains. The synchronous motor can be run unloaded, but more often it is used to drive some item of equipment necessary for the operation of the plant—for example, air or hydraulic compressors, high-frequency alternators, large fans and blowers or high-pressure water supplies. An added advantage can be an economic incentive offered by distribution entities for ensuring a certain minimum-value power factor in an installation. For example, the charge per kWh may be reduced if the power factor does not drop below 0.75 (or some similar figure). Where large amounts of power are being distributed and power factor correction is needed, specially designed synchronous motors are run without any load connected. Under these circumstances, the over-excited synchronous motor is called a ‘synchronous capacitor’ or ‘condenser’.

Voltage control An important application of synchronous motors is in the control of voltage for transmission lines. Synchronous motors are installed at suitable positions along the line and their excitation adjusted as desired to cause them to draw lagging or leading currents in order to raise or lower the voltage. When synchronous motors are installed under these conditions, there is greater stability of the voltage on the transmission line.

Low-speed drives A synchronous motor has good efficiency, and at low speeds its high initial cost is adequately compensated for by the comparatively lower running cost. At low speeds, the induction motor has a decreasing efficiency, whereas the synchronous motor retains its high efficiency.

Rock- and ore-crushing heads This application requires a crushing head that moves slowly and has a very heavy rotating flywheel to provide kinetic energy as sudden shock loads are placed upon the crushing head.

6.8.16  Starting methods of synchronous motors Auxiliary motors Some synchronous motors are equipped with a special motor designed for use only during the starting period. The auxiliary motor runs the synchronous motor up to speed, at which stage it is first synchronised and then connected to the supply. It is an expensive method, particularly if high starting torques are required.

Induction motor starting In this method, a reduced line voltage is applied to the stator windings and the d.c. winding on the rotor is short-circuited. With the aid of the amortisseur windings, the complete machine behaves as an induction motor as it accelerates up to a speed slightly below synchronism. At an appropriate time, the short is removed from the rotor winding, d.c. is applied to the rotor winding and the full line voltage is applied to the stator winding. As the speed is only slightly less than synchronous speed, the rotor field can lock in with the stator field and accelerate to synchronism.

6.8.17  Single-phase synchronous motors The primary purpose of single-phase synchronous motors is to meet constant speed requirements, even though they have very low efficiency. Their use is usually limited to operations where speed is critical and torque requirements are low. Small synchronous motors are built in a variety of types and constructional details, but are almost invariably one of the two types described below. 387

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Electrical Principles

6.8.18  Reluctance motors The stator winding of the reluctance motor is similar to that of the split-phase or capacitor-start motor, and the windings are of the usual squirrel cage type. The rotor, however, is assembled from laminations from which a number of teeth are cut to form definite salient poles. This can be seen in Figure  6.73(b), where the slots in the rotor lamination will still (a) (b) contain the normal parts of a squirrel cage winding. Cross-section of a Cross-section of the rotor The gaps or slots cut in the rotor will often be of reluctance motor showing of a reluctance motor showing unequal sizes to assist the starting function. The stator and rotor both the gaps and the holes for the squirrel cage bars number of poles in the stator is not necessarily equal to the number of poles on the rotor. Figure 6.73  Internal configuration of a reluctance motor The motor starts as an induction motor and the starting winding is open-circuited by the centrifugal switch at approximately 75% synchronous speed. Because the load applied to this type of motor is comparatively light, there is small slip. The salient rotor poles tend to become magnetised by the stator poles and become locked together. The stator poles are changing at twice the supply frequency. The rotor is attracted by the stator poles during the periods of the cycle when they are fully magnetised. During the period when the stator flux is low, the inertia of the rotor carries it past the position of one stator pole and it is then attracted by the next stator pole during the build-up of the stator flux. Each rotor pole therefore travels through the space of two stator poles per cycle of supply frequency. The reluctance motor starts as an induction motor, locks into synchronism and continues to run at a constant synchronous speed. If the number of salient poles on the rotor is some multiple of the stator poles, the motor will operate at a constant speed, which is a submultiple of the synchronous speed. This is called a ‘subsynchronous reluctance motor’.

6.8.19  Hysteresis motors In the hysteresis motor, the rotor is constructed from a specially hardened steel cylinder instead of the normal thin laminations. It is supported on a non-magnetic form called an ‘arbor’ and has substantial hysteresis losses. The effect of hysteresis is thereby increased and opposes any change in magnetic polarities of the rotor once they are established. The rotor poles lock into the stator poles of the opposite polarities. The details of the rotor are shown in Figure 6.74. Normally, a synchronous motor has no starting torque and is therefore not self-starting without additional means. One method of providing movement for the rotor is to use the shaded pole principle. The movement of the stator flux across the pole face pulls the rotor along with it. Because the stator and rotor fluxes are magnetically locked together, the rotor runs at a synchronous speed determined by the number of stator poles and the supply frequency.

Hysteresis ring

Bearings

Non-magnetic arbor

Mild steel shaft

Figure 6.74  Rotor arrangements for a hysteresis motor

6.8.20  Applications for singlephase synchronous motors Typical uses of single-phase synchronous motors are in wireless and radio communication installations, recording devices, electric clocks and synchronous servo-systems. A further use is in the aircraft industry, where a.c. frequencies are normally around 400 Hz, although they can be much higher.

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As a rule of thumb, the size of a.c. equipment operating at 400 Hz is reduced (400/50)2 times when compared with the usual powerline frequencies; that is, the amount of iron in the core is reduced approximately 64 times. This results in a major reduction in size and weight. Typical applications are in gyro-compasses and other aircraft instrumentation.

6.9  Alternators and generators 6.9.1  Standby power supplies Standby power supplies are generally intended to provide mains power at a specified voltage and frequency. There are two main forms of standby power-supply units. The first type of unit (uninterruptible) is meant for use where no interruption to a power supply can be tolerated— for example, to computer, hospital and aircraft navigation equipment. Losing power at a crucial moment in an operation could mean loss of life, or in the middle of a computer calculation could mean the loss of valuable data. There is also an increasing use of this type of power supply for portable work because it can often be run from a 12 V vehicle battery. It is quick, convenient and quiet. The second type of standby unit is where momentary losses of power can be tolerated. Such uses would include emergency lighting, theatres and industrial uses such as fully environmental meat-chicken sheds. Delays of several seconds in restoring power can be acceptable in some circumstances. This type of standby power supply would also be suitable for lifts and high-rise buildings. A subsection of this latter category includes portable power supplies such as small generating plants that can be carried from job to job in a vehicle.

6.9.2  Uninterruptible power supplies (UPS) A block diagram of a UPS is shown in Figure 6.75. It can be seen that the unit runs off the mains supply with a battery permanently ‘floating’ on charge from an inbuilt battery charger. Effectively, the battery bank is supplying an inverter, which converts d.c. to a.c. at mains voltage and frequency. In the event of losing mains power, the unit continues to operate as long as the battery has sufficient charge. More critical loads usually have an engine-driven alternator on standby to ensure that the battery charge is maintained. The battery capacity has to be great enough to supply the circuit power while the alternator and engine are being started and run up to speed. Extra operating time allowances have to be made for non-starting incidents with the engine and also to provide greater flexibility as a back-up in an emergency. When using a vehicle battery, the d.c. values will be high, so care must be taken to ensure that the battery does not go flat. For example, a 500 W television set draws about 20 A on 32 V d.c. The current drain would easily exceed 50 A on 12 V.

a.c.

Mains supply

Changeover contactor

a.c.

Charger

d.c.

Battery

d.c.

Inverter

a.c.

Load

a.c.

Monitor

Standby alternator

Figure 6.75  Block diagram of an uninterruptible power supply (UPS) with back-up

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Electrical Principles

6.9.3  Engine-driven alternators A large range of engine-driven alternators is available, so a choice has to be made on the basis of several factors. Choices range from buying a small portable unit at the best possible price to carefully planning for the most suitable unit for a particular purpose. It is not simply a matter of selecting an alternator with respect to the load it has to supply; the choice should take into account many other considerations. Some of these factors are listed below and their order of importance is governed by the actual intended use for the alternator. Figure 6.76 shows the essential components of standby power supply using an engine-driven alternator.

Purchase price The overall cost of smaller units may be lower, but in terms of cost per kVA they are more expensive and operate at lower efficiencies. As the size of the unit increases, the cost per kVA reduces, while the operating efficiency increases.

Type of prime mover The economy of the prime mover in terms of efficiency has a bearing on its selection. This in turn is affected by the type of service it will encounter. For example, a steam turbine has good economy throughout its entire load range. However, it is expensive, large and needs a long time to get the unit on load from cold. An internal combustion engine has poor efficiency at light loads but is much cheaper Mains Changeover Load to buy initially. For some loads it is cheaper to supply contactor buy several smaller alternators than one large unit. Problems of paralleling the units must then be considered. Standby Monitor The cost and availability of fuel must alternator always be a consideration. While distillate is more expensive initially, as is the diesel engine itself, the fuel cost per hour is less, Figure 6.76  Block diagram for an engine-driven standby alternator while maintenance costs are far higher than those for a petrol engine. The petrol engine is cheaper to buy, the fuel is readily available and the prime mover is suited to smaller units used purely for portable power supplies on intermittent duties. In the long term, the diesel engine runs better on full loads than the petrol engine. The petrol engine is more tolerant of dirty fuel than the diesel engine and does not need specialised skills for maintenance purposes. Figure 6.77 shows a portable generating unit driven by a singlecylinder petrol engine. Two 15 A outlets are available for connection of equipment.

Starting methods

Figure 6.77  Self-contained portable power supply. The alternator, rated at 5.5 kVA, is driven by a petrol engine. The size and weight of the unit is such that it can be moved to any site where power is required

Starting methods are governed by the intended use of the generating unit. The quicker the changeover to auxiliary power, the more expensive is the starting method. The cheapest method involves merely

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starting the unit manually when it is evident that the main power supply has failed. A more expensive method involves the use of an automatic changeover contactor that drops out when the main supply fails. In turn, this connects a starting motor to the engine and, when the alternator is up to speed, connects it to the load.

Load sizes and alternator capacities Smaller generating plants are usually intended for standby purposes for short periods. They usually have only one load connected to them at a time, such as a portable tool or a small lighting load. With middle- and larger-sized alternators, consideration has to be given to the possible connection of intermittent larger loads, such as the starting currents of motors. The unit then has to have the electrical capacity and engine power to maintain both the output voltage and the frequency during these current surges to avoid interruptions to other equipment connected to the same supply.

Operation of alternators With the exception of some manually operated equipment, most standby and back-up alternator operations are now beyond the control of the operator. Where some degree of manipulation is available, there are two important factors that should always be considered—voltage and frequency. In most cases, the voltage is governed by automatic voltage regulators while the frequency is controlled by the engine governor. The order of operation is to set the speed first, which in turn sets the frequency, and then adjust the voltage of the unit. To do this in the reverse order is to alter the voltage each time the speed is altered. A study of the output voltage formula will confirm the soundness of this method. ​​V​  g​​ = 4.44 Φf n ​k​  d​​ ​k​  p​​​ In an operating alternator, the above formula can be reduced to the following: ​​V​  g​​ = k Φ f​ where k is a constant consisting of all the components of the formula that cannot be altered in an operating alternator. The flux value is altered by changing the d.c. excitation and the frequency is altered by changing the set point on the engine governor.

6.9.4  Prime movers Low speed Most diesel engines used as prime movers for driving alternators operate within the range 500–1000 rpm and this necessitates the use of rotors with many pairs of poles. Hydroelectric turbines have water-driven impellers that operate at low speeds, and consequently they also drive rotors with many poles. While the diesel-driven alternator usually has its shaft in the horizontal plane, the hydroelectric unit has its shaft in the vertical plane. This method of construction means that special thrust bearings have to be fitted to take the end thrust of the rotating component.

High speed Turbine prime movers, whether steam or gas, operate efficiently at speeds of about 3000 rpm. An alternator driven by a turbine and producing a frequency of 50 Hz at 3000 rpm must consist of only two poles. The relationship between speed, frequency and the number of poles can be determined from: n p ​f = ____ ​    ​​  120 391

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Electrical Principles

by transposition: 120 f ​n = _____ ​   ​​     p where:





n = rpm f = frequency in hertz p = number of poles

For a large-diameter rotor of 24 poles at 50 Hz: 120 × 50 n = ________ ​       ​ ​​ ​  ​  ​ 24  ​​    = 250 rpm For a turbine-type rotor of two poles at 50 Hz: 120 × 50      ​ n = ________ ​  ​​​ ​​ ​  ​    2   = 3000 rpm

EXAMPLE 6.7 At what speed would the governor of a 12-pole diesel-driven alternator have to be set to enable a frequency of 60 Hz to be generated? 120 f n = _____ ​   ​     p ​​    ​  ​  120 × 60 ​  ​​​ n = ________ ​   ​     12   = 600 rpm

An alternator in the speed range given in Example 6.7 will have a large diameter and a comparatively short axial length. With turbines, the extra expense and auxiliary machinery needed restricts their use to larger sizes. Higher outputs mean that the length of the alternator must be increased, and the increase in length causes complications in cooling. A typical standby motor-driven alternator is shown in Figure 6.78. This type of alternator is used as a back-up in the event of a power failure.

6.9.5  Alternator cooling Low speed With engine-driven or hydroelectric alternators, there is no great difficulty in providing adequate ventilation because of the characteristically large diameter and short axial length. In addition to the large surface area available for direct radiation of heat, there is a fanning action due to the rotation of the fields, an action that can be increased by the addition of fan blades if necessary. 392

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Alternating current rotating machines  Chapter 6

When the axial length is short, the heat developed in the embedded windings is quickly conducted to the ends where it can be dissipated by the fanning action. As the machine size becomes larger, it is often necessary to provide ventilation ducts within the core to provide paths through which the cooling air can flow.

High speed The provision of adequate cooling facilities is a problem in high-speed machines of large capacity, if the operating temperature of the windings is to be kept within safe limits. The surface area available for cooling in a high-speed machine is less than that in a Figure 6.78  Skid-mounted generating unit low-speed machine of the same capacity. The diameter of the rotor must be small enough to keep the surface speed down to a safe value, so for large capacities the length of the machine must be considerable. This long axial length causes difficulty in cooling the central portion of the core because the heat generated cannot be conducted away quickly enough to limit the temperature rise in the core to a value that will protect the windings and the insulation. These considerations gave rise to the necessity of completely enclosing the alternator and allowing the use of forced ventilation to carry away the heat produced. Where cooling air is used, it must be filtered to keep it clean and sometimes washed by passing it through a spray chamber to prevent a build-up of dust within the machine. Washing the air has the added advantage of cooling it, further reducing the temperature of the alternator, allowing the rating of the machine to be increased. To increase alternator ratings still more, hydrogen gas is used instead of air because of its greater ability to absorb heat. The machine is completely enclosed and the hydrogen is blown through the alternator and then through a heat exchanger before being cycled through the alternator again. The total exclusion of air from the fully-sealed machine is necessary to prevent an explosive air/hydrogen mixture from forming. Considerable care is taken to ensure the purity of the hydrogen gas. The oil pressure for the bearings is at a higher value than the pressure of the hydrogen being pumped through the machine. This ensures that the oil flow through the seal is towards the hydrogen gas so that it is retained in the machine. The oil may then be passed through a vacuum process to remove any hydrogen gas or air before being reused in the machine. These cooling methods require considerable power and auxiliary equipment, so the output from the alternator must be increased by an appreciable amount for the method to be economically feasible. Accordingly, it is used only on very large capacity machines.

6.9.6 Excitation The usual method for d.c. excitation of the rotor windings is for each machine to have its own d.c. generator called an ‘exciter’. The exciter can be belt driven or geared down from the synchronous machine, but the usual practice is for the exciter to be directly coupled to the rotor shaft. The exciter armature rotates within the influence of the exciter field, causing a d.c. voltage to be generated in the armature. The exciter output is fed into the field windings of the synchronous machine. By adjusting the rheostat in the exciter field circuit, the strength of the magnetic field in the rotor can be varied. The basic diagram of an alternator and its exciter is shown in Figure 6.79. With very large alternators, the d.c. excitation requirements are substantial. This means that the d.c. generators have to be large also—so large that they might not be able to self-excite. Because of this, the d.c. generator might need an exciter of its own, one that is able to self-excite and provide power for the field of the main generator, which in turn supplies the rotor field of the alternator. 393

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Electrical Principles

Exciter

Exciter field

Alternator

G

Brush gear and sliprings

Stator windings

Rotor field

Figure 6.79  Basic alternator circuit Exciter field

Exciter rotor

Rectifier

Rotor field

Alternator stator Output

All within dashed box rotates

Voltage regulator

Figure 6.80  Brushless excitation

Some alternators use a brushless excitation system in which the exciter armature has been replaced by a small threephase alternator that rotates within the influence of a small residual magnetic field. This causes a small three-phase voltage to be generated in the exciter. When converted to d.c. by an internal rectifier, it supplies the main field of the alternator, resulting in an a.c. output voltage. A sensor unit connected to the output of the machine monitors the output voltage and load current of the alternator and sends electrical signals to a controlled rectifier, which in turn controls the strength of the exciter field. The sensor unit and the controlled rectifier are, in a sense, the voltage regulator of the machine. A basic circuit of a brushless generating system is shown in Figure 6.80.

6.9.7  Generated voltage The value of the generated a.c. voltage depends on the strength of the rotor flux and the speed at which it cuts the windings. Because the speed must be constant (and is linked to the frequency required), the sole remaining factor determining the value of the generated voltage is the strength of the rotor flux. For an alternator, the generated voltage is found from: ​​V​  g​​ = 4.44 Φ f N ​k​  d​​ ​k​  p​​​ where:



Vg = generated voltage per phase (RMS) Φ = flaux per pole in webers f = frequency in hertz N = number of turns per phase kd = a constant, dependent on winding distribution kp = a constant, dependent on coil pitch

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Alternating current rotating machines  Chapter 6

EXAMPLE 6.8 Calculate the line voltage of a 50 Hz star-connected alternator, given the following details: 0.67 Wb  Φ = ________ ​   ​      pole ​k​  d​​ = 0.85 ​k​  p​​ = 0.98 36 turns  N = ________ ​   ​      phase ​​               ​       ​  ​  ​ ​  ​ ​ ​​​ ​V​  g​​ = 4.44 Φ f N ​k​  d​​​  k​  p​​ ​ = 4.44 × 0.67 × 50 × 36 × 0.85 × 0.98   = 4460 V then ​V​  L​​ = ​√3 × ​V​  p​​​ ​ = 1.732 × 4460 ​ = 7725 V

6.9.8  Effect of load on alternator voltage

I G 3~

An alternator can be considered to consist of three components in series:

1. an a.c. generating source 2. a resistor—representing iron and copper losses 3. an inductor—representing the inductance of the windings and magnetic leakage.

Any load placed on the alternator must be assumed to be in series with these components (see Figure 6.81). The series impedance of the resistance and inductance provides a drop in voltage before the generated voltage can reach the connected load. Additionally, the load current in the a.c. windings produces an armature reaction, which also affects the output voltage. With a unity power factor load, the armature reaction merely distorts the main field and the effect on voltage is minimal; the voltage drop is mainly due to the series impedance. Figure  6.82(a) shows that the resistive voltage drop IR is in phase with the load current I and the voltage drop due to the reactance IX is at 90°E to the IR drop. These two values combine to form a voltage drop IZ due to the impedance of the alternator windings. The phasor sum of the output voltage and IZ gives the generated voltage Vg. For a load with a lagging power factor, however, the magnetic effect of the stator currents opposes that of the rotor (see Figure  6.82(b)). This results in a weakened rotor field and reduces the output voltage

R

Alternator

Load

Z

L

Figure 6.81  Equivalent circuit of an alternator Vg IZ I

V

IX IR

(a) Unity power factor Vg IZ

IX

V IR I (b) Lagging power factor Vg I

IZ V

IX IR

(c) Leading power factor

Figure 6.82  Phasors for various power factor loads on an alternator

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Electrical Principles

Leading power factor

Output voltage

Unity power factor Lagging power factor

Load current

further than the resistive load alone did. As before, IR is in phase with the load current I. IX is at 90°E to IR, so placing IZ at a different angle from the previous case. In a similar manner, Vg is equal to the phasor sum of the output voltage and IZ. For a load with a leading power factor, the flux caused by the stator currents assists that of the rotor, resulting in an increased output voltage (see Figure 6.82(c)). The characteristics of the three types of loads are shown in Figure 6.83.

Figure 6.83  The effect of power factor on the output voltage of an alternator

6.9.9  Voltage regulation An alternator is required to give a prescribed terminal voltage at full load. The difference in output between no load and full load is a measure of its voltage regulation. The difference is compared with the full-load value in a similar manner to that for d.c. machines. Per cent voltage regulation: V ​ ​  NL​​  − ​V​  FL​​ ​​V​  R​​%  = ​ _________      ​ × 100%​ ​V​  FL​​

EXAMPLE 6.9 A three-phase star-connected alternator has an output voltage of 3300 V at full load, with unity power factor. When the load is removed and the excitation is unchanged, the voltage rises to 3350 V. Find the percentage regulation. ​V​  ​​  − ​V​  FL​​ ​V​  R​​% = _________ ​  NL  ​      × 100% ​V​  FL​​ ​​

3350 − 3300 ​ = ​ __________     ​   × 100% 3300​ ​           ​  ​ ​ ​​

50 × 100 ​ = ​ ________  ​     3300 ​ = 1.5% at unity power factor The regulation must also be referred to the load power factor because at any other power factor these figures would be different.

6.9.10  Alternator ratings An alternator is rated according to three basic factors: 1. frequency 2. voltage 3. current. 396

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Alternating current rotating machines  Chapter 6

The frequency fixes the speed at which the alternator must be driven, the voltage rating sets the designed output voltage and the rated current is the full-load current output. The last two factors help establish the volt-ampere rating, usually expressed in kVA. The alternator rating cannot be given in kilowatts because the power factor of any load placed on the alternator is beyond the control of the manufacturer, and because its value could vary considerably.

Summary 6.8–9 ∙ A synchronous machine rotates at a speed that depends on the line frequency and the number of poles. ∙ Larger machines have a three-phase winding in the stator, while the rotor is excited with direct current. ∙ An alternator is driven mechanically at a suitable speed to enable it to produce alternating current at line frequency. ∙ Low-speed machines have short rotors with many salient poles, while high-speed machines have long cylindrical rotors and few poles. ∙ Cylindrical rotors are more common for high-speed work because of the mechanical forces created. ∙ Prime movers are often engine driven for low-speed machines. ∙ Hydroelectric alternators are commonly low-speed machines with the shaft mounted in the vertical plane. ∙ High-speed machines have high-pressure turbines, which are either steam or gas driven. ∙ Air cooling is used for low-speed synchronous machines. It may be natural flow or forced air cooling with fans. ∙ Cooling of high-speed machines is more complicated because of the long rotors. Forced air cooling is rarely used with very large alternators. ∙ Hydrogen blown through a sealed machine is a cooling method. The hydrogen gas is cooled by passing it through a heat exchanger. ∙ Alternators often have a direct-current generator coupled on the same shaft to provide d.c. for the rotor excitation. In some cases, the exciter is so large that it has its own exciter to provide d.c. for the larger exciter field. ∙ An alternator is rated according to its output voltage and the maximum current flow permitted in its windings. It is a volt-ampere (VA) rating because the manufacturer has no control over the power factor of the load. ∙ When an alternator is operating independently, the frequency can be adjusted by adjusting the set points on the governor; the output voltage can be adjusted by adjusting the field current regulator. ∙ Alternators have series resistance and reactance that leads to a voltage drop on load. This also leads to a problem when being paralleled with another alternator. ∙ Alternators have to satisfy several conditions when being placed in parallel: – identical voltage – identical frequency – same phase rotation – being in phase with each other when finally connected. ∙ Smaller alternators can be synchronised with each other by using lamps connected in series. These can only be used where some degree of error can be tolerated. ∙ There are two types of connections: – three dark lamps – two bright, one dark lamp. ∙ A more exact method is using a synchroscope. The instrument can be portable or built into a control panel. Larger alternators are brought onto load gradually after being synchronised. 397

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Electrical Principles ∙ To adjust the power sharing between two similar alternators, connected in parallel, the governor set point on one alternator is increased and, at the same time, the governor set point on the other alternator is decreased. ∙ To change the system frequency, when two similar alternators are connected in parallel, without changing the power sharing between the two, the governor set points on both alternators must be simultaneously adjusted up or down. ∙ To adjust the power factor of the load supplied by two similar alternators, connected in parallel, simultaneously increase the field current on one alternator and decrease the field current on the other alternator. ∙ To alter the system voltage when two similar alternators are connected in parallel, the field currents of both alternators are increased or decreased simultaneously. ∙ To change the power supplied by a single alternator connected to the grid, the set point on the governor of the alternator is altered. ∙ To change the power factor of the load supplied by a single alternator connected to the grid, the field current regulator on the alternator is adjusted. ∙ Alternators have minor speed variations during rotation. These are known as ‘hunting’. The amount depends on the driving engine and causes ripple or harmonics superimposed on the output voltage. ∙ Compensation for hunting in low-speed engine-driven machines is achieved with heavier-than-normal flywheels and other rotating parts. ∙ In high-speed machines, hunting is usually caused by variations in load and efforts by the governor to compensate for them. ∙ There are two main purposes of standby power supplies: – power supplies where a break in supply cannot be tolerated. Uninterruptible power supplies (UPS) are used. They are usually based on a battery-operated inverter circuit that converts d.c. to a.c. The battery supplies electrical energy until alternative power supplies are operated. – power supplies where a break of short duration can be tolerated. They are basically engine-driven alternators of various sizes and capacities. The units may be of the portable type or fixed in a suitable position, depending on intended use. This category also includes battery-operated inverters that are intended for portable use. Current drain can be heavy for larger units. ∙ A synchronous motor has no starting torque and, if used as a motor, it has to be brought up to synchronous speed mechanically or by adjusting the connections to, and in, the motor to bring it up to speed as an induction motor. ∙ The rotor of a synchronous motor is magnetically locked to the rotating field in the stator and is effectively ‘pulled’ around. ∙ Excessive loads cause the magnetic link to be broken and then the rotor will cease rotating. ∙ Varying the rotor field excitation will affect the power factor of the motor. ∙ Decreasing excitation will cause a lagging power factor. ∙ Increasing excitation will cause a leading power factor. ∙ Excitation has to be kept within specified limits for stability of operation. ∙ Setting excitation values outside this range leads to the possibility of stalling the machine or creating uncontrolled hunting. ∙ Hunting also occurs in synchronous motors. It is mostly caused by fluctuating loads such as reciprocating pumps. ∙ Hunting in both motors and alternators can be reduced by embedding special windings in the pole faces of the rotor. ∙ A synchronous motor is usually started by one of two methods: – using another motor or an engine to get the synchronous motor up to speed. This is seldom used because of cost. – reconnecting the synchronous motor as an induction motor until it gets up to speed and then reconnecting it to provide d.c. to the rotor. This is the most common method. 398

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Alternating current rotating machines  Chapter 6 ∙ Single-phase synchronous motors are generally one of the following two types: – the reluctance motor; like the three-phase types, it is not self-starting. It can be started manually or be provided with a starting winding. The rotor has salient poles machined in it to induce synchronism. – the hysteresis motor also has no starting torque. The rotor is made of a magnetically harder material than a normal induction motor. ∙ Single-phase synchronous motors are inefficient and have low torque. Consequently, they are made only in small sizes where a specific use calls for an exact or constant speed.

Questions Exercises 6.1 Describe how the rotating magnetic field is produced in a three-phase motor. 6.2 Explain why an induction motor always runs at less than synchronous speed. 6.3

What is meant by: (a) the synchronous speed of an induction motor (b) the actual speed of an induction motor (c) the slip speed of an induction motor?

6.4 What is the relationship between these speeds? 6.5 How can the direction of rotation be reversed in an a.c. series motor? 6.6 Describe a method for finding which phase has an earth fault in a three-phase delta-connected motor. 6.7 Describe a procedure for testing an armature with a growler. 6.8 Explain why the power factor of an induction motor increases towards unity as the load increases. 6.9 Briefly describe the construction of: (a) squirrel cage rotors (b) wound-rotor motors. 6.10 What is meant by the term ‘locked rotor torque’? 6.11 What is meant by the term ‘breakdown torque’? 6.12 What is meant by the term ‘split phase’? 6.13 Briefly describe the split-phase method of starting single-phase induction motors. 6.14 Why is a centrifugal switch used in most single-phase induction motors? 6.15 Briefly describe the principle of operation of the capacitor-start, induction-run motor. 6.16 How is the direction of rotation reversed in a split-phase motor? 6.17 Explain the principle of operation of the shaded-pole motor. 6.18 Draw a simple circuit diagram for a permanently-split capacitor motor. Give the typical operating characteristics and list an application for this type of motor. 6.19 List three types of single-phase induction motors and briefly describe the characteristics of each one. 6.20 Give one example of why an overload current could occur in a motor circuit. 6.21 Give one example of why a fault current could occur in a motor circuit. 6.22 Explain how the temperature of a motor increases when it is loaded. 6.23 What is the function of a HRC fuse? 399

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Electrical Principles 6.24 Why must a magnetically operated overload have a delaying device fitted when starting an electric motor? 6.25 Explain the difference between a 20 A type ‘C’ circuit breaker and a 20 A type ‘D’ circuit breaker. 6.26 What is meant by a thermal overload device? Where is it connected into a circuit? 6.27 Why are PTC resistors in a motor control circuit considered to be automatically resetting? 6.28 Explain how electronic overloads sense the value of current. 6.29 State two features that are available on an electronic overload unit. 6.30 What are the constructional differences between low-speed and high-speed alternators? 6.31 Explain why a low-speed synchronous machine has a large salient pole-type rotor. 6.32 What are the types of losses that reduce the efficiency of an electric motor? List all the types of losses and give a means to reduce each.

Calculations 6 .33 Determine the percentage slip for the following three-phase motors: (a) 50 Hz four-pole motor running at 1420 rpm (b) 50 Hz six-pole motor running at 960 rpm (c) 50 Hz eight-pole motor running at 720 rpm. 6 .34 Determine the slip speed of the following three-phase motors: (a) 50 Hz four-pole motor at 4% slip (b) 50 Hz two-pole motor at 6% slip (c) 50 Hz eight-pole motor at 5% slip. 6 .35 The rotor frequency of an unloaded two-pole motor is 0.5 Hz when running on a 50 Hz supply. Calculate: (a) the synchronous speed (b) the actual speed. 6 .36 A six-pole motor runs at 875 rpm on a 50 Hz supply obtained from a diesel-powered alternator. Calculate: (a) the synchronous speed of the motor (b) the slip speed, rotor slip frequency and percentage slip. What would be the synchronous speed of the motor if the frequency was allowed to drift to 55 Hz? 6.37 A two-pole motor is operating at 50 Hz. Determine the synchronous speed of the rotating magnetic field. 6.38 The synchronous speed of a four-pole capacitor-start, induction-run motor is 1500 rpm. Determine the frequency of supply. 6.39 The rotor speed of a 50 Hz capacitor-start, capacitor-run motor is 2800 rpm. How many poles would this motor have? 6.40 Complete the diagram below of a capacitor start motor. Use the figure below in addition to the start capacitor shown in Figure 6.33(a). Run winding

Start winding Centrifugal Switch

a.c. supply

Parts of a split phase motor

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Alternating current rotating machines  Chapter 6 6.41 Complete the diagram below of a capacitor start motor. Run winding

Start winding Centrifugal switch a.c. supply (a) Electrical connections

Parts of a capacitor start motor

6.42 A motor has a winding resistance of 15 Ω at 22°C. After running, the resistance is measured as 18 Ω. What is the temperature of the windings after running? 6.43 How many poles must a synchronous machine have to operate at 250 rpm and a frequency of 50 Hz? 6.44 What supply frequency would be required to run a four-pole synchronous motor at 3300 rpm? 6.45 What step-up gear ratio would be required to drive a 60 Hz four-pole alternator with a 50 Hz four-pole synchronous motor? 6.46 A diesel-driven alternator is governed to 720 rpm. If the alternator has ten poles, what is the frequency of the alternator output? 6.47 Find the power rating of a three-phase 3300 V 100 kVA alternator at power factors of 1.0, 0.8 and 0.65. What is the maximum current of the alternator in each instance? 6.48 A three-phase 415 V 125 kVA alternator supplies its rated load at a power factor of 0.8 lagging. Given that the efficiency of the alternator is 89%, what power is the prime mover required to deliver? 6.49 An 11 kV star–delta distribution transformer has 326 turns on each of its primary windings. Calculate the number of turns required on each secondary winding if the delta-connected secondary output is 6.6 kV. 6.50 An 11 kV step-up distribution transformer is connected in delta–star configuration. The delta-connected primary windings have 566 turns each. Ignoring losses, calculate the number of turns required on the star-connected secondary windings if its line output is 33 kV. Given an output current of 150 A at a power factor of 0.95 leading, calculate: (a) primary line current (b) primary phase current (c) output power being delivered (d) output rating in kVA.

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Develop and connect electrical control circuits

7

CHAPTER OBJECTIVES • • • • • • • • • • • •

examine basic relay circuits identify relay circuits and drawing conventions shown in Australian Standard AS/NZS 1102 identify remote stop/start control and electrical interlocks examine time delay relays design circuits using contactors design circuits including jogging and electrical interlocks examine the operation of various control devices examine the operation and applications of programmable relays examine three-phase induction motor starters explain the need for reduced voltage starting on three-phase induction motors examine three-phase induction motor reversal and braking examine three-phase induction motor speed control.

7.1   Basic relay circuit All circuits require some form of control, even if it comes in the form of a simple switch to turn on the lights in a room. For higher-powered devices, the cost of making a switch capable of interrupting large currents and being safe to operate becomes quite expensive. To be able to fit switches to such devices while keeping them safe and cost effective, designers came up with the solution of separating out the functions of operation and switching into two devices. This has resulted in low-cost/low-powered switches like push buttons being able to control circuits with large currents and voltages. The switching of the large power devices was left to specialised switches known as ‘contactors’ and ‘relays’—switches that are capable of interrupting large currents but require a signal to operate. This is provided by low-powered switches being operated; the resulting signal or current that flows through the contactor coil causes the circuit to be opened or closed. So, a basic relay circuit consists of:

1. 2. 3. 4.

a relay through which power flows to the device or machine to be controlled the operation controls provided by push-button switches (or the like) the cables to connect the relay and the operating controls a power source to operate the relay. 403

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Electrical Principles

7.2   Relay circuits and drawing conventions 7.2.1  Circuit diagrams When, in the nineteenth century, people first started to notionalise electrical circuits, they drew simple sketches of what they saw. Eventually, they realised that no matter how carefully and accurately they drew what they saw, the various connections were hard to see clearly. In an attempt to rectify this, the drawings were simplified and stylised, and the components symbolised. The wires and components were now deliberately separated and drawn distinct from one another, even though the drawing no longer looked like the real layout. Rather than being a mechanical representation of the structure of the circuit, the circuit diagram is intended to illustrate the connections between components and the power flow (or signal flow) through the circuit. As time passed and circuits became more complex, people who drew them often made up their own symbols to represent components (see Figure 7.1). Usually, a symbol key was given with the drawing, listing what the symbols represented. Soon, local and national standard styles of drawing and standard symbols were adopted by groups of people who needed to share drawings. Eventually an international body, the International Electrotechnical Committee (IEC), formulated an international standard of graphical representation. Some countries and organisations at first ignored the IEC standards and kept their own symbols. Countries that adopted the SI (or metric) standard of measurement mostly adopted the IEC symbols. AS/NZS 1102 is very close to the IEC standard, and most Australian organisations follow it. In December 2016, AS/NZS 1102 was marked as withdrawn. This indicates either that the document is no longer relevant or that its designation has changed. Standards documents may be withdrawn for any of the following reasons:

∙ ∙ ∙ ∙

they are technically out of date they do not reflect current practice or research they are not suitable for new and existing applications (products, systems or processes) they are not compatible with current views and expectations regarding quality, safety and the environment.

However, it is permissible for an industry, community or government to choose to keep using a withdrawn standard. Reasons for doing this include the lack of readily available replacement documentation.

7.2.2  Electric symbols

h1

h4

h6

h4 h2

h7

h1 h8

h3 k

h7 h11

h10

j

j a

Figure 7.1  Early electrical circuit drawing (1897)

Some of the more common AS/NZS 1102 symbols are shown in Figure 7.4. Although there is no fixed size, all symbols in the same drawing should be the same relative size and proportion. Electrical circuits are controlled by devices that can be broken into two main categories: the devices that physically either open or close a circuit and the devices that cause them to operate. Make and break contacts are in the first category as they make a circuit close and break open. A contactor is made up of contacts (often make and break contacts) as part of its design. The relay coil is the device that physically causes the contactor to operate. This occurs when current is allowed to flow through the relay coil; the resulting magnetic field causes the contactor to be

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attracted into the coil, closing make contacts and opening break contacts. Although the contactor and relay coil are often housed in the same component, they are often shown separately in Conductors schematic diagrams. + Resistor of negligible − Circuit breakers and fuse switches are devices containing resistance contacts that are manually operated by the installer or user to close the circuit. However, in the case of circuit breakers and fuse switches, the opening of the circuit is dependent on the protection mechanism that is used. In the case of fuse switches, Figure 7.2  Conductors between components in a it is the melting of the wire inside; for circuit breakers, it is the circuit are considered to have negligible resistance bending of the bimetallic strip. Push-button switches consist of contacts that are manually operated by the user. These switches are like contactors in that they may either be normally open or normally closed. Push buttons are used extensively in the electrical industry in applications such as start buttons and simple light switches. Depending on the task required, push-button switches may be selected to have multiple inputs and outputs, for example, double or triple pole. They may also allow for multiple throws.

7.2.3  Conventions in line work The components in actual circuits are connected by conductors, which may be actual wires or copper tracks on a printed circuit board. In most circuits, the conductors are considered to have negligible (no) resistance. The line used to represent a conductor is therefore nothing more than a statement that the two components are connected. The length of the conductor is not important to the circuit diagram. This is illustrated in Figure 7.2, where a battery is connected to a load.

Straight lines Conductors are always represented by straight lines with right-angle turns, regardless of the path the actual conductor takes. These lines may join to the circuit components or to other conductors.

Joins in conductors When conductors connect to other conductors, the joint is usually indicated by a distinctive dot (see Figures 7.3(a), 7.3(c) and 7.3(d)). When lines representing conductors in a schematic circuit diagram have to cross, they should do so at right angles or as close to right angles as possible. There is no need to indicate that crossing conductors are not joined, and no dot is shown at the point of crossing. Figure 7.3(b) shows conductors crossing but not connected to one another. In some diagrams, some conductors cross while others join. To avoid any confusion, the conductors are often offset, where the ends of the lines representing the conductors are displaced sideways at 45° for a distance of 2 or 3 mm. A dot is then placed at the point of each join.

Line types Ordinary conductors are a simple single-weight line, which in many circuit diagrams is the only type necessary.

(a) Joined (superceded)

(c) Joined

(b) Not joined

(d) Joined

Figure 7.3  Representation of conductors joining and not joining

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In some diagrams, however, some conductors carry more or less power than ordinary conductors. Power conductors are shown as bold or double-width lines, while signal conductors are shown as thin or half-weight lines. Temporary connections may be shown as dashed or dotted lines.

Line identification Due to the number of wires on a page when drawing a schematic, it becomes hard to identify cables. This can be overcome by the use of a label or numbering system that numbers and names both terminals and cables. The convention used is often up to the customer or design engineer but will be either a label based on the page reference or the terminal device input/output. For example, a wire that appears on a drawing may be labelled according to its grid reference, for example, J/25. The same cable may also be labelled according to the name of the device it is going out of and into. SWB-R3-PUMP2-L would be a cable coming from circuit breaker on red phase in position 3 of the switch board, going to the second pump and terminating in the active terminal on the pump.

7.2.4  Placement of circuit components Connections to symbols Connections to circuit symbols in schematic circuit diagrams should be made at some distance (around 5 mm) from the circuit symbols and not on the symbols themselves. This is done so that the outlines of the symbols are not confused with closely drawn conductor lines. Computer drawn symbols usually have connection ‘tails’ to connect to rather than the symbol itself.

Arrangement of components Symbols should be placed in line (aligned), or in the same relative position if they are similar. They should be spaced evenly so that they are easy to see and interpret. Repetitive parts of the circuit should be identical to avoid confusion (see Figure 7.5).

Parallel components In electrical circuits, two components are often placed in parallel. If one symbol has more importance, it is placed in the same line as the conductor and the parallel component symbol is offset. If they both have the same importance, then they are placed evenly each side of the conductor line. These features can be seen in Figure 7.6. Temporary connections should be shown with a dashed line.

7.2.5  Drawing schematic circuit diagrams To make schematic circuit diagrams easier to read, certain conventions are used in their layout. One is that the flow of energy, or flow of ‘signal’ and sequence of operation or events, is from left to right and top to bottom. It is not always possible to adhere exactly to this, but it is followed as closely as possible. Take the simple schematic circuit diagram in Figure 7.5. The power supply is on the left, and power flows to the right through the main switch to operate the three loads. Load 1 and switch 1 are to the left of load 2 and switch 2. Similarly, load 3 and switch 3 are further to the right. When each switch is operated, current flows from top to bottom through the respective load. Both switches and loads are in line to make the diagram easier to read and understand. The important thing to remember is that a schematic circuit diagram might have no resemblance to the actual physical components of the circuit—a schematic circuit diagram represents the components and the connections between them. A circuit diagram shows how an electrical circuit operates whereas wiring diagrams show how a circuit is actually constructed. Examine the more complex schematic circuit diagram of the electric motor starter in Figure 7.7. There are special features in this circuit representation. Note the thicknesses of the lines: the left-hand part of the circuit is drawn in lines 406

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or

(a) Switches

(d) Capacitors

(i) Time contacts

30° (i) Single pole (general symbol)

(i) Normal

(ii) Two pole

(ii) Polarised

(iii) Three pole

(iii) Variable

(i) Delayed on closing after energisation

(ii) Delayed on opening after energisation

(k) Overload relays

Attached

(e) Fuse

Detatched

(iv) Two way (f) Indicating instruments

(I) d.c. field windings

V (iv) Muti-position

Series field

Interpoles

(i) Voltmeter

Shunt field

A (m) Transformers and inductors

(ii) Ammeter

(vi) Intermediate

W Normally closed

(i) Iron cored inductor

(iii) Wattmeter kWh

Normally open

(iii) Air-cored inductor

(iv) Kilowatt-hour meter

(vii) Push-buttons (b) Resistors

(g) Lamps

(iv) Current transformer

(n) Motors

Luminaire and signal

(i) General symbol

(ii) Transformer complete

M

a.c. cage induction motor (six leads brought out)

M

a.c. wound-rotor induction motor

3

(i) Gaseous discharge (h) Earthing connections

(ii) Variable

3

Earth (ii) (iii) Variable three-terminal

(iv)

NTC

(i) Contactors (i) Coil Control

−t°

Normally open

Normally closed

a.c. single-phase induction motor

M

a.c. induction motor (three phase)

G

d.c. compound generator

(iii)

Power (i) Contacts

(c) Cells and batteries

(i) Single-cell battery +

M

3

(iv)

−

(ii) Three-cell battery +

110 V

−

(ii) Complete contactors

(iii) 110 V battery

(v)

Figure 7.4  Some commonly used electrical circuit symbols

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Electrical Principles

+ 12 V −

Figure 7.5  Symbols placed symmetrically are easier to interpret

V

(a) Resistor more important than capacitor

(b) Both resistors of equal important

(c) Voltmeter supplementary to resistor

Figure 7.6  Parallel connection of circuit components

L1

L2

L3

K1.1 K1.2 K1.3

K2.1 K2.2 K2.3

K2.4

K1.4

M 3~

Power circuit

K1/5

K2.5 F

K1.5 R

K2/5

Control circuit

twice as thick as those on the right-hand side. This is because this section represents the power circuit of the motor starter. Power passes from the supply at the top to the motor beneath. The starter conducts current through either one of two contactors to the motor windings. One contactor allows the motor to rotate in one direction while the other allows reverse rotation by reversing the connections to two of the motor phase windings. The control circuit is drawn in thinner lines because it plays no part in transferring energy to the motor. In fact, the actual currents in the circuit may be only approximately 100 mA. The thinner lines emphasise this. When the start forward push-button switch is pressed, current flows through the normally closed stop push button through the normally closed interlock K2.5 to the relay K1/5. It then flows through the normally closed overload contact and back to line. When K1/5 is energised, it open-circuits the interlock contact K1.5 and isolates the reversing contactor K2/5. The coils K1/5 and K2/5 are part of contactors. When energised, they operate all their associated switch contacts—that is, power and control. The figure 5 in contactor K1/5 signifies that it has five associated contacts. So, when this coil is energised, all its associated switch contacts (K1.1, K1.2, K1.3, K1.4 and K1.5) operate. The first three switch contacts supply power to the motor, whereas the next two switch contacts are for control. As contact K1.4 is part of the control circuit and because it is in parallel with the start push-button switch, it takes its place in the circuit. The ‘start’ switch can be released and K1/5 remains energised. These contacts are commonly referred to as ‘auxiliary hold-in contacts’. To stop the motor, the stop push-button switch is pressed and all coils and contacts return to their ‘off’ state. The flow of energy and the sequence of events  was either from left to right, or top to  bottom. All the contacts of the switches are drawn in their normal or de-energised condition. When switch contacts are operated, either manually or from their associated coils, the line representing the operating part of the switch rotates clockwise.

Figure 7.7  Schematic circuit of a forward/reverse motor starter

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7.2.6  Other circuit representations Schematic circuit diagrams are the most useful type of diagram for understanding the operation of an electric circuit, but they can be represented in other ways, such as:

∙ block diagrams ∙ one-line (or single-line) diagrams ∙ wiring diagrams.

Block diagrams A block diagram shows what a circuit does, not how it works. It is an overall picture of why a particular circuit is used and the function of groups of components within it. Block diagrams are useful when a circuit is relatively complex. In many cases, an electrical worker might first look at a block diagram of a circuit before reading the schematic circuit diagram. Figure 7.8 is a block diagram of a small AM transistor radio receiver. Although the actual circuit might appear complex, it is made from seven separate sections. The block diagram shows these seven sections. Without knowing exactly how the radio circuit operates, the function of the circuit can be easily explained from the block diagram. Compare this with the actual schematic diagram shown in Figure 7.9. This circuit is not for study purposes but is only an illustration of how a complicated circuit can be represented by a simple block diagram.

Tuning

Mixer

IF amplifier

Detector

Audio amplifier

Output

Oscillator

Figure 7.8  Block diagram of an AM radio receiver

Tuning

Mixer

IF amplifier

Detector

Oscillator

Audio amplifier

Audio output

Power supply

Figure 7.9  Schematic circuit diagram of a small AM radio receiver

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Block diagrams usually do not show any power supply. As they do not represent actual circuit Power Load Filter Regulator supply connections but merely explain what the circuit does, there is no need to include these details. Figure  7.10 is a simpler block diagram. It Figure 7.10  Block diagram of a regulated power supply represents a regulated supply connected to an electrical load. The input from the mains passes to a block on the left called the ‘power supply’. This Seriescould be an a.c.-to-d.c. rectifier unit. Its output then Supply Line M starting contactor passes through another block called a ‘filter’ to a resistors block labelled ‘regulator’. This regulates the voltage to a predetermined value. The regulated voltage is Accelerating then passed to the load. contactor Figure 7.11 is a block diagram of a motor starting circuit. The arrows on the lines indicate the sequence Control circuit and purpose of each circuit block. The a.c. supply from the mains is connected to the line contactor. However, it cannot operate until allowed to do so Figure 7.11  Block diagram of a motor starting circuit by the control and timing circuit. When the control circuit is activated (usually by a push-button switch), the line contactor closes and supplies energy to the motor through the current-limiting starting resistors. The motor starts up and, after a predetermined time, when it is nearly up to full speed, the accelerating contactor closes and bypasses the starting resistors. Full supply is now provided to the motor, enabling it to develop full power. By operating a stop push-button switch, the control circuit opens all the contactors and the motor stops. Figure 7.13 shows a wiring diagram for this starter.

One-line (or single-line) diagrams In power and transmission lines, a one-line diagram (or single-line diagram (SLD)) is a simplified notation for representing a three-phase power system. The one-line diagram has its largest application in power-flow studies.

Wiring diagrams A wiring diagram is much closer to the real thing than a schematic circuit diagram, being a stylised true representation of the components and wiring of an electrical circuit. It would be possible to take a photograph of the wiring of a circuit, but it would be of little use if it was necessary to know exactly how all the connections are made. The problem is that the wires may be bunched together, or connections may be made in an area below or behind another object. This would make a photograph extremely difficult to follow. In a wiring diagram, lines representing the conductors are drawn straight and separate. They are usually evenly spaced and are all connected to circles representing the terminals on the circuit components. In addition, where more than one conductor line terminates at a terminal, all lines are angled to the terminal circles, so there is a clear indication where each line (representing a conductor) starts and finishes. A representation of the wiring of two lights can be seen in Figure  7.12. In this diagram, the actual circuit components (switches and lamp holders in this case) are drawn in the same relative position that they would be in an actual circuit. The terminals of the lamp holders and switches have been emphasised to show exactly where each conductor connects. For clarity, the lamps have been separated from the lamp holders in this instance. A wiring diagram is seldom drawn to scale, but in some cases it may be in direct proportion to the shape of the object represented. In Figure 7.12, both the lamps and switches could be some distance apart. If it were drawn to scale, or even in proportion, the component parts would be too small to be of any use; all the lines representing the wires have been shortened so that their actual connections to the components are clear. 410

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Another wiring diagram, of the previous motor starter, is shown in Figure 7.13. In this case, all the components are in proportion, both in outline and position. It is a true representation of the motor starter but is not drawn to any particular scale. Note that the outlines of all components are drawn as dashed lines. In addition, the schematic circuit diagram symbols have been inserted to show the actual operation of the circuit components. Greatest prominence is given to the lines representing the wiring conductors and the circles representing the terminals. The main point to note about wiring diagrams is that the conductors are all separated and, as far as possible, equally spaced. Note also the manner in which many conductors have been angled as they connect to the terminals. In a wiring diagram, connections are only made at terminals. In a schematic circuit diagram, connections between conductors are made away from the components and may be shown at any point on a given conductor. Schematic circuit diagrams do not represent the actual physical circuit layout; wiring diagrams do. Drawing a wiring diagram is, in effect, wiring up the circuit or apparatus on paper. Each conductor line drawn between terminals represents an actual insulated cable, cut to length, bared of insulation at the ends and connected properly to each terminal. Because of this, a wiring diagram is invaluable for actually wiring up a piece of equipment or checking equipment when looking for a fault. In many cases, the designer of a piece of equipment may first produce a block diagram, then design a schematic circuit diagram and finally produce a wiring diagram.

Lights Junction boxes

E N A

Switches

Figure 7.12  Wiring diagram of a simple lighting circuit

K1/5

K2/4

7.2.7  Contactors and relays A relay is simply an electromagnetically-operated switch. A contactor is also an electromagneticallyoperated switch that controls power to a load. A contactor is actually just a large relay, and it is sometimes difficult to say whether a device should be called a relay or contactor in any given circuit application. Standard convention is that relays are typically low powered and contactors are high powered. In effect, the two terms are the same. In this section, the term ‘contactor’ is generally used but reference could also be made to ‘relay contacts’ and ‘power contacts’, all of which are operated from the same device.

1 2 3 E

A

B

C

M 3~ E

Figure 7.13  Wiring diagram of an automatic motor starter

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Electrical Principles

Fixed contact Contact terminal

Movable contact (spring loaded)

Construction and operation of contactors

A contactor consists of three basic parts: the operating coil, the associated magnetic circuit and the contacts that are actuated by the coil. Figure 7.14 Contact is a representation of a very old type of contactor. terminal Armature It clearly shows the coil, the operating part of the magnetic circuit and a single contact. Modern Coil Insulation Spring terminals contactors look like the one shown in Figure  7.15, Flexible conductor but the principle of operation is exactly the same Hinge as the representation in Figure  7.14. When the coil Coil is energised, a magnetic field is produced in the Magnetic circuit magnetic circuit. This attracts the hinged armature, Figure 7.14  Operating components of a contactor against the tension of the spring, to complete the magnetic circuit. The movable contact attached to, but insulated from, the armature closes against the fixed contact. When the coil is de-energised, the armature springs open and also opens the contact. Contactors consist of normally open or normally closed contacts which are indicated by labelling. This labelling may be the schematic symbol or the letters NO (standing for ‘normally open’) for a make contact or NC (‘normally closed’) for a break contact. Typical contactors, especially larger ones, will have a combination of NO or NC contacts activated by the same coil. Contactors may have many contacts, but those used in power work seldom have more than six. In most contactors there are at least three power contacts. These are designed to carry the full rated current of the contactor. When used for Figure 7.15  Typical contactor Reproduced with permission of NHP Electrical Engineering Products Pty Ltd motor-starting duty, they are designed to carry five times their rated current for a short time. The other contacts on the contactor are often termed ‘auxiliary contacts’, or sometimes ‘control contacts’. While one or two of them might be able to carry full-load current, in most circuits they only carry control current, which may be around 100 mA. A common application illustrates why this is. Take a three-phase contact for a motor. The three main contacts are normally open so that when the relay coil is activated they allow power to flow to the motor. The other contacts (termed ‘auxiliary’) are not rated to carry full current. Of these, one that is normally open creates a current path for the coil current when energised so that the on button does not have to be held in. The other is a normally closed contact that opens when there is power to the motor, preventing it from being put in reverse at the same time. What is often required is switching to be based on certain timings—for example, lights turned on and off for a specific period of time or hot water systems heated up at night to be ready for morning. These applications and the many others that exist are the results of timers. Timers allow control of a circuit to be based not on direct input for the installer but on time. Timers are actually contactors, and they work by receiving power—either turning a mechanical wheel or dial in older-style analogue systems or powering an electronic circuitry. When the dial reaches set points determined by the installer, the switch will operate to either close or open, depending on the settings. On an electronic system, the installer programs on and off times and, on more advanced devices, can program multiple set points per day and per week. Timers in general have one set of contacts controlled by the timing mechanism with both a normally closed and a normally open contact sharing a common contact. Along with the contacts are what are commonly called the ‘coil terminals’. 412

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These are designated either ‘A1’ and ‘A2’ or ‘L’ and ‘N’. The number of different manufacturers and the lack of universal standards for labelling the terminals mean that the installer has to read the manufacturer’s specific wiring diagram to identify the terminals correctly. Another type of contactor is the thermal overload contactor. This is a switch controlled by the heat generated by current flow. Usually attached to the power contact of a motor, the thermal overload contactor works by having a bimetallic strip opening on over temperature, which causes normally open contacts to close and normally closed contacts to open. The coil of the power contact is wired in series with the normally closed contacts of the thermal overload—if the overload is activated, the power coil is de-energised, which protects the motor from over-temperature conditions. As the thermal overload is designed to be attached to the power contactor, it looks like a plug with straight pins on one side with terminals for cables on the other. The terminals for the NO and NC contacts are normally situated above the power terminals and are labelled with either ‘NO’ or ‘NC’ lettering or symbols. Although overloads act as a form of protection for any device where over temperature is a problem, they are mainly used for electric motors.

Drawing contactors in circuits In terms of symbols, AS/NZS 1102 makes no real distinction between power contacts and control contacts. It merely provides two symbols labelled ‘form 1’ and ‘form 2’. In the interests of clarity, many people use the former for control contacts and add a small circle (see Figure 7.16), using form 2 contacts for the power part of the circuit. Figure  7.16 shows the different types of contact symbols. Form 1 contacts and contactor symbols are used extensively throughout this book. Both power and control contacts may be either ‘normally open’ or ‘normally closed’. The word ‘normally’ in this context means that the contactor is not energised (i.e. power is not applied to the coil). When the contactor coil is energised, the contacts change their state. Normally open contacts close, and normally closed contacts open. In drawings they are always shown in the de-energised state. The operation of contact symbols (whether opening or closing) is always considered to be in a clockwise direction. Some contactors may have contacts that are Form 1 Form 2 Contactor ‘timed’. These timed contacts will close, or open, after a designated period (say, five seconds). The (a) Normally open contacts timing device may be mechanical or electrical. When electrically timed contacts are required, a timing relay is quite often used. Timing relays (b) Normally closed contacts are usually connected in parallel with the coil of Figure 7.16  Symbols for contacts and contactors a contactor and may be adjusted to open or close contacts. Any timed contacts are designated by a special symbol—a semicircle—to indicate the contact is slowed down in operation. Timed contact (a) (b) (c) symbols of various forms are shown in Figure 7.17. Some contactors (or relays) are inherently timed (a) initial make contact but delayed on opening by their construction. That is, they close their (b) make contact delayed when closing (c) break contact delayed when opening contacts some time after they are energised. These relays are drawn with two diagonals in a rectangle on one end of their coil symbols. Some are slow Figure 7.17  Various timed contact symbols to release after de-energisation, and these are designated with a filled-in rectangle on one end of their coil symbols. The symbols for the three types are shown in Figure  7.18. Usually, this type only operates in d.c. circuits. Schematic circuits may have no bearing on their Timed-closing Timed-releasing Normal coil coil coil actual physical placement or arrangement in a circuit. Contactors may be drawn in circuits in a number of Figure 7.18  Normal and timed relay coils 413

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Electrical Principles

ways, one of which is illustrated in Figure 7.19(a). This shows a contactor with its operating coil and K/4 all its associated contacts. The broken line enclosing the components indicates that they are all part of the one assembly. This type of attached representation is seldom used in schematic circuits because it does not lend itself to a logical circuit arrangement. A second method is to indicate by a dashed line that the contactor coil operates the contacts joined by the line. This method of semi-detached representation (a) Contacts and coil— (b) Contacts and coil— attached semi-detached is sometimes seen in diagrams, especially when the components on the contactor are close together or in Figure 7.19  Symbolic representation of coils and contactors line. It is illustrated in Figure 7.19(b). The most common method is termed ‘detached L 1 L2 L3 representation’. In this, the contactor coil is not only labelled with the contactor designation but also with the K1.4 K1.1 K1.2 K1.3 number of contacts it operates (see Figure 7.20). The contactor is designated as K and, in the coil symbol, the K1/4 indicates that there are four associated contacts. Sometimes the coil designation is placed beside the coil symbol. In this case there are three normally open M power contacts, and one normally open control contact. K1/4 3~ However, there could be more or fewer contacts, and some could be normally closed and others timed. Power circuit Control circuit The detached representation makes the diagram Figure 7.20  Motor starter circuit—detached representation easier to read. The broken line indicates that all three contacts close simultaneously. Power is supplied to the motor when the three power contacts K1.1, K1.2 and K1.3 close. Also in the power circuit are three symbols indicating that they are thermal overload detectors. If an overload occurs, they will cause an associated contact to open. The coloured lines representing the power conductors have been drawn thicker than the control conductor lines. This method differentiates between power and control circuits. A broken line is shown here separating the two parts of the circuit, but this is not regular practice. Two control conductor lines are connected to two of the power lines. This circuit uses line voltage for the control circuit. To start the motor, the start button is pressed. The symbol indicates that when the button is released, the switch contact will open again. Current passes to the coil through the normally closed stop push-button switch and energises the coil of the contactor, K1/4. It is not regular practice to designate the start and stop push-button switches unless there is a special need. Just the nature of the symbols is enough to show that a normally open pushbutton switch is a start switch and a normally closed one is a stop switch. The moment the start switch is pressed, K1/4 is energised, which then operates all K1 contacts. In this case, they are all normally open contacts so they all close. K1.1, K1.2 and K1.3 supply power to the motor, allowing it to start up. K1.4 takes the place of the start push-button switch when the start push button is released. Pushing the stop push-button switch opens the circuit to coil K1/4 and all the associated contacts open. The motor then stops and cannot be re-started until the start push-button switch is pressed again. If an overload condition occurs, the thermal overload detectors open the overload contact and again the motor will stop. Some thermal overload relays are self-setting, while others must be reset before the motor can be started. The circuit layout with the flow of energy and sequence of events moves from left to right and top to bottom. All components have been spaced across the drawing and kept in line as much as possible. Any drawing should be laid out in this manner, even if it is only a pencil sketch. It makes it much easier to read and interpret later. The stop and start push-button switches in motor and other control circuits are convenient ways of operating them. It is easier to press a button than operate a toggle or turn a handle. K K/4 4

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7.3   Control circuit variations 7.3.1  Two-position control So far, only circuits with one start and one stop push button have been discussed. To provide extra start positions, all that is needed is to connect extra start push buttons in parallel with the first. To stop or de-energise the circuit, extra stop push-button switches are placed in series with the first. In Figure  7.21, there are two start and two stop push-button switches. As is usual, the start push buttons are normally open and the stop push buttons are normally closed. They are labelled ‘start 1’, ‘start 2’, ‘stop 1’ and ‘stop 2’ for clarity. A variation on the control circuit in Figure 7.21 is the provision of only one start position with multiple stop positions. This can arise when a number of emergency stop positions might be required in a plant. Only one push-button switch will start the operation, but if there is a malfunction in the plant it can be stopped by operators at any number of positions. It requires that all the stop push-button switches are connected in series (see Figure 7.22).

Stop 1

Start 1

Stop 2 K1/4

K1.4 Start 2

Figure 7.21  Two start and stop control positions in a circuit

K1 K1/4 4 K1.4

Figure 7.22  Multiple stop control positions

7.3.2  Local or remote operation In some operations it may be necessary to shift the operating position of the stop/start push-button switches. To avoid the possibility of someone operating the machine at the incorrect position, the circuit of Figure 7.22 is amended so that only one position at a time can be used. This is often referred to as ‘local’ or ‘remote operation’. Figure 7.23 is a circuit representation of this type. On the left side of the diagram is a hand-operated changeover switch, which switches into circuit either the upper local or lower remote push-button switches. This type of circuit requires an extra contactor contact and only a simple changeover switch.

7.3.3  Two-wire control Many motor control circuits use an automatic start control. This could be, for example, from a thermostat on a refrigerator, a float switch on a water tank or a pressure switch on an air compressor. Because there is no other stop/start control and only two wires need to be run to the actuating device, is it usually referred to as ‘two-wire control’. Figure  7.24 is a simple two-wire control circuit. In this case, the controlling device is a pressure switch, which is represented by the lower-case p in the square.

Local Local/remote switch

K1.4

K1 K1/5 4 5

Remote

K1.5

Figure 7.23  Remote or local operation control

7.3.4  Two-wire and push-button control In some cases it might be necessary to start a motorcontrolled device using a push-button switch but allow another control to turn it off. This type of

K1/4

p

Figure 7.24  Two-wire control by a pressure switch

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Electrical Principles

K1 K1/4 4 K1.4

Figure 7.25  Combined stop/start and automatic control

Start

circuit is shown in Figure  7.25. It has normal stop/start control with a float switch connected in series with the stop push button. This would enable a pump to be started and then switch off automatically when a tank is full. The motor could be stopped at any time while running, but could not be restarted after an automatic stop until the water level fell and the float switch closed again.

Stop K1/4

7.3.5  Jogging control

When a push-button switch is connected so that a circuit operates only while the switch is held depressed, it is Jog K1.4 called ‘jogging control’. It is sometimes necessary to ‘jog’ Figure 7.26  Jogging push-button switch in a control circuit a machine to a certain position so that adjustments can be made. It would be possible to juggle both start and stop push buttons using two hands, but it is neither good practice nor reliable—and it could be dangerous. It is more efficient to install a special push button for this function. In the schematic circuit diagram in Figure 7.26, the jogging push-button switch is a push-button changeover switch with a normally closed and a normally open position. In its normal position the circuit operates as a simple stop/start control. When the jogging button is pressed, the hold-in contact, K1.4, is isolated and the start pushbutton switch is bypassed. While the jogging button is pressed, coil K1.4 is energised. When the button is released, the circuit to the coil is opened and then remakes the normally closed contact so that normal operation is possible. The jogging push button sometimes includes a small delay on reclosing to give the contactor time to open contact K1.4. Often, due to the normally closed contact as part of the jogger push button, the jogger push button can be used to stop the machine’s operation without using the designated stop button.

7.3.6  Reversing circuits To reverse a three-phase motor, all that is necessary is to interchange two supply lines to the motor. This can be accomplished by using two contactors, as in the schematic circuit diagram in Figure 7.27. When either K1.1, K1.2 and K1.3, or K2.1, K2.2 and K2.3 contacts close, the motor will operate either in a forward direction or in the reverse. Examination of the power circuit will show that two supply lines would be short-circuited if both contactors closed at the same time.

7.3.7 Interlocks Short circuits due to reversing of the supply lines by activation of the forward and reverse contactors at the same time can be prevented in two ways. The small equilateral triangle and the broken lines between the two sets of power contacts signify that the two contactors are ‘mechanically interlocked’. This means that if one contactor is closed, it is mechanically impossible for the other to close or make connection. The usage of an interlock device normally positioned between the two contactors provides the physical connection. Two pegs or bars from the interlock device are attached to the contactors and are moved when one contactor is actuated. The pegs are attached inside the interlock to two flaps that physically block the other from moving. As the contactor moves the pegs also move; it then is positioned such that, even if the second contactor’s coil was to be energised, the contactor would not be able to be moved. The use of a mechanical interlock allows the device to be physically isolated. This is generally the preferred method and the only method recognised by the Australian Standards as providing 100% assurance of interlocking should a contact fail. The second method is to use ‘electrical interlocks’ in each contactor coil circuit. This can be seen in Figure 7.27, where the normally closed contact K2.5 is in the forward coil circuit and the normally closed contact K1.5 is in the reverse coil circuit. This means that when contactor coil K1/5 is energised, contact K1.5 will open. Then, 416

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if the reverse push-button switch is pressed, coil K2/5 cannot be energised. The same applies to the reverse operation. However, electrical interlocks should only be used as a back-up for mechanical interlocks or on systems where the risk of harm is minimal. This is because failure of the contacts to open on the normally closed of the energised contactor will allow the second contactor to energise, causing a short. The switching system where one contactor must de-energise and open before the second can energise is called a ‘break before make’ system. Only one stop push button is used and the thermal overload contact is also in series with the stop button. By necessity, the stop push-button switch is ahead of the forward and reverse push buttons so that it can control both.

L1

L3

L2

K1.1 K1.2 K1.3

K2.1 K2.2 K2.3

M 3~

Power circuit

7.3.8  Ladder diagrams

K2.4

K1.4 K2.5 K1/5 F

K1.5 K2/5 R

Control circuit

Figure 7.27  Schematic circuit diagram of a reversing contactor

Control circuits in particular can be drawn as ‘ladder’ diagrams. They are so called because the L1 L2 supply lines are drawn on each side like the stiles K2.5 F of a ladder and the circuit component parts are K1/5 drawn across them like the rungs of a ladder. K1.4 Ladder diagrams also follow the requirement K1.5 R K2/5 that energy flow and sequence of events move R from left to right and top to bottom whenever K2.4 possible, similar to common drawing practice in this country. These diagrams are a step towards programming logic controllers and are mostly Figure 7.28  Control circuit of Figure 7.27 drawn with a horizontal layout used  with programming in mind. The control circuit of Figure  7.27 has been redrawn in a L1 L2 horizontal orientation and is shown in Figure 7.28. R2 Symbols as recommended in AS/NZS 1102 are Stop F used. The circuit, however, is identical to that of OL OL OL the control circuit in Figure 7.27. F1 In other countries, different standard symbols F2 are often used. In the USA, more than one set of R standards is used, but a popular one is the NEMA (National Electrical Manufacturers Association) standard. Figure  7.29 shows the control circuit of Figure 7.28 redrawn to NEMA standards. It Figure 7.29  Reversing control circuit drawn to NEMA standards is still the identical circuit except that now each overload is shown separately as three normally closed contacts. Many of the programmable logic controllers in this country and others use this standard, and the programmers are oriented towards it. Circuit diagrams supplied with the controllers are, more often than not, drawn to NEMA standards. 417

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7.4   Control devices 7.4.1 Introduction As their name suggests, control devices allow for control of some function on the circuit. Although they are often mentioned alongside circuit protection, it is important to understand that control and protection are two distinct aspects of circuit design and components. Confusion often arises on this point as the actions of the two aspects seem similar. Both provide some form of manual and automatic disconnection. Protection devices respond to overcurrent, overloading, overvoltage or earth leakage and automatically disconnect via blowing a fuse or tripping a circuit breaker or residual current device. Control devices respond to nearly any other circumstance or input. Although switches or sensors are the most common types of control devices, variable resistors can also be used as control devices.

7.4.2  Types of control The two general types of control are:

1 control methods that limit or affect the current 2 control that limits or affects the voltage.

Current control is the more common type. Basic electrical theory states the simple relationship between voltage, current and resistance and how either the voltage or current can be varied by varying the resistance. This allows voltage control by the use of a variable resistor or resistor load banks. By increasing the resistance, the voltage drop across the resistor is increased, reducing the amount of available voltage for the remainder of the circuit. This is most commonly used for speed regulation on a motor where the reduction in voltage causes a reduction in speed. Current controls are often simpler to understand. Since there is only one current path in a series circuit, it should be clear that open-circuiting the circuit means that current will no longer flow and it will stop operating. This is done via switches or the use of contacts and relays.

7.4.3  Control devices Two common types of variable resistor are the potentiometer and the rheostat. Common types of switches include:

∙ bimetallic strips ∙ contactors ∙ float switches ∙ light sensors ∙ limit switches ∙ magnetic limit ∙ photoelectric cells ∙ pressure switches ∙ proximity switches ∙ push-button switches ∙ relays ∙ rocker switches ∙ timers.

All the switches in this (far from exhaustive) list respond to an input by changing state. Bimetallic switches, used in thermostats or overcurrent breakers, respond to heat, causing the metal to bend. Contactors and relays respond to current flowing in their coil, causing them to operate. Float switches, used in bore water pumps to stop the pump 418

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from pumping dry, respond to water level by movement of a ball operating contacts or a magnetic reed switch. Light sensors, used for street lighting, operate by detecting light falling on either phototransistors, which limit current according to amount of light falling on the sensor, or on photoresistors, which vary the amount of their resistance according to light. There are switches whose operation is based on the position of objects, the two main types being the limit switch and the proximity switch. Limit switches work by being operated by an object as it moves to a position where it is to stop, for example by an automatic door being opened and actuated by a limit switch when it has reached its limit of travel. Proximity switches operate by producing either electromagnetic or infrared radiation as either a beam or electromagnetic field and detecting the return signal. Proximity switches can be seen in use detecting items on supermarket conveyer belts. The problem with most control switches is the need for manual input. Their contacts inevitably wear out and cause failure. Control devices that use resistors or the like do not require manual input, but are more susceptible to over-power situations which cause them to burn out. Control switches, like proximity and limit switches, require care in placement as they may detect the wrong object, or may even detect no object at all. The advantage that manual control devices have over automatic devices is that they are robust and cheap. Some devices do not need manual input as they receive an automatic input, such as light, rather than human intervention. Switches operate in two states: by interrupting the flow of current when opening the circuit or by allowing current flow by closing the circuit. As simple and limited as these two states may seem, it is possible to create complex responses to inputs. An example of this is the float switch that will not allow a pump to turn on if the water level is too low, even if it is set via a timer to do so. This is an example of what is called a ‘logic circuit’. Logic circuits are the foundation for automation and are commonly used in large plants and factories. Prior to the widespread adoption of transistors, the logic was handled by large, complex combinations of mechanical relays that formed control circuits that were hard to understand, prone to failure and hard to add to or modify. The selection of control devices for a circuit depends on the following factors:

1 2 3 4 5

the power the device is expected to handle the type and amount of voltage seen across the device the type and amount of current flowing in the device and how long it will do so the type and number of circuits to be controlled how the circuit is to be affected, meaning whether it is to be opened or closed.

These factors are often called ‘duty ratings’ and must be considered when selecting all manner of components— from push buttons and pilot lamps to relays and timers. The selection of devices and components may have been specified in a bill of materials or specification from the client or engineer; equally, though, the installer may be required to source components themselves, from either the manufacturer’s catalogue or website. When installing the control components into a circuit, the general rule is to place them at the start but after the circuit protection. The multiple devices that perform control allow for parallel configurations, but care should be taken when using limit and proximity switches: while they are control devices, they perform functions not dissimilar to protection devices and therefore should be installed in series with emergency stops and other control devices.

7.5  Programmable relays 7.5.1 Introduction Relays and contactors were the origins of automatic control—indeed, relays can perform many of the functions required for automatic control. Contacts of relays can be normally open, normally closed or even a combination of both. The basic relay provided adequate control for automatic control and industrial processing for many years. But, as the demand for improvement grew, the limits of the relay became apparent. Mass production industries 419

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required improvements that the relay could not provide in terms of high speeds, reliability of service and minimum maintenance. The rise of cheap electronics and the need for greater automation and control brought about the programmable relay. The programmable relay is a relay that can have multiple sensors (such as photovoltaic, temperature and flow-level sensors) or control inputs (such as start/stop buttons and timers) and be able to perform decisions based on the logic that has been programmed into it via its on-board software. Programmable relays are more commonly referred to by the term ‘PLC’, which stands for programmable logic controller. Modern PLCs can be regarded as little computers made up of solid-state circuitry. Solid-state circuitry was introduced initially because of its ability to operate as an on/off device and to repeat the operation millions of times—more than a relay could and with minimal maintenance. Its being in either an on or an off state depended on an input signal from an external device called a ‘transducer’. Generally speaking, a transducer provides an input signal to the solid-state device and this in turn operates the required device. As an example, a thermostat can be manufactured to close its contacts at a specific temperature. Closure of the contacts acts on an electronic component, which can then start an air-conditioning system. When the temperature in the monitored area drops sufficiently, the contacts of the thermostat open and the air-conditioner stops. The system has only two states—on or off. In this example, the thermostat replaced the start push button of the relay circuit and a solid-state device such as a triac replaced the contacts of the relay (traics are control devices for switching circuits). For industrial process control, this on/off method does not provide the accuracy needed for many products. Devices such as the thermostat mentioned above cannot operate at the one temperature for both on and off states. This introduces a differential—if the contacts open at 22°C, it is extremely unlikely that they will also close at this temperature. Depending on the circuit, the closing temperature might be 18°C, giving a differential of 4°C. This led to the introduction of the programmable controller. Originally intended to be a replacement for the relay panel, initially it did little more than manage the on/off sequencing of motors and solenoids. It gradually evolved into the intelligent item of equipment that it is today. The modern programmable logic controller has a relatively low cost, and its original program can easily be reprogrammed to monitor something completely new when manufacturing requirements change. A logic control program is stored in its memory, and this tells the central processing unit when certain events should take place and the sequence in which they should occur. It makes these decisions based on information it receives from sensors connected to its input terminals combined with user-programmed instructions.

PLC Control relays

Relay contacts Push-buttons Sensors

Input modules

Microprocessor

Output modules

Limit switches

Motor controls Annunciators Alarms

Data access and display module

Printer

Programmer

Recorder/ loader

Figure 7.30  Block diagram for a programmable controller

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Programmable relays are becoming so common that there are now very few situations where they are not used. As PLCs are replacement relays, they can be installed wherever a relay would have been installed, for example, instead of a timer and a relay. Instead of a stop/start control circuit with relays, a PLC can handle the inputs and control the motor. The rise of home automation is in part due to a PLC’s ability to control the domestic environment.

Feedback (Information) Pilot devices switches program

(Decision) PLC

(Power control) Starters controllers

Input

(Action) Motors Output

Figure 7.31  Block diagram for an automatic starter

Clock

7.5.2 Programming Microprocessor Prior to the adoption of graphical user interfaces (GUI), unit the use of PLCs required a technician skilled in the use of Boolean algebra and the concept of ladder logic (in this context, ladder logic refers to the use of ‘if–then’ Memory statements, which looked like a ladder when written out). The arrival of GUIs removed the need for that particular skill set and the programming of the relays can be done without being able to code as the software Interface adapter for each relay now uses a drag and drop graphical user interface. Each brand has its own proprietary software to program their relays, and while they are designed to Input/output be easy to use, it is recommended that some training port is done. In general terms, though, the user selects what model relay they have, then on the interface page drags down function blocks and connects the inputs Input/output devices that trigger the functions. The user then specifies what connecting output is to be controlled and the software then compiles the machine code ladder logic. Once Figure 7.32  Block diagram of a microcomputer completed, the program can be downloaded onto the relay via a USB disk or ethernet cable. Older models may still use a serial cable. Figure  7.31 shows a block diagram for a programmable logic controller. The inputs to the PLC receive information from external sources while the PLC outputs send information to the controlled process, whether it is the starting of an electric motor Figure 7.33  A typical PLC or some other appropriate task. Courtesy of Rockwell Automation, Inc. By introducing a PLC into the starting process for the motor controller shown in Figure 7.31, there is no longer any need for an attendant to be on hand to start or stop the motor. At the heart of the PLC is a decision-making unit called a ‘microprocessor’. The basis of this is shown in the block diagram of Figure 7.32. The microprocessor is part of the PLC. Technically, there is a difference between a microcomputer and a microprocessor. A microcomputer contains a microprocessor and various other circuits to store information, provisions to connect it to the process being automated and a clock. The clock provides specific electric pulses at specific times to control the internal processes of the unit. The various sections of a typical modular PLC can be seen in Figure  7.33. From the left end are the power supply, the processor, then various input and output modules.

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Microprocessor programs A group of instructions that enable a microprocessor to perform a specific task is called a ‘program’. A program is a step-by-step procedure to solve a problem, initiate certain actions or manipulate data that it stores within its memory. The program consists principally of numbers that have to be placed in a read-only memory (ROM) within the processor. It is then able to control the process under control repeatedly without variation until it is reprogrammed from an external source. Programming the PLC requires some knowledge of what it needs to operate. For the most part, this is in relation to the inputs and outputs of the relay. The inputs to a PLC are from what are known as a ‘peripheral’ device (meaning in this case from outside the PLC). These inputs can either be digital inputs (i.e. a switch with binary states of ON or OFF, where ON may be the presence of a voltage and OFF the absence) or analogue (e.g. a thermostat). When it receives the inputs, the PLC then writes the information into a list or table to be processed. This list could, for example, include that there is voltage on input 1, how much voltage is on input 2, etc. The PLC then processes the information and sends signals to the outputs. The outputs are either relays, transistors or triacs.

7.5.3  Connecting, checking and troubleshooting Connecting peripheral devices like proximity switches or thermostats to the PLC is made easier by using cable and terminal numbers corresponding to a diagram. Common methods of identifying the inputs and outputs include using straight numbering (1, 2, 3, etc.) or using letters and numbers (I1, I2, O1, O2, etc., where the use of I indicates input and O output). As each PLC has a number of inputs, the diagrams showing connections will invariably also show the numbers so they can be connected. Most PLCs are DIN mounted so are installed the same way as a circuit breaker or RCD. Any control device can be connected as an input. Most can also be connected as an output. Switches like proximity, limit or light sensors cannot be used as outputs for obvious reasons. If the device connected to the PLC is connected as a normally closed device, care should be taken so that the desired operation is obtained. This method can be problematic as a PLC may interpret the lack of input from a pressed NC switch as being unoperated when in fact the wire to the switch is damaged and, rather than opening the circuit as expected, the PLC does nothing. The software that comes with the PLC will include a checker that will verify the correct set-up of the PLC. This software will also allow for the simulation of the PLC operation, with the user able to operate the switches and check its operation. This includes the ablilty to check the set value of timers and time remaining. The error checking of the PLC software is invaluable for fault finding. The most common faults found as part of a PLC installation are the other components failing, i.e. the switches used as inputs or relays used as outputs. The first step towards diagnosing the fault is to operate the switches manually and see if the PLC operates correctly. If the other components are working but the PLC is not controlling them properly by either turning the wrong outputs on or failing to react to an input, download the program from the PLC to a laptop and run the error checking. If no errors are found and the circuit works correctly when simulated, re-upload the software to the PLC. Often, the PLC program has either been altered by a careless operator or has become corrupted by a failing battery or memory chip. Re-uploading the software will fix this type of error.

7.5.4  Features and advantages Programmable relays offer numerous advantages and almost limitless features, thanks to the software handling the logic. For example, as the relay has its own clock it is possible to set up multiple timers for multiple events. Programmable relays can accept almost any sensor input provided to it via various types of transducers. Also, having fewer moving parts makes them more reliable than the older mechanical relays. Fewer components makes fault finding easier.

Transducers By definition, a transducer is a device where any variation in energy magnitude of any form is able to reproduce that variation in another measurable form—generally these days as electrical voltage, even though it may be in millivolts. 422

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A thermocouple is a type of transducer where two dissimilar metals produce a voltage on being heated at their junction. For example, a copper/constantan thermocouple with the cold end kept at a constant temperature produces 4.3 mV at 100°C and 14.8 mV at 300°C. A graph of a range of these values is approximately linear over a restricted range, and can be used to indicate the temperature on a voltmeter that has been suitably calibrated to read temperature. Alternatively, the thermocouple can be connected to a PLC and be part of the control process. Mechanical devices can be used as electrical limit switches to indicate to a PLC that some machine has reached the limit of its position. Pressure switches can be fitted with a pair of contacts to indicate an on/off relationship, or, if fitted with certain types of resistive material, can provide an infinite number of pressure readings to a PLC. Positive and negative temperature coefficient resistors (thermistors) can also be used as temperature indicators, provided they are suitably calibrated.

7.5.5 Disadvantages Programmable relays have significant shortcomings: a computer with the proprietary software installed is required to work on the relay and make changes; they need a battery to ensure the PLC works; they are costly.

7.5.6 Safety PLCs and safety Safety in relation to programmable controllers needs to be looked at from the following three aspects.

PLC safety and protection PLCs in an industrial environment require a certain amount of mechanical protection as well as basic electrical protection. The transducer connections radiate out from the controller and are subject to spurious voltages being induced in the connecting cables. This is generally referred to as ‘electrical noise’ and can be misinterpreted by the microprocessor as a form of input. It can produce erratic equipment operation and incorrect data entry—and can prove difficult to trace as the source of trouble. In the industrial context, there are usually many machines and other equipment being switched on and off continually. This causes voltage spikes and surges in the main supply. Since a PLC operates at a low voltage, a transformer is employed to reduce the mains voltage to a suitable value, and consequently these surges in voltages are transferred through the transformer to the processor. Suppression of this electrical noise becomes quite an essential requirement for satisfactory operation of a PLC. This might mean applying special runs with shielded wiring to the transducers as well as noise suppression actually at the transducer.

Controlled equipment safety Where machinery is controlled by a PLC, precautions have to be taken to ensure that erratic operation by a PLC does not lead to the destruction of that machinery. This usually means that extra equipment has to be installed. For example, a second limit switch might have to be installed as a back-up to one that is actually controlled by the PLC. With heating baths, a second temperature sensor might have to be installed as a back-up to the main one that sends information to the processor and overrides any function of the PLC.

Safety of personnel Operators or maintenance personnel must be protected against any erratic behaviour of the controlled process or task. Unexpected starting or stopping of equipment due to spurious signals getting into the system wiring can cause accidents. An emergency stop button should be included as part of the installation to override all other input signals. AS/NZS 3000 has made it mandatory for isolating switches to be provided in equipment not directly under the control of a worker. These isolation switches have to be capable of preventing the PLC from bypassing them. The isolation must be a physical barrier and not just the switching off of electronic equipment. 423

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7.6  Three-phase induction motor starters 7.6.1 Introduction The full advantages of an electric motor drive can be realised only when there is compatibility between the following three major components:

1. the drive motor 2. the driven machine 3. the control equipment.

There are many forms of motor-starting methods, and at least as many forms of speed control. Motors— particularly large ones—might have to meet starting current requirements, as well as running a machine up to operating speed without imposing severe mechanical shocks on the system.

7.6.2  Requirements of motor control equipment The prime function of a motor starter is to connect the motor and its coupled machine to the supply without disturbance to other machines and users. It must do this with due consideration to the mechanical inertia of the driven machine, its permitted acceleration and the allowable time taken to get it up to operating speed. It must do this repeatedly and with minimal maintenance problems. Under these conditions, the selection of a motor starter must take into consideration the following factors:

1. the limitation of starting current to values acceptable to distribution entities, thus causing minimal disturbance to the line voltages of other local users 2. control of starting and accelerating torque from the viewpoint of mechanical shocks to the machine system and the motor driving shaft 3. protection of the motor against overloads and overheating 4. isolation of the motor in the event of a fault 5. provision for interlocking the motor’s operation with that of other motors and machines 6. motor reversal 7. speed control 8. motor braking.

7.6.3  Limitation of starting currents All Australian distribution entities require the starting currents of motors to be contained within certain limits, depending on the power of the motor. The distribution entities in turn have varying requirements, and enquiries might have to be made to them in specific cases. Since there are so many different circumstances and so many types of installations, it is almost impossible for a distribution entity to lay down firm rules and hope to cover all cases for all installations. It is worth noting that their information booklets often use the phrase: ‘Notwithstanding any of the above, the entity’s engineer may decide . . .’ The regulations governing the starting and running currents drawn by electric motors and the maximum demands of an installation are long and involved. There is the further complication that the local rules might vary from one distribution entity to another. The intent of these regulations is to prevent the creation of large transient currents that could cause voltage surges on consumers’ mains, to the detriment of other users.

7.6.4  Speed–torque relationships When a three-phase squirrel cage motor is connected directly to the supply, it will draw a large starting current. This current, which usually lasts only a second or two, can be up to seven times the motor’s full-load current. Figure 7.34 424

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700 Current

300

500 400

200

Torque

300 200

100

Per cent full-load torque

600 Per cent full-load current

shows the characteristics of the current and torque for a standard squirrel cage motor. It can be seen that the current is almost proportional to the rotor slip; as the motor builds up to speed, the slip decreases and the current decreases. A principal aim of a starter on an induction motor is to reduce the starting current as much as possible while at the same time providing adequate torque to meet the requirements of the load. This will be a compromise because, in order to reduce the starting current, it is necessary to reduce the voltage supplied to the motor. However, a reduction in voltage will also result in a reduction in torque, as the motor torque is proportional to the fraction of the voltage squared. That is:

100 0 0

10

20

30 40 50 60 70 80 Per cent synchronous speed

90

0 100

Figure 7.34  Speed vs. current and torque for a standard squirrel cage motor

​T ∝ ​V​​  2​​ This means that with 100% of the rated voltage, 100% of the rated torque will be available; however, if 90% of the rated voltage is applied to the motor, the torque will be reduced to (90%)2 = 81% of the available torque. If the motor is being started in a no-load condition, this will be adequate; but if the motor is loaded, there may not be enough torque to overcome the load and the motor will stall.

7.6.5  Direct online starting Direct online (DOL) starting is the simplest way to start an induction motor. Full voltage is applied directly to the stator windings of the stationary motor. The effect is often severe. At the instant of connection to the supply, the stator is completely demagnetised and, as the winding resistance is low, there is a high inrush of current from the mains. At switch-on, the rotor bars behave like the short-circuited secondary winding of a transformer and aggravate the effect. It is quite usual for the starting current to reach a value seven times that of normal full-load current (see Figure 7.35). The starting torque produced is two to three times that of the full-load torque. This is transmitted to shafts, bearings, belts and the driven machine so quickly that a considerable mechanical shock is transmitted to all connected parts. If the motor is capable of starting the connected load, acceleration is swift. For very large motors (which implies a heavy load), the mechanical shock from DOL starting can shear shafts or cause severe belt slip, which results in accelerated wear.

DOL starting is generally restricted to comparatively small-size motors. Motors up to 4 kW are normally started DOL, but in special circumstances those up to 25 kW have been started this way. DOL starting is also usually restricted to situations where there is little or no load imposed on the motor when being started. DOL-starting a centrifugal pump is one instance where the major part of the load appears after the motor has been started when the load is gradually imposed by an increase in pressure on the liquid being forced through the pump.

600

Delta current

300

500 400

200 Delta torque

300

Star current

200 100 0

100

Star torque

0

10

20

30 40 50 60 70 80 Per cent synchronous speed

Per cent full-load torque

700

Per cent full-load current

Applications

0 90 100

Figure 7.35  Comparison of current and torque characteristics for star and delta connections

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Electrical Principles

7.6.6  Star–delta starting Torque and input power 1 10 A — 3 of ‘run’ condition L1

Forstar–deltastarting,thesixendsofthethreewindingshave to be brought out to the motor terminals (see Figure 7.36). 10 A 230 V A reduced voltage to the windings is achieved by first 400 V 400 V 17.3 A connecting the windings in the star configuration, then L2 L2 switching to delta to apply rated voltage when the motor L3 L3 is up to speed. For a 400 V winding, the applied voltage Start (star-connected) Run (delta-connected) for each phase is reduced to 230 V or 58% of the rated voltage. Effectively, this reduces the starting torque to Figure 7.36  Comparison of star and delta starting 33% (T ∝ V2) of that obtained with DOL starting. Note that (58)2 = 33%. If the star connection has sufficient torque to run the motor up to around 75% or 80% of full-load speed, the motor can be reconnected in delta configuration to enable it to accelerate to full speed for normal operation. It also means that there has to be a short time-lag between the starting and running periods while the motor windings are isolated from the power supply and reconnected in delta configuration. In the star connection, the line and phase currents are equal, but when the windings are reconnected in delta __ configuration, this condition no longer applies. The phase voltage increases by a ratio of ​​√ 3 ​​ or an increase of 173%. Consequently, the phase currents increase by the same ratio. The line current increases to three times its value in the star connection. These values are illustrated in Figure 7.36 for a winding impedance of 24 Ω. During the transition period, the inertia of the motor and connected machine must allow free running with little deceleration. It also means that while ‘coasting’ it might generate a voltage of its own and, on reconnection to the supply, this voltage can randomly add to, or subtract from, the applied line voltage. In most cases, it causes a transient current that can be up to twenty times that of normal running current. While it only lasts for a few milliseconds, it still causes voltage surges or spikes on the supply lines. These are referred to as ‘changeover transients’. In an endeavour to eliminate any changeover transients caused during the open-circuit interval, a closed-circuit transition star–delta circuit was developed. It has resistors in parallel with each phase winding. The resistors must be substantial enough to withstand starting currents. In this method, when the star point of the windings is opened for reconnection to delta, the resistor star point remains closed and current flows through the resistors and windings in series. This reduces the tendency for the motor to slow down and eliminates many of the transients. After connection to delta, the resistors are short-circuited to eliminate any current flow through them. This starter is much more expensive than a conventional star–delta starter. It needs at least one extra contactor as well as the extra resistors. Because of the expense and its relatively few advantages, the starter is seldom used. It is only mentioned here to illustrate the point that transients can be troublesome in an installation. L1

30 A

Applications Star–delta starting is a relatively simple way to get a motor up to speed without causing excessive starting currents. It can be used in any application where the motor can be started ‘unloaded’. Other applications include driving centrifugal pumps where little starting torque is required until the pump is up to speed and working. Other uses are on farm dam pumps, and at the end of long runs where DOL starting would cause an appreciable voltage drop. Another use is in lathes where a clutch is incorporated in the mechanism. The motor is started and later the clutch is engaged to turn the lathe. Many large fans or blowers can be started with a star–delta starter.

7.6.7  Primary resistance For primary resistance starting, resistors are connected in series between the supply lines and the motor terminals, although inductors are occasionally used in place of resistors. The intention is to reduce the actual voltage at the motor terminals and so limit starting current. Starting torque is reduced at the same time. 426

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Metallic resistor starters

Metallic resistors or separate liquid containers

L1 The traditional method of primary resistance starting is to insert metal resistors in series with the supply for starting (see Figure 7.37). Once the motor has accelerated M to around 75% to 80% of its rated speed, full voltage is L2 3~ then applied to the motor. This is usually done by shortcircuiting the resistors in each phase. While this type of starter is more expensive than a DOL-type starter, the L3 method does have advantages. As the motor accelerates, its starting current decreases. Figure 7.37  Basic power circuit for primary resistance motor This in turn causes a decreased voltage drop across the starting resistors and an increased voltage at the motor terminals. The overall effect is to give an increased torque as the motor accelerates. Opposing this is the effect of the resistors getting hot during the starting process and slightly increasing their resistance. Because the motor is not disconnected from the supply when the resistors are shorted out at the changeover from the start to run connections, there is no transient current.

Liquid resistor starters A similar technique uses liquids in lieu of metallic resistors. Liquid containers are far bulkier and less robust than metallic resistors, but modern liquid electrolytes have the ability to reduce their resistance as they are heated up by starting currents flowing in the liquid. Compared with older types, where metal electrodes were manually wound down into a liquid to accelerate the motor, today’s types of starter use a liquid that can be adjusted in E L1L2L3 N U VWE E content to suit particular applications. Often non-corrosive, it is placed in sealed and insulated containers to reduce contact with the atmosphere. Occasionally a non-reactive Line Run Start timer oil may be placed on the surface to further isolate the electrolyte from the atmosphere and prevent evaporation. The electrodes are permanently immersed in the liquid (see Figure 7.38). Once in position, they need no further adjustment. Depending on the manufacturer, the plates may be flat and parallel or consist of a series of short concentric cylinders placed one inside another. Each phase winding Tol has its own separate container and set of electrodes. When the motor is first started, the liquid has a resistance modified to suit the application. Starting current and torque is limited to predetermined values. The voltage appearing at the motor windings is reduced and the starting torque is also reduced. When properly adjusted, the motor is able to start and accelerate smoothly without mechanical shocks. As the starting current flows, it heats the liquid and its internal resistance is reduced. Consequently, the voltage to the motor increases and this action is a progressive one up to around 80% to 90% of full-load speed, when the resistance of the liquid stabilises. Then a timer operates a contactor, which bridges out the electrodes in the liquid and the motor can accelerate to full speed. Figure 7.38  Typical liquid resistance starter 427

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Electrical Principles

The primary resistance starter takes more power from the line than some starters but does so at a higher power factor. The liquid starter possibly increases the acceleration rate of the motor so that it reaches full-load speed more quickly. Like the metallic resistor starter, there is no open-circuit transition stage, so it eliminates transients in both starting current and torque. The first method uses a metallic positive temperature coefficient resistor while the second method uses a liquid negative temperature coefficient element. It is this fact that enables the liquid-type primary resistance starter to have an advantage over the metallic resistor type.

Applications Because of the lowered starting torque, the primary resistance method of starting induction motors is limited to loads where initial starting torque requirements are comparatively low—that is, loads where the running torque only comes into play at full speed. Fans, blowers and water pumps are common applications.

EXAMPLE 7.1 A 400 V, three-phase induction motor draws 160 A when connected DOL. If a primary resistance starter is connected to the motor so that the voltage to the motor is reduced to 280 V for starting, determine the: (a) per cent of rated voltage applied to the motor during starting (b) starting current taken by the motor (c) percentage of DOL starting torque produced. (a) Per cent rated voltage: 280 × 100 Per cent voltage = _________ ​   ​     ​​ ​    ​   ​​​ 400 ​ = 70% (b) Starting current: ​I​  S​​  = 70% of DOL starting current     = 70% of 160 A  ​​           ​​ ​ ​ ​  = 0.7 × 160    = 112 A  (c) Per cent starting torque: 70% 2 ​T​  S​​% = ​​ ____ ​   ​  ​​​  ​ = 0.72 = 0.49 ​​      ​  ​  ( 100 )  ​​​  0.49 × 100 = 49% DOL torque

7.6.8  Autotransformer starters Autotransformer starters generally use two autotransformers connected in an open-delta configuration to provide reduced-voltage starting. Taps are usually provided on the transformers to enable selection of the required starting torque. The principle is illustrated in Figure 7.39. Points to note are:

1. The motor starting current varies directly with the applied motor voltage. 2. The line current varies as the square of the motor voltage. 3. The torque varies as the square of the motor voltage.

Point 2 means that the starting current with an autotransformer starter is less than that obtained with a primary resistance starter. This is its major advantage—for the same starting current, the motor torque is increased. Point 3 means that if a 50% voltage tapping is chosen, the resultant starting torque is 25% of full-load torque. A tapping has to be selected that will be the minimum that enables the motor to start against its load. The major characteristics of this type of starter are: 428

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1. 2. 3. 4. 5.

low line current low line power low power factor open-circuit transition periods acceleration is in a series of steps; it is not continuous or smooth.

The provision of tappings on the transformers makes it possible for a choice of voltages (and hence currents) to be available for starting purposes. The use of a transformer makes it possible to reduce the line input current at a greater rate than that at which the torque is reduced. With a transformer:

L1

L2

M

3

L3

Figure 7.39  Starting connections for an induction motor using an open-delta transformer

input voltage × input current  =  output voltage × output current       ​​  ​​​ that is, ​V​  1​​  × ​I​  1​​  = ​V​  2​​  × ​I​  2​​   (neglecting all losses  ) During starting, a reduced voltage V2 is applied to the motor, thereby reducing the starting current I2. Because of transformer action, however, the input current is reduced still further. It can be illustrated by the following example.

EXAMPLE 7.2 A 400 V, three-phase induction motor draws 160 A when connected DOL. If an autotransformer starter, with the motor connected to the 70% tapping, is used to start the motor, determine the: (a) voltage applied to the motor during starting (b) starting current taken by the motor (c) starting current drawn from the supply. (a) For 70% tapping: motor voltage = 70% of input voltage ​ = 70% of 400 V ​            ​ ​ ​ ​ = 0.7 × 400 ​ = 280 V ​​ (b) For 70% tapping: motor current = 70% of DOL starting current ​ = 70% of 160 A ​            ​​ ​ ​ ​ ​ = 0.7 × 160 ​ = 112 A (c) For a transformer: ​V​  1​​ ​I​  1​​ = ​V​  2​​​I​  2​​ ​​

​V​  ​​ ​I​  ​​ __________ 280 × 112 =​  ____ ​  2 2 ​ ​     = ​  ​  ​     ​​ ∴ ​I​  1​​​    ​ ​V​  2​​ 400 ​ = 78.4 A I1 I2 V1 = 400 V V2 = 70% of V1

Figure 7.40  Circuit diagram for Example 7.2

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Electrical Principles Table 7.1   Comparisons between primary resistance and autotransformer starting Starter type

Voltage applied to motor

Starting current

Starting torque

Primary resistance

49%

49%

(49%)2 = 24%

Autotransformer

70%

49%

(70%)2 = 49%

Note that the motor voltage has been reduced by 70% to 290 V. Because I ∝ V2, the torque will have been reduced to (70%)2 = 49% of the DOL value. While the motor current has been reduced to 70% of the DOL value, the line input current has been reduced to 49% of the DOL value by transformer action. For a primary resistance starter to give the same reduction in line input current, the voltage applied to the motor would need to be reduced to 49% of the DOL value, further reducing the starting torque. For comparison purposes, see Table 7.1. Start Transition Run A more expensive form of autotransformer starter designed to alleviate the problem of open-circuit transients Figure 7.41  Autotransformer Korndorfer switching is the Korndorfer starter. This uses three autotransformers and an extra contactor. Its use is limited to applications where there is no reasonable alternative. It maintains a continuous torque during the transition periods of reconnection (see Figure 7.41). The diagram in Figure 7.41 shows that, during the transition period, the motor is connected to the supply by part of the transformer windings, which act as series inductors during the transition time. L1

L2 L3

L1

L2 L3

L1

L2 L3

Applications Owing to the high cost of autotransformer starters, their use is restricted to heavy loads that have to be started from rest. Such applications are larger-type refrigeration units and air-compressors where the motor might have to start against a substantial head pressure. In some cases, electrically operated relief valves might also have to be fitted to release the head pressure to enable the motors to start.

7.6.9  Soft start Three-phase induction motors are designed to operate at standard line voltages and frequencies. In Australia, induction motors are intended to run on a three-phase line-to-line voltage of (usually) 400 V and a frequency of 50 Hz. This results in the flux density in the air gap of the motor being within defined limits. Any motor starter designed to reduce the line voltage to a motor also has a tendency to reduce the current flowing to the motor, thereby reducing starting torque. The autotransformer method of starting goes part way to solving the problem of maintaining starting torque and current at a reduced voltage, but the method also has disadvantages. It was reasoned that if the motor starting current could be manipulated to satisfy the above requirements, then the voltage and frequency might also be controlled. This gave rise to the electronically controlled starter, which was developed to include such refinements as control over the following:

∙ starting currents ∙ overload currents ∙ over- and under-voltage monitoring ∙ motor protection ∙ frequency

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∙ ∙ ∙ ∙ ∙ ∙

motor isolation sequencing other motors dynamic braking low-speed operation slip compensation (better speed regulation) remote computer control.

In an electronically controlled starter (see Figure 7.42), the controlling circuits are more involved than in a normal relayoperated starter. The general principle is to convert the alternating current supply to direct current, which is then fed through a filter to remove most of the transients. The d.c. is then supplied to an inverter to convert d.c. back to a.c. using a high-speed switching sequence. This is shown in block diagram form in Figure 7.43. The units can be programmed to monitor and control motor currents during starting and stopping sequences. This gave rise to the term ‘ramping’, which describes the control of a motor current during the starting and stopping sequences. If a graph is drawn for motor current against time, the characteristic is a straight line. In those terms, the motor can be ramped up or down, as shown in Figure 7.44. These linear characteristics are highly variable and depend on the information programmed into the unit. The motor current is controlled to remain within two values by the starter programming: 1. to ensure that the current never exceeds a predetermined maximum value 2. to provide a sufficient minimum value of current to ensure that the motor has sufficient torque to enable starting.

Three-phase input

Figure 7.42  Electronic soft starter

Reproduced with permission of NHP Electrical Engineering Products Pty Ltd

Rectifier

Filter

Inverter

Input to

Control

Monitoring

Three-phase output

Feedback

control During the starting sequence, as the motor accelerates up to speed and the motor current tends to decrease, the starter increases the available Figure 7.43  Block diagram for electronic motor control current, keeping the available torque constant to keep the motor accelerating up to a speed governed by the frequency of the supply. During the stopping sequence, the motor is disconnected from the supply and brought to a rapid and controlled stop by the starter—that is, it is ramped down. See Section 7.7 for various methods of braking a.c. motors. On a production line, time spent waiting for a machine to coast down to a stop is time wasted, and is usually not tolerated. In a starter of this type, there is considerable interaction between the applied voltage, the motor Run current and the starter-generated frequency. All three Initiate stop sequence Torque are monitored electronically within the starter, and the result is a voltage and a frequency supplied to the motor that meet the prevailing motor conditions. Ramp down Ramp up For example, an increased voltage will Start increase the starting current (say 10%), while an increased frequency will decrease starting current Accelerating Braking (approximately 5%). These are two opposing period period Stop 0 Time effects. Similarly, increasing the applied voltage will increase the starting torque, but an increase in frequency will decrease the starting torque. Figure 7.44  Ramping control

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Electrical Principles

Figure 7.45  Basic power circuit for secondary resistance motor starting

The inverter and the d.c. being supplied to it have to be continually monitored. The inverter also has the task of converting d.c. to a.c. It does this by breaking the d.c. up into small units of either polarity. The resulting alternating voltage wave is only vaguely similar to a sine wave and, as a result, generates harmonics at a ratio many times higher than the fundamental frequency. The current waveform is filtered to some extent by the inductance of the motor windings and is closer to a sinusoidal shape.

Applications This method can be a more expensive way of starting squirrel cage motors, although initial costs are being reduced  constantly, and for smaller motor starters the initial cost is now approaching a comparable value. Care should be taken in selecting motors to be used in conjunction with these types of starters. The starters are capable of running squirrel cage motors at speeds well above and below their designed levels. In circumstances where there is a need to start them regularly or run them at slow speeds for extended periods, consideration must be given to cooling requirements. The units can be made at ratings in excess of 300 kW. Since costs for the units are high, careful consideration must be given to their possible use. Centrifugal fans are one possible use, which is more than justified in printing workshops where a printing press must be run up to speed slowly and smoothly because of the rolls of paper being fed through. Another typical use is on production lines, where several motors must be controlled and their speeds integrated to ensure smooth and coordinated processing.

7.6.10  Secondary resistance Despite the predominant use of squirrel cage motors and their improved starting methods, there are still applications where the wound-rotor motor has advantages that more than compensate for its initial cost. Apart from the high starting torque characteristics, there are still current-surge limitations that cannot be met by a squirrel cage motor combined with any of the above starters. The speed–torque characteristic of any induction motor depends largely on the relative proportions of resistance and reactance in the rotor circuit. When the rotor resistance is equal to the rotor inductive reactance, maximum torque  is produced. At the instant of starting, while the rotor is still stationary, the frequency of the  currents  in the rotor  will  equal the line frequency. This causes increased inductive reactance in the rotor circuit. With the introduction of external resistance into the wound-rotor circuit, the rotor resistance and impedance values can be adjusted to produce maximum torque at starting, and at the same time minimise starting currents (see Figure 7.45).

Metallic resistor starters For a wound-rotor motor, the rotor windings are connected internally in either star or delta configuration and the connecting leads are brought out to slip-rings. With secondary resistance starting, it is possible to control motor performance and still satisfy the local requirements for starting currents. If the speed–torque characteristics of a wound-rotor motor are examined, it will be found that the incidence of maximum torque can be made to occur at different speeds by adjusting the value of external resistance placed in the rotor circuit. While external resistance is connected in the rotor circuit, the starting torque is almost proportional to the starting current. It cannot be truly proportional because of the inductive reactance of the rotor windings. Full line voltage is applied to the stator windings for starting and the external rotor resistance is progressively reduced as the motor accelerates. An equal value of resistance in the circuit of each phase is the norm, but

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occasionally these resistances can be made unequal, resulting in unbalanced rotor currents. As the resistance is reduced either manually or by contactors, the motor accelerates in a series of stages. The greater the number of resistance stages, the smoother the acceleration.

Liquid resistor starters The introduction of liquids in chambers was an attempt to replace metallic resistors and eliminate the steps or stages in the starting process. This method makes starting smooth, with a gradual acceleration in speed until the final step where the liquid resistor is finally shorted out. Consequently, transient effects are minimal. The passage of current through the liquid causes partial vaporisation of the electrolyte in the chamber. This affects the value of the resistance between electrodes. The greater the current flow, the greater the vaporisation. As the liquid heats up, the resistance between the electrodes is progressively reduced and the motor can accelerate smoothly up to working speed since the current flow controls the relative proportions of liquid and vapour in each of the liquid chambers. The final stage of the starting sequence occurs when a timed contactor shorts out the liquid chambers.

Applications The wound-rotor motor is ideal for driving machines designed to handle impact loads. Such machines are presses, drop forging hammers and guillotines. Heavy loads are applied suddenly and reliance is placed on the inertia of the heavy rotating parts to complete the action of the machine. It means also that the drive motors can be of lesser power since, apart from starting the machine, their sole purpose is to make up the losses of the rotating parts. It follows that heavy rotating parts of machines, including large flywheels, might take considerable energy to get them rotating at the required speed. For an electric motor to get the machine rotating at this speed, a lengthy starting sequence is usually required. Overhead cranes sometimes use wound-rotor motors since the resistance in the rotor circuit forms part of a variable speed process. Variable speed characteristics are discussed in Section 7.8.

7.6.11  Three-phase motor starter circuits The following are push-button motor starter circuits for the more common types of starters. It must be emphasised that the circuits presented are only representative. There are many variations between each type and further variations from one manufacturer to another. L1 L2 L3 These circuits present the principles of operation only and it is to be expected that other starters encountered might have different circuits.

7.6.12  Direct-on-line contactor starter circuit (Figure 7.46) Circuit operation 1. Pressing the start button completes a circuit from L3 through the normally closed stop button to coil K1/4 and the overload to L2. 2. Main contactor coil K1/4 then closes and applies full line voltage directly to the motor via contacts K1.1, K1.2 and K1.3. 3. Contact K1.4 bridges out the start button contacts so that, on the release of the start button, the contactor remains in the operational state. That is, the control circuit is latched in the ‘on’ position. Pressing the stop button disables the latching circuit and allows the main contactor to revert to the ‘off’ state.

K1.1 K1.2 K1.3 K1.4

M

3

Power circuit

K1/4

Control circuit

Figure 7.46  Contactor circuit for DOL starting

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Electrical Principles

L1 L 2 L 3

7.6.13  Star–delta contactor starter circuit (Figure 7.47) Circuit operation

1.   Pressing the start button completes a circuit from L3 through the normally closed stop button B1 and two normally closed contactor contacts C1 A1 K4.1 K2.4 K1.4 (K4.1  and K3.4) to coil K2/5 and the overload B2 C2 K3.4 K2.5 K3.5 A2 contact to L2. K2/5 K3/5 K4/1 K1/4 2.  When K2/5 operates, it causes the ends of the Power circuit Control circuit three windings to be joined in star configuration Figure 7.47  Contactor circuit for star–delta starting via contacts K2.1, K2.2 and K2.3. 3. Simultaneously, coil K3/5 is open-circuited by K2.5. This is the delta-connecting coil and it must be isolated when the star connection is in operation. Similarly, when the delta connection is in operation, the star connection must be isolated, using a method called ‘electrical interlocking’. As a precaution, the star and delta connecting contactors are often mechanically interlocked, in addition to the electrical interlocking provided by contacts K2.5 and K3.4. 4. When K2.4 closes, a voltage is applied to the timer K4/1 and to coil K1/4. This allows K1.4 to close and bridge the start button. 5. Contacts K1.1, K1.2 and K1.3 close and apply a voltage to the ‘starts’ of the motor windings. 6. The voltage applied across the windings at this time is only a proportion of full line voltage (58%), and the starting current is reduced accordingly. 7. When the time delay period has elapsed, contact K4.1 opens and forces contactor K2/5 to disconnect the star connection. The dropping-out action of K2/5 causes contact K2.5 to close and energise coil K3/5. This action open-circuits the interlocking contact K3.4 and also switches off the timer K4/1 via K3.5. 8. Contacts K3.1, K3.2 and K3.3 close and complete the delta connection, allowing full line voltage to be applied to the motor. 9. Pressing the stop button de-energises all coils and allows the starter to revert to the ‘off’ state. K1.1 K1.2 K1.3

K3.1 K3.2 K3.3

K2.1 K2.2 K2.3

Stop

Start

L2

L1

7.6.14  Primary resistance contactor starter circuit (Figure 7.48)

L3

Circuit operation

K1.1

K1.2

K1.3

K2.1

K2.2

K2.3

K1.4

M

3

Power circuit

K1/5

K1.5

K2/3

Control circuit

Figure 7.48  Contactor circuit for primary resistance starting

1.  P  ressing the start button completes a circuit from L3 through the normally closed stop button to coil K1/5 and the overload to L2. 2.  The main contactor K1/5 operates. Contact K1.4 closes and bridges out the start button contacts, so that on release of the start button the K1/5 contactor circuit remains latched. 3.  Contacts K1.1, K1.2 and K1.3 close, and a reduced line voltage is applied to the motor through the resistors in series with each line to the motor. The starting current is limited by the resistors to a value below that of DOL starting. 4.  Delayed-action contact K1.5 operates after a predetermined delay and completes the circuit for coil K2/3. Its operation causes contacts

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K2.1, K2.2 and K2.3 to close and allow full line voltage to be applied to the motor. 5. Pressing the stop button de-energises all coils and allows the starter to revert to the ‘off’ state.

7.6.15  Autotransformer contactor starter circuit (Figure 7.49) Circuit operation

L1

L2

K1.1 K3.1

L3

K1.2

K1.3 K3.2 K1.4 K2.3

K2.1 K2.2 1. Pressing the start button completes a circuit K2.4 K1.5 from L3 through the normally closed stop K3.3 button, a normally closed delay contact K1.5, K2/4 K1/5 K3/3 electrical interlock K3.3, coil K2/4 and the M 3 normally closed thermal overload contact to L2. Power circuit Control circuit 2. When K2/4 is activated, it closes the contacts K2.1 and K2.2, connecting the ends of the Figure 7.49  Contactor circuit for autotransformer starting autotransformers to line L2 in an open-delta configuration. 3. The operation of K2/4 simultaneously closes contact K2.3 and opens contact K2.4, the electrical interlock, to prevent K3/3 operating while K2/4 is active. 4. K2.3 supplies power to coil K1/5, which is also activated. Contacts K1.1, K1.2, K1.3 and K1.4 close. Full line voltage is connected to the autotransformers and a reduced line voltage is supplied to the motor via the transformer tapping. Contact K1.4 ensures that a voltage is available to the control circuit when the start button is released. 5. The delayed opening contact K1.5 opens after a predetermined time lapse, de-energising K2/4 and opencircuiting the delta connection. Contact K2.4 then closes again and coil K3/3 is activated. 6. Contacts K3.1 and K3.2 close, and full line voltage is applied to the motor through the K1/5 contacts in series with two lines. The electrical interlock contact K3.3 opens and isolates coil K2/4. 7. Pressing the stop button de-energises all coils and allows the starter to revert to the ‘off’ state.

7.6.16  Secondary resistance contactor starter circuit (Figure 7.50) Circuit operation

1. Pressing the start button completes a circuit from L3 through the normally closed stop button, coil K1/4, L1 L2 L3 and the thermal overload contact to L2. Coil K2/1, I which is in parallel with coil K1/4, is activated at the same time as K2/1 but only operates after a predetermined time delay. 2. Contact K1.4 bridges out the start button contacts K1.1 K1.2 K1.3 so that, on the release of the start button, the B C Stop A contactor remains in the operational state, that is, D F E K1.4 the control circuit is latched in the ‘on’ position. Start K5.1 K5.2 3. Contacts K1.1, K1.2 and K1.3 close and apply K3.1 K2.1 full line voltage to the stator terminals of the K4.1 K4.2 motor. The rotor has two resistors in series with K2/1 K3/1 K1/4 K4/2 K5/2 each winding and, because the ends are connected Control circuit in star configuration, current flows in the rotor Power circuit windings and the motor is able to generate torque and commence turning. Figure 7.50  Contactor circuit for secondary resistor starting 435

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Electrical Principles

L1

L2

L3

Voltage sensing

Motor protection Current sensing Starting circuit Overload circuit Current ramp Manual input Starting torque (stop, start, Current limit fwd, rev.) Starting mode select

Microprocessor

CTs SCRs

SCR gate firing board

M 3

Figure 7.51  Block diagram of an electronic reduced-voltage motor-starter





4. After the delay time, K2/1 operates and closes contact K2.1. This causes K4/2 to be energised, along with K3/1, a second time-delay relay. 5. Contacts K4.1 and K4.2 then close and reduce the amount of resistance connected across the slip-rings. This action enables the motor to attain a higher speed. 6. After a further time delay, coil K3/1 operates and closes contact K3.1. Coil K5/2 is then activated and closes contacts K5.1 and K5.2. This action removes the remainder of the resistance in the rotor circuit and the motor is in its normal running mode. 7. Pressing the stop button de-energises all coils and allows the starter to revert to the ‘off’ state.

7.6.17  Solid state reduced-voltage starter Figure 7.51 shows a block diagram for a solid state reduced-voltage starter for a three-phase motor. It can be seen that the central processor unit has three inputs to receive information from the starting circuit, the line voltage and the line current. This enables it to start and operate the motor efficiently. It monitors the line current at all times, particularly during the start-up sequence, to limit the amount of current that can flow into the motor at that time. This is often set at around 300% of full-load current. If at any time any one-phase voltage deviates outside set limits or disappears altogether, the motor protection circuit conveys this information to the processor and the processor takes the required action to protect the motor. Similarly, the motor is also protected against overloading and overheating. Note that there has to be an operator on hand to push the necessary buttons for the motor to start and stop.

7.7   Three-phase motor reversal 7.7.1 Introduction The rotor of a three-phase motor always tries to rotate in the same direction as the rotating magnetic field. Since the direction of the rotating magnetic field depends on the phase sequence of the applied voltages, the direction of rotation can be reversed by interchanging two stator leads. 436

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In practice, this is generally achieved by using two mechanically interlocked contactors to change the stator connections when required. In addition, the two contactors are usually interlocked electrically to prevent energising the contactor not in use. If both contactors were to be allowed to energise at the same time, two phases would be connected together as a dead short. Where the contactor panel is located on moving machinery such as a crane or hoist, it is vital to have mechanical as well as electrical interlocks as the two contactors could be closed due to inertia if the crane runs into the end stops. Figure  7.52 shows typical circuit connections for a DOL forward-reverse starter circuit. The same principle applies to all forms of three-phase motor starting.

L1 L2

L3

K1.1 K1.2 K1.3

K2.1 K2.2 K2.3 K1.4

K2.4

K2.5 M 3

Power circuit

K1/5

K1.5 K2/5

Control circuit

Figure 7.52  Two-contactor DOL reversing circuit

7.7.2  Three-phase motor braking In many installations, it is quite satisfactory to allow a machine to coast to a halt as its inertia is dissipated in friction losses within the machine. This inertia, which can be considerable in larger machines, can be dissipated more quickly by some form of braking. The braking system used must be of a type to suit the machine and its requirements. The major types of braking in use are:

1. mechanical 2. eddy-current discs 3. dynamic 4. regenerative 5. plug braking.

7.7.3  Mechanical braking The principle of mechanical braking is to bring equipment to a complete halt and act as a parking mechanism. Generally, mechanical braking consists of creating deliberate friction between rotating and stationary components. Machine braking systems might use more than one braking method. For example, an overhead crane might use the dynamic method for slowing down a load, and a solenoid-operated mechanical brake for holding the load stationary. In the interests of safe working, the mechanical brake has to be made fail-safe by being applied automatically when power is removed. This is a protection in the event of a power failure. Travelling cranes commonly use this form of solenoid braking on all directional movements. In Figure 7.53, the brake shoes are held in the ‘on’ position against a flat pulley by a substantial spring. An application of power to the motor also energises the solenoid, which releases the brake and allows the pulley to rotate. Three-phase motors can be supplied by the manufacturer with a mechanically operated disc-brake as an integral part of the motor. Figure 7.53  Mechanical braking with brake shoes and solenoid 437

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Electrical Principles

Brake discs

DC supply

Magnetic coil

Tension spring Cover shown removed

Back plate

Figure 7.54  Typical three-phase motor with integral disc brake

L1

L2

L3 L2

L3 K1.1 K1.2 K1.3 K1.5

K1.4

K2.4

In Figure  7.54, the brake pressure is applied by means of a spring. The spring tension can be adjusted so that the braking pressure suits the particular application. The brake is released by means of a magnetic coil, which is supplied with a d.c. voltage by means of a rectifier in the motor terminal box. When supply is applied to the motor terminals, it is also connected to the rectifier and hence the brake is released. This type of brake is inherently ‘fail-safe’ because, if the supply to the motor is interrupted at any time, the brake is automatically applied. Another system of mechanical braking uses a flat disc rotating in a mixture of finely powdered iron dust. The dust may be in a dry form or a paste immersed in a liquid. A coil surrounds the container and, on the application of a d.c. voltage, the iron powder grips the disc and holds it firmly against the container. If two discs free to rotate are used, the device can be used as a clutch mechanism. It is worth noting that the mechanical system of braking usually brings the machine to a complete halt and can be used as a holding brake as well.

7.7.4  Eddy-current disc braking

K3.1

An eddy-current disc consists of a sturdy disc connected to the machine shaft and free to rotate with the machine M between a set of coils held firmly in a stationary position. 3 When a voltage is applied to the stationary coils, eddy Power circuit Control circuit currents are set up in the rotating disc and form a load on the machine. As the machine slows down, the induced Figure 7.55  Braking an a.c. motor by d.c. injection voltages and currents become less and so does the rate (dynamic braking) of deceleration. Eddy-current discs are not capable of bringing a machine to a complete stop, nor are they capable of being used as a holding brake. They simply increase the rate of slowing down of the machine. K2.1 K2.2 K2.3

K1/5

K2/4

K3/1

7.7.5  Dynamic braking Dynamic braking works on the principle of using the motor as a generator and dissipating the machine’s inertia as electrical energy. In a.c. motors, this is often achieved by disconnecting the rotating motor from the power supply and applying d.c. to the windings. Because the rotor is still moving, circulating currents are generated within the rotor. These form a load on the machine and slow the motor rather more quickly than just coasting to a halt. Like the eddy-current disc method, it only hastens the slowing process and cannot bring the motor to a complete stop. A mechanical braking system is still needed as a holding brake. A typical circuit is shown in Figure 7.55. The main contactor and the contactor applying direct current to the stator windings are electrically interlocked and, on pressing the start button, the main contactor K1/5 is energised, K1.1, K1.2 and K1.3 connect the supply to the motor and contact K1.5 isolates contactors K2/4 and K3/1. When the stop button is pressed, K1/5 drops out and the normally open section of the switch completes the circuit to contactor K2/4. When it is activated, it isolates the main contactor and simultaneously applies direct current to 438

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the stator windings. At the same time as K2/4 is energised, the time delay contactor K3/1 is also energised. After a preset time lapse, it operates and switches off the direct current. During the stopping process, the stop button must be held in the ‘stop’ position for a short period to activate the braking system. The direct current is usually obtained from a rectified a.c. supply. A typical use for dynamic braking is in electric trains, where the driving motors are used as generators and the energy generated is dissipated in banks of resistors. Some large cranes also use this system but, as with other applications, a system of mechanical braking is also required for bringing all movement completely to rest. Another form of dynamic braking is the use of what is known as an ‘induction generator’. Capacitors are connected across the input terminals of a three-phase motor. When it is necessary to stop the motor, the power supply source is removed and resistors are connected across the motor terminals. The motor, while it still rotates, generates alternating currents, which are dissipated within the resistors. The system involves extra contactors, resistors and large capacitors, but is an excellent way of controlling the speed of motors and equipment connected to overhauling loads.

7.7.6  Regenerative braking Regenerative braking uses the inertia of a moving load to convert mechanical energy into electrical energy and feed it back into the power supply source. This method is not used very often with a.c. sources; it is a more involved method than those described above and involves the use of extra equipment. The electrical energy fed back into the supply source has to be considerable to justify the additional expense. It follows that the mechanical energy available to supply it also has to be considerable. A typical application of regenerative braking is its use in electric traction systems such as trains or trams. There are often thousands of tonnes on the move, and this constitutes considerable inertia. If this energy can be transformed into electrical energy and slow down the train or tram, a large saving in electricity costs can be achieved. There will also be a saving in wear and tear on the brake shoes used in a mechanical system. The system becomes less effective as the vehicle slows, and mechanical braking is also required. At some point, the electrical energy being generated will be insufficient to be fed back into the supply line and the system has to be disconnected from the supply. Occasionally, the system may then use dynamic braking as a further slowing process. Because of the expense of fitting extra equipment to machines, plus the fact that the method cannot completely stop and hold machinery in a stationary position, the applications of regenerative braking are limited. For a.c. working, its main use is in controlling overhauling loads—such as cranes lowering heavy loads.

7.7.7  Plug braking Plug braking with three-phase motors is the system of reconnecting a motor to rotate in the reverse direction while still rotating in the forward direction. It is a sudden and almost violent method for bringing a motor to a complete stop. The actual time taken depends on the amount of inertia in the accompanying machine. In order to use plugging as a stopping mechanism, some means must be provided to remove all power from the motor at the instant of change in direction. This can be done with a friction-operated single-pole changeover switch mounted on the motor driving shaft. Another method uses an eddy-current disc rotating between magnets to activate contacts, which in turn control the main contactors. The starter circuit has push buttons to activate rotation in the required direction and the movement of the shaft closes the appropriate contact, allowing the main contactor for that direction to energise. A stop button allows the contactor in use to drop out and also activates the contactor for the opposite direction. This is latched in until the first amount of reverse movement occurs. This movement opens the holding-in contact of the starter and removes all power from the motor. A circuit for a three-phase motor using the plugging method of braking is shown in Figure 7.56. The operation of the circuit is a follows.

1. Pressing the start button energises K1/5 via the stop button and the TOL contact. K1.1, K1.2 and K1.3 close and connect the supply to the motor so it runs in the normal direction. K1.5 energises K2/2. 439

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L1

L2

L3

L1

K1.1 K1.2 K1.3

K3.1 K3.2 K3.3

L2

K1.4

K1.5

K4.2

K2.2

K4.3

K4.1 K3.1

M

3

K1/5

Power circuit

K2/2

K2.1 K3/4

S1 K4/3

Control circuit

Figure 7.56  Typical diagram for plug braking of an a.c. motor





2.  K  2.1 opens and prevents K3/4 from energising. K2.2 closes and energises K4/3 via the nowclosed shaft rotation switch S1. Note that S1 opens whenever the shaft is stationary. 3.  K4.1 and K1.4 close and bridge out the start button so that, on release of the button, K1/5 remains energised. 4.  When the stop button is pressed, K1/5 drops out and K1.5 opens and de-energises K2/2. Contact K2.1 now closes and as K4/3 is still energised via S1, K3/4 energises and connects the supply to the motor in the reverse direction. When the shaft stops rotating, switch S1 opens and K4/3 and K3/4 both drop out.

Motors generally have to be specially designed for this application by having stronger driving shafts. The drive shaft has to withstand the forces created by the driven machine’s inertia in bringing the machine to a halt. The rotor bars also have extra mechanical forces exerted on them. Again, if it is necessary, some mechanical brake may have to be applied to hold the machine in position. One plugging stop is generally recognised as being equivalent to around three repetitive normal starts. The motor windings might also have to be specially designed if the application calls for repeated starting and stopping. It is characteristic of a three-phase motor that the amount of current flowing when plugging is applied is almost equal to normal starting current. Also, the starting current flow is applied for almost the same length of time as normal starting. Probably the most common application is in larger production lathes doing repetitive process work. In such an application, a mechanical holding brake might not be needed. Electronic starters equipped with current limiting or ramping circuits can use this system of braking with some success. The inverter circuits can sometimes be reversed in action and the excess generated energy converted to direct current and dissipated by dynamic braking. Normally, it cannot be fed back into the supply source as can be done with a standard regenerative braking system.

7.8  Speed control of a.c. induction motors 7.8.1 Introduction Torque is produced in an induction motor through the interaction of two magnetic fields. The first rotating magnetic field is created by currents flowing in the stator windings. This rotating field cuts the conductors in the rotor and induces a voltage in them. The rotor voltage causes currents to flow in the rotor and produce a second magnetic field. The two magnetic fields interact and cause the rotor to rotate in the direction of the rotating stator field. It accelerates to approximately 96% of the speed of the rotating stator field. This 4% difference in speed on full load is the slip speed. Without slip, an induction motor cannot develop torque. The speed of an induction motor is always governed by the rotating magnetic field in the stator. This stator field always rotates at a synchronous speed governed by two factors:

1. the number of pairs of poles 2. the frequency of the applied voltage.

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The synchronous speed can be found from: 120f ​n = ____ ​   ​​    p where:

n = synchronous speed f = line frequency.

The number 120 is derived from the product of the number of seconds in a minute and the fact that magnetic poles always come in pairs. The other two quantities are called ‘variables’. It is important to note that there are only two variables. If the frequency increases, the speed increases: ​n ∝ f​ If the number of poles increases, the speed decreases: 1 ​n ∝ __ ​    ​​ p These two basic principles are the only factors that can affect the change in speed of an induction motor, although the methods adopted to achieve this are many.

7.8.2  Speed control by changing the number of poles Changing the number of poles in a stator winding always involves an abrupt step change from one speed to another. On a 50 Hz supply, a two-pole motor will rotate at 3000 rpm (ignoring slip speed). If a change is made to a four-pole stator, the speed will quickly change to 1500 rpm. The change in speed can transmit minor transients into the supply lines. With larger motors, a short time delay should be introduced when changing from one winding to the other. The most common method is to design windings that can be interconnected to change the number of poles. It is invariably a 1:2 ratio—that is, a two-pole winding converts to a four-pole winding, or a four-pole to an eight-pole winding, and so on. Figure 7.57(a) illustrates the principle and connections involved for a four-pole to eight-pole conversion. Only one phase is drawn; small rectangles are used to represent pole-phase groups and the arrows indicate the sense of winding direction. It is necessary for the pole windings to be connected in pairs opposite each other as shown. Note that the centre-tap (TA) of the winding has been brought out so that it can be accessed externally. In Figure 7.57(b), the four pole-phase windings have been redrawn in a vertical line. If A1 and A2 are bridged and connected to line L2 and the centre-tap TA connected to line L1, the motor will have four conventional poles, as indicated by the arrows. In Figure 7.57(c) the bridge has been removed. Consequent A1 is reconnected to line L1 and A2 left connected to L1 pole positions A1 A1 line L2. As indicated by the arrows, the current flows N S A1 L2 through all four pole-groups in series and all give the TA S TA N L1 N N same polarity—for example, as shown there would be N N L2 A2 four north poles. A2 A2 TA The magnetic flux is diverted in the stator and exits (b) Convential (c) Consequent (a) Phase A four-pole eight-pole between the north poles, as indicated by the broken connections connections connections lines. The resulting magnetic circuit of the motor is that of an eight-pole machine. Figure 7.57  Series-parallel connection for a two-speed motor 441

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Electrical Principles

To get around this 1:2 ratio limitation, some stators have been designed to accommodate two electrically separate windings. Only one winding is used at a time. These windings need not be in the ratio of 1:2 but can be in any reasonable relationship. For example, one winding could be a two-pole winding, the other a six-pole winding. Activating the two-pole winding would cause the motor to rotate at 3000 rpm. During this period, the other winding, if not connected in star configuration, must have the delta bridges open-circuited to prevent induced currents flowing in the unused winding. When provided with a suitable switch, the windings could be exchanged without stopping the motor or its coupled machine. The motor would then change speed to 1000 rpm. Step speed control with pole amplitude modulation (PAM) is a rather lesser-known system. It was developed for close speed ratios, such as changing a four-pole to a six-pole and an eight-pole to a ten-pole. It relies on the principle of unequal coil groupings within the motor when manufactured. Connections are made with special contactors to control speed steps. PAM windings are covered by copyright but can be manufactured under licence. PAM motors are made as small as 0.5 kW but have been made in sizes up to 7 MW.

7.8.3  Speed control by changing frequency One important aspect of this method of speed control is that, at higher frequencies, the standard induction motor runs at speeds well above the base design value. At increased speeds, air circulation is improved, resulting in improved cooling. Better cooling permits higher current densities to be used, even though there is increased friction and windage losses due to higher speeds. There are also increased iron losses due to the higher frequencies. At higher frequencies, the impedance of the windings is also increased and, to ensure a constant flux density in the air gap, a higher supply voltage is required. At constant flux density in the air gap, torque is proportional to current flow. Since power is dependent on both torque and speed, it can be seen that the power output of the motor increases at a faster rate than the speed increase. Increasing the frequency of a complete plant would ensure all motors ran at a faster speed, and this might not always be desirable. Decreasing the frequency would ensure that all motors ran more slowly, and produce the same undesirable result. In general, frequency changing as a method of speed control is limited to specific machines or groups of machines, as in a series of transport rollers in a steel mill. There are two main methods for frequency changing. The first uses rotating machinery to achieve the desired result. It is expensive, although less efficient than some other methods; but it is extremely reliable, with very few maintenance problems. Therefore, it is still in use. The second method uses electronic switching to synthesise an irregular-shaped alternating current wave from d.c. It is a comparatively new procedure and has become very popular.

7.8.4  Rotating machinery for frequency control One common motor control system is the Schrage motor, where the speed is altered by adjusting the brush positions for each phase. Figure  7.58 illustrates another method for speed control—the Kramer method for controlling the speed of a wound-rotor motor. It can be seen that four rotating machines are used to control the speed of one motor. The system can only be justified economically for extremely large motors or integrated groups of motors in heavy industry. Where Schrage motors have practical limitations, the Kramer system can be built in megawatt ranges. Reliability and minimal maintenance have been well established in both systems.

7.8.5  Wound-rotor motors The slip in any induction motor is proportional to the rotor copper losses. In a wound-rotor motor, the rotor resistance can be varied with the addition of external resistance, so rotor copper losses and speed can be adjusted with a controller. 442

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Because rotor current is proportional to the developed torque, it follows that rotor losses vary with the applied load, thereby affecting the speed. This method of speed control has the characteristic of a variation in speed for a variation in load; that is, increasing the load causes the speed to decrease, while decreasing the load results in a speed increase. For this reason, speed control of a wound-rotor motor by varying the rotor resistance is satisfactory only for a steady load. Speeds lower than half fullload speed are not practical and increased losses at lower speeds lead to high operating temperatures, which might exceed the ratings of the motor. Motor efficiency is poor, speed regulation is poor and the external resistances consume power wastefully. Various methods for speed control have been tried. The two most common are:

Main motor

Synchronous motor

Variable speed set

1. unequal voltages applied to stator windings 2. unequal resistances inserted in rotor windings.

Unlike the rotating machinery systems described above, these speed changes are step changes. Probably the most common application is in the hoist and lowering mechanism of overhead cranes.

Constant speed set

Figure 7.58  Kramer drive using rotating machines

7.8.6  Electronic frequency control The rapid advances made in semiconductor technology have led to much more efficient and effective means of altering mains frequencies. Figure 7.59 shows block diagrams of inverter drives. Figure 7.60 shows a typical control unit for these drives. The three-phase supply is first converted to a d.c. supply. There are at least two possible conversion methods in general use. One is to use a fixed or uncontrolled rectifier circuit and the other is to use a controlled rectifier circuit. Each type of circuit has its advantages and disadvantages.

Uncontrolled rectifiers The output voltage from an uncontrolled rectifier circuit (for example, a bridge rectifier) is governed by the a.c. input voltage. The d.c. output is then fed to a ‘chopper’ circuit whose function is to switch the d.c. on and off at a rate higher than the fundamental frequency of the supply. The on/off action adjusts the average d.c. voltage level supplied to the inverter. M Chopper Figure 7.59(a) shows the approximate square-wave shape of the chopper output. This is then fed through Rectifier Varies d.c. level Filter Inverter a filter circuit to remove as many transients and spikes (a) Uncontrolled rectifier as economically reasonable, and it then becomes the Fixed input to the inverter circuit. frequency M d.c. link

supply

Controlled rectifiers A controlled rectifier circuit such as one using silicon-controlled rectifiers with phase control has the advantages of a fast response, relative cheapness

Controlled rectifier

Filter

Inverter

(b) Controlled rectifier

Figure 7.59  Block diagrams of variable frequency motor drives

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Electrical Principles

and the ability to maintain a regenerative action of feeding power back into the mains. It has the disadvantage of operating at a lagging power factor. Because the d.c. from the controlled rectifier does not have to be fed through a chopper circuit, it tends to be less complicated and is possibly a more efficient circuit. The output is generally filtered before being supplied to the inverter section (see Figure 7.59(b)). To maintain optimum performance of an a.c. motor with a varying frequency supply, it is necessary to maintain the designed magnetic flux conditions in the magnetic circuit of the motor. This is generally achieved by ensuring that the ratio of supply voltage to frequency is kept constant. Any change in frequency must then be accompanied by a change in voltage, that is: V  __ ​​   ​ = k​  f

The actual type of circuit and the control method depend largely on the motor application. A balance has to be selected between the desired factors of speed, torque and power. Other factors are the type of circuits in the unit and whether the final output sends a signal of its own performance to the unit’s input for monitoring and self-adjustment of the unit.

Summary a. The inverter controls the output frequency. b. The motor voltage is set by the d.c. link voltage. c. Other parameters such as current, slip and slip compensation minimum and maximum speeds can be controlled. d. Acceleration and starting current ramps up and down can be controlled. Types of motor speed control are listed in Table 7.2. Table 7.2   Types of motor speed control

Type of motor

Figure 7.60  Typical electronic frequency control unit for an induction motor Courtesy of Rockwell Automation, Inc.

Speed characteristic, no load to full load

Type of speed control

a.c., squirrel cage, multi-speed

Speed drop up to 5% from or two or more initial speeds

Pole changing. Windings of different pole numbers, or reconnect one winding to change the pole number

a.c., squirrel cage, single-speed

Speed drop up to 15%, depending on design

Primary voltage control. Stator frequency control at constant volts per cycle

a.c., slip-ring

Speed drop up to 50%, depending on rotor resistance

Secondary resistor connected to slip-rings. Machine and solid-state conversion feedback of rotor power

a.c., synchronous

No speed drop. Speed set by stator frequency

Adjustable frequency from motor generator set or solid-state frequency converter

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Summary ∙ Schematic circuit diagrams should: – show exactly how a circuit operates – be laid out in a neat and logical manner – show the sequence of events, energy flow or signal flow from left to right and/or top to bottom if possible – use AS/NZS 1102 symbols. ∙ Block diagrams are useful because they: – show what the circuit does – provide an overview of a circuit – are an aid to understanding a circuit – can provide a design starting point for a circuit. ∙ A good, clear wiring diagram should have the following features: – Prominence should be given to the conductors and terminals. – All conductors should be evenly spaced where possible. – Where more than one conductor connects to a terminal, each conductor should be angled to the terminal. – All changes of direction of conductors should be at right angles, if possible. ∙ Relays and contactors are both electromagnetically operated switches: – A contactor is used in a power circuit. – A contactor can have both power and control contacts. – Both contactors and relays consist of an operating coil, a magnetic circuit and associated contacts. ∙ There are various types of contacts controlled by contactors and relays. Some of these are: – normally open – normally closed – timed on closing – timed on opening – timed on both closing and opening. ∙ In motor control schematic circuit diagrams, the control circuit is drawn in lighter lines than the power circuit. ∙ In detached representation in schematic circuit diagrams: – The contactor coil is designated with both the contactor designation and the number of contacts it operates. – The coil designation, for example, K1/3, may be placed on or beside the coil symbol. – Each contact has the designation of the contactor and a number usually representing its importance or its order of operation, for example, K1.1. ∙ In push-button switch control: – Extra start push-button switches are all placed in parallel. – Extra stop push-button switches are all placed in series. ∙ Control by some automatically operated switches is termed ‘two-wire control’.

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Electrical Principles ∙ When reversing contactors are used: – they are mechanically interlocked – they are also electrically interlocked in the control circuit. ∙ A jogging control will allow the circuit to be energised only while it is held depressed. ∙ When drawing schematic circuit diagrams, the top-to-bottom and left-to-right rule should be followed, when possible. ∙ Control diagrams are usually drawn as ladder diagrams. In these: – the ladder stiles are the supply lines – the ladder rungs are the various circuit lines. ∙ A motor starter is intended to start and protect the motor it controls. ∙ A starter limits starting currents, monitors any overloads and stops or isolates the motor if necessary. ∙ There are several methods for limiting starting currents: Direct on line

Line voltage starting

Star–delta

Reduced voltage starting

Primary resistance

Reduced voltage starting

Autotransformers

Reduced voltage starting

Electronic

Reduced voltage starting

Line voltage starting. Resistor in rotor circuit Secondary resistance ∙ Each starting method has its own advantages. ∙ Starting torque varies with each starting method. ∙ Alternating current starters can be manual, push-button or automatic. ∙ Three-phase motors are always reversed by reversing the phase rotation, i.e. reversing any two lines. ∙ Three-phase motor braking methods are: – mechanical—friction with brake shoes; the only holding method – dynamic—electrical energy dissipated in resistance; includes eddy-current discs – regenerative—converts mechanical energy to electrical energy and returns it to the supply source – plugging—full reversing power applied; power to be removed when motor stops. ∙ The speed of a three-phase motor can be controlled by changing the number of poles in the windings or by changing the line frequency. ∙ The number of poles can be changed by altering winding connections or by having more than one winding. The general principle is to convert the alternating-current supply to direct current, which is then fed through a filter to remove most of the transients. The d.c. is then supplied to an inverter to convert d.c. back to a.c., using a high-speed switching sequence. ∙ Wound-rotor motors are only partially adaptable to speed control with external resistors. They have poor performance and efficiency. ∙ Direct current motors are generally started by inserting resistance in series with the armature. The resistance is gradually reduced as the motor accelerates and current decreases. ∙ Voltage control as a means of controlling starting currents is usually available only in selected motors. Extra equipment is needed. ∙ Direct current motor starters can be manually or push-button operated. Full automatic starting and stopping is available with special starters.

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Develop and connect electrical control circuits  Chapter 7 ∙ Acceleration, torque and starting currents can be controlled with timed relays, voltage-sensitive relays and electronic control. ∙ Direct current motor rotation can be changed by reversing the current flow through the fields or the armature—but not both. ∙ Interpole fields must not be altered once correctly connected. ∙ It is usual to reverse armature current on larger motors to change the direction of rotation, rather than alter field connections. ∙ Direct current motor braking is usually by dynamic braking backed up by mechanical braking. ∙ Regenerative braking is an economic proposition only for very large inertial loads, for example, electric trains. It has to be supplemented with other types of braking. ∙ Diesel-electric trains use dynamic braking because they operate on their own generated supply. It is the most common form of electrical braking for all machinery. ∙ Plug braking is not recommended for d.c. motors unless special equipment or special motors are used. ∙ Automatic control of electrical equipment is attained with programmable logic controllers that are pre-programmed to make decisions based on signals conducted to them by transducers.

Questions Exercises 7.1 When switching a large current or voltage, what is the advantage of using a relay or contactor rather than an ordinary switch? 7.2 Name the four parts of a basic relay circuit. 7.3 Name the International Standard that relates to electrical drawing convention. 7.4

Draw the schematic circuit diagram symbols for the following: (a) fuse (b) relay coil (c) timer contact—delayed on closing after energisation (d) ammeter

7.5 What is the convention for representing the flow of energy, or flow of ‘signal’ and sequence of operation or events, that was adopted to make schematic circuit diagrams easier to read? 7.6 What is the main difference between a circuit diagram and a wiring diagram? 7.7 Briefly state what a block diagram of an electrical circuit represents. 7.8 Name the three basic parts of a contactor. 7.9 Explain the operating principle of a contactor. 7.10 To provide two-position control in a control circuit, how are (a) the two ‘stop’ push buttons connected and (b) the two ‘start’ push buttons connected? 7.11 Draw a detached control circuit showing two ‘start’ and two ‘stop’ push-button switches, plus the maintaining/ holding contact. 7.12 Explain what is meant by ‘jogging control’. 7.13 How is a three-phase motor’s direction of rotation reversed by electrical means?

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Electrical Principles 7.14 Name two types of interlocks. 7.15 State an application for ladder diagrams. 7.16 State two general types of control allowed by control devices. 7.17 Name five common types of switches that are used as control devices. 7.18 Name five factors that must be taken into consideration when selecting control devices. 7.19 Define a transducer. 7.20 Why is a direct online starter (DOL) not suitable to start large induction motors? 7.21 Why is a star–delta starter referred to as a ‘reduced-voltage’ starter? 7.22 Explain why the starting torque in a star–delta starter is 33% of full-load torque. 7.23 Briefly describe the main advantage of using a primary resistance starter rather than a DOL starter. 7.24 List the five major characteristics of an autotransformer starter. 7.25 Name a major advantage of using a soft starter rather than reduced-voltage starters. 7.26 Name five refinements that a soft starter can control, compared to a reduced voltage starter. 7.27 Name a major advantage of a secondary resistance starter (wound rotor motor). 7.28 Explain the operation of a DOL starter, as in Figure 7.46. 7.29 Name the five major types of three-phase motor braking. 7.30 Explain how mechanical braking is accomplished. 7.31 Explain the operation of eddy current disc braking. 7.32 Explain the principle of dynamic braking. 7.33 Explain the principle of regenerative braking. 7.34 Explain the principle of plug braking. 7.35 Explain how torque is produced in an a.c. induction motor. 7.36 The stator field rotates at synchronous speed. State the two factors that govern the synchronous speed.

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Reference section

8

CHAPTER OBJECTIVES • • • • • • • • • • •

understand the SI system of units use SI base units in calculations and in deriving other units use derived units and recognise that they are built from base units recognise the purpose of multipliers and sub-multipliers use multipliers and sub-multipliers in calculations use engineering notation in calculations transpose typical electrical formulas understand the concepts of work, energy and power as applied to electrical and mechanical calculations recognise and use scalar and vector quantities use Pythagoras’ theorem and trigonometry in solving basic right angle triangle problems understand the purpose of typical types of graphs and charts, and be able to read and interpret simple graphs.

Resources • Periodic table

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Electrical Principles

8.0  Introduction To understand electrical principles, it is necessary to understand mechanical principles. This in turn requires an appreciation of a system of units—in the case of Australia and New Zealand (and many other countries), the units of the SI system, formally called the ‘Système international (d’unités)’ but better known as the ‘metric’ system. Electricians often need to manipulate mechanical, as well as electrical, values to come up with a method of wiring or repairing an electric circuit. An understanding of graphs, methods of graphical solution and trigonometry is required, as is knowledge of the relevant mathematical processes. This chapter gives a working understanding of the units of measurement, mathematical processes and simple mechanics that are used by electricians.

8.1   Mathematics, numbers and units In school, maths starts by concentrating simply on numbers and then evolves to manipulating values such as length, weight and time. These concepts are progressively built upon, and eventually algebra’s use in the applied maths in electrotechnology comes into focus. Having a good grasp of school-level mathematical concepts will be useful in getting the most from the content in this chapter.

8.2  SI units The international metric system consists of seven base units, two supplementary units and many derived units. Australia legislated to use the metric system in the early 1970s, and the Australian Standard is defined in AS ISO 1000-1998.

8.2.1  Base units Base units are not formed from other units, although the SI system defines them as having specific dimensions which are derived from physical constants. Much of the maths used by electricians works with these base units and the derived units.

Length—the metre The original ‘metre’ was intended to be the distance from the equator to the Pole divided by 10 000 000. However, the metre is now defined as being equal in length to 1 650 763.73 wavelengths in a vacuum of the orange–red line spectrum for the isotope krypton-86. To make it easier for non-scientists to understand, there is a prototype ‘metre’ in France which is a length of platinum bar which (at standard temperature and pressure) is exactly one metre long.

Mass—the kilogram The kilogram was first defined as the amount contained in 1 litre of pure water at 0°C. It is now defined as the mass of a particular piece of platinum (another prototype) stored under special conditions in France. Although ‘weight’ is usually measured in kilograms, weight and mass are not the same. Weight is the force caused by the mass of the body. 450

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Reference section  Chapter 8

Time—the second A second is an interval of time corresponding to 9 192 631 770 oscillations of a caesium-133 atom. As this is clearly impractical to use as a measure, time is now synchronised to atomic clocks around the world.

Electric current—the ampere An ampere is the current flowing in each of two parallel conductors of infinite length and negligible cross-section which, when separated by a distance of 1 metre in free space, produces a force equal to 0.000 000 2 newtons per metre length of conductor, between those conductors.

Temperature—the kelvin A kelvin is the unit of temperature equal to ​1/273.16​of the triple-point temperature of water. One degree Celsius is equal to one kelvin, but 0°C is 273.16 kelvin. The kelvin is used for absolute temperature measurements on the basis that absolute zero is the temperature of a mass with absolutely no energy; this is zero kelvin or −273.16°C.

Luminance—the candela Candela (cd) is defined as the luminous intensity in a given direction of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and has a radiant intensity in that same direction of 1​ /683​watt per steradian (unit solid angle).

8.2.2  Supplementary units Amount of a substance—the mole A chemical substance containing 6.02214076 × 1023 constitutive particles including atoms, molecules, ions and electrons, is defined as one mole of that substance

Plane angle—the radian A radian is the angle between two radii of a circle which mark off on the circumference an arc equal in length to the radius of the circle. By the formula for circumference, there are two 3-pi radians in a circle, and therefore ‘2π’ appears in many of the formulas that electricians learn. One radian is equal to 360 degrees divided by 2π or ∼57.3 degrees. Scientific calculators work in degrees or radians.

Angular area—the steradian This is the area on the surface of a sphere which is bound by two 1-radian arcs perpendicular to one another. This unit is used in defining the radiation of light and other radiating quantities.

8.3  SI derived units The seven base units cannot cater for all situations that arise in measurement. Many situations require units that are derived from the three basic units of length, mass and time. The units used in this book can be subdivided into three groups: mechanical, electrical and magnetic (but there are many more derived units described in AS ISO 1000).

8.3.1  Mechanical derived units Volume—the litre The unit of volume is based on the cubic metre, which is a large unit for most applications. For liquid measures involving smaller quantities, the litre is used. One cubic metre equals 1000 litres. The litre in turn has its submultiples such as the millilitre (mL)—1000 mL = 1 litre. 451

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Electrical Principles

Force—the newton A newton is the force which, when applied to a mass of 1 kilogram, causes an acceleration of 1 metre per second.

Pressure—the pascal This is the pressure that occurs when a force of 1 newton is applied to an area of 1 square metre.

Energy and work—the joule When a force of 1 newton is applied to a mass, causing it to move a distance of 1 metre, the work done (or energy expended) is 1 joule.

Power—the watt A watt is the power used when energy is expended at the rate of 1 joule per second.

Temperature—degrees Celsius The temperature expressed in degrees Celsius (°C) is equal to the temperature expressed in kelvins (K) less 273.16. The interval of one °C is identical to one kelvin. Absolute temperature is not called ‘degrees kelvin’ but simply ‘kelvin’ (K).

Angular velocity—radians per second There are 2π radians in one revolution. Angular velocity (or the speed of rotation) is traditionally measured by revolutions per minute (rpm), which is accepted as an Australian Standard. In engineering and scientific calculations, radial velocity is measured in radians per second (rad/s). Table 8.1   SI base quantities and units Quantities

Units

Physical quantity

Symbol

Name

Symbol

length

l

metre

m

mass

M

kilogram

kg

time

t

second

s

electric current

I

ampere

A

temperature

T

kelvin

K

luminous intensity

I

candela

cd

mole

mol

radian

rad

plane angle

θ

degrees

°

area

A

square metre

m2

capacitance

C

farad

F

density

ρ

kilogram/cubic metre

kg/m3

diameter

d

metre

m

efficiency

η

per cent

%

electric current

I

ampere

A

SI-derived quantities and units (selection)

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Reference section  Chapter 8

Quantities

Units

Physical quantity

Symbol

Name

Symbol

electric potential

V

volt

V

electrochemical equivalent

z

kilogram/coulomb

kg/C

energy

W

joule

J

force

F

newton

N

frequency

f

hertz

Hz

frequency (angular)

ω

radians/second

rad/s

heat capacity

C

joules/kelvin

J/K

illuminance

E

lux

lx

inductance (mutual)

M

henry

H

inductance (self)

L

henry

H

impedance

Z

ohm

Ω

luminance

L

candela/sq. metre

cd/m2

luminous flux

F

lumen

lm

luminous intensity

I

candela

cd

magnetic field strength

H

amperes/metre

A/m

magnetic flux

Φ

weber

Wb

magnetic flux density

B

tesla

T

magnetic reluctance

Rm

ampere turns/weber (/henry)

/H

magnetomotive force

Fm

ampere/turn

A

mass

m

kilogram

kg

number of poles (in a machine)

p

poles

p

number of turns

N

turns

t

permeability (actual)

μ

henry/metre

H/m

permeability (absolute)

μ0

henry/metre

H/m

permeability (relative)

μr

(ratio)

μ/μ0

permittivity

ε

farads/metre

F/m

power (apparent)

S

volt ampere

VA

power (reactive)

Q

volt ampere reactive

var

power (true)

P

watt

W

power factor

PF

(ratio)

cosθ

pressure

P

pascal

Pa

quantity of charge

Q

coulomb

C

radius

r

metre

m

reactance

X

ohm

Ω

(continued) 453

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Electrical Principles

Quantities

Units

Physical quantity

Symbol

Name

Symbol

resistance

R

ohm

Ω

resistivity

ρ

ohm metre

Ωm

rotational speed

n

revolutions per minute

r/min

solid angle

ω

steradian

sr

slip

s

per cent

%

specific heat capacity

C

joules/kg.kelvin

J/kg.K

temperature (absolute)

T

kelvin

K

temperature (customary)

t

degrees Celsius

°C

time

t

second

s

time constant

τ

second

s

torque

T

newton metre

Nm

transformation ratio of a transformer

K

–

–

turns

t

–

–

turns ratio of a transformer

n

–

–

volume

V

cubic metre

m3

work

W

joule

J

8.3.2  Electrical derived units Quantity of electric charge—the coulomb A coulomb is the quantity of electric charge that is nominally equal to 6.24 × 1018 electrons. The one-time definition of the ampere was a current of 1 coulomb per second or 6.24 × 1018 electrons passing a point in 1 second.

Potential difference—the volt A volt is the potential difference existing between two points on a conductor carrying a current of 1 ampere when the power dissipated is 1 watt.

Resistance—the ohm The ohm is the value that allows 1 amp to flow when a potential difference of 1 volt is applied to a circuit of 1 ohm resistance.

Power—the watt A watt is the power used when energy is expended at the rate of 1 amp per volt or 1 joule per second.

Frequency—the hertz A hertz is the number of periodic oscillations per second (frequency). Frequency was once known as ‘cycles per second’ or ‘c/s’. 454

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Reference section  Chapter 8

Capacity—the farad A farad is the measured capacity that exists between two plates of a capacitor when a charge of 1 coulomb causes a potential difference of 1 volt.

8.3.3  Magnetic derived units Inductance—the henry An inductance has a value of 1 henry when an electromotive force (EMF) of 1 volt is produced by a current changing uniformly at a rate of 1 ampere per second.

Magnetic flux—the weber A weber is the magnetic flux that, when reduced to zero at a uniform rate in 1 second, produces 1 volt in a conductor. The weber was once defined as a unit of 108 lines of force.

Magnetic flux density—the tesla The tesla is the magnetic flux density of 1 weber per square metre.

8.3.4  Scientific notation When dealing with very large or very small numbers, the standard number system becomes too hard to work with— numbers like 0.0000000301 or 6060842000000 are difficult to calculate, either manually or with a calculator. Scientific notation is a system that represents these numbers differently. The magnitude of the number is converted into an exponent, and the value of the number (sometimes referred to as the ‘mantissa’) is expressed with one digit before a decimal place. For example, the number 6060842000000 expressed in scientific notation would be: 6.060842 × 1012—the exponent 1012 means that the number is 1 000 000 000 000 multiplied by the mantissa or the decimal point is moved 12 places to the right. A similar rule applies to small numbers like 0.0000000301, which would be: 3.01 × 10−9—the exponent 10−9 means the mantissa is multiplied by 0.00000001 or the decimal point is moved nine places to the left. Variations in calculators make it important to understand how individual models manage scientific notation. For example, the exponent key may have ‘EXP’ on it, or it may have ‘10x’—it depends on the calculator. There are a couple of popular brands, and tutors can help with advice on purchases. The advantages of using scientific notation include representing very large or small numbers more easily as well as its direct use in calculations. The use of significant figures generally means scientific notation uses no more than three or four digits in the mantissa.

8.3.5  Engineering notation Engineers and tradespeople often need to talk about the numbers they use, perhaps when buying components and making installation decisions. Scientific notation is cumbersome for use in language, so engineering notation is used instead. In engineering notation, the whole numbers are not 1 to 9 as in scientific notation, but 1 to 999, and the exponent is given in multiples of three—103, 106, 109, etc. These are also given names that are easy to remember and in fairly common usage, such as 103 = kilo, 106 = mega and 109 = giga. Table 8.2  Engineering notation Tera (T)

Giga (G)

Mega (M)

kilo (k)

Units

milli (m)

micro (μ)

nano (n)

pico (p)

Engineering notation

1012

109

106

103

100

10−3

10−6

10−9

10−12

Exponential notation

E12

E9

E6

E3

E0

E –3

E –6

E –9

E –12

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Electrical Principles

8.3.6  Using multiples and sub-multiples The words used before a unit are known as ‘multiples’ and ‘sub-multiples’. (To get the most from this book, try to memorise the multipliers in Table 8.2.) To get used to using them, it is helpful to start by using familiar values. Thinking about, for example, how many millimetres are in a metre or how many metres are in a kilometre makes the leap to thinking about milliamps less daunting.

EXAMPLE 8.1 How many metres would a person have to walk to cover 2.37 kilometres? The term ‘kilo’ means ‘thousand’, so 2.37 kilometres is the same as 2.37 thousand metres or 2370 metres.

EXAMPLE 8.2 How many farads are there in 125 picofarads (125 pF)? From Table 8.2, it can be seen that there are 1 000 000 000 000 picofarads in one farad. Therefore: 125/1 000 000 000 000  =  0.000 000 000 125 farads. The convenience of the former figure of 125 pF is self-evident. ‘125E-12’ would be entered into a calculator.

8.4  Transposition The ability to work with transposition is vital in dealing with formulas and doing calculations. Transposition is used when the maths is algebra—letters are used to represent numbers so formulas can be made. There is a useful acronym that represents the order in which mathematical functions are dealt with. It is usually written as ‘BODMAS’, which stands for Brackets Order Division, Multiplication, Addition and Subtraction. Sometimes, however, it is written as BOMDAS, which demonstrates the fact that it makes no difference whether Multiplication is tackled before or after Division. Also, it makes no difference whether addition or subtraction is completed first. With multiplication and division, and with addition and subtraction, work from left to right. Both forms of the acronym are used in this book.

TRANSPOSITION 8.1 The acronym BODMAS is the order of functions in simple maths: B = Brackets (X), {X }, [X   ] ,  _____

O = Order √ ​  X, ​X​​  5​ ​  X  D = Division X ÷ Y, __ ​   ​    ​​                 ​  ​  ​ Y​ ​ ​  ​​​ M = Multiplication X × Y A = Addition X + Y, X − (− Y), sum(X )  , Σ X S = Subtraction X − Y, − X, X + (− Y ) 456

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Reference section  Chapter 8

The reason that multiplication and division (as well as addition and subtraction) can be completed in any order is because they are, in fact, special cases of each other. That is to say that a division can be written as a multiplication with some slight changes. This is true of addition and subtraction too.

TRANSPOSITION 8.2 Divide is a special case of Multiplication . . .

X 1 __ ​​   ​  =  X ÷ Y = X × ​ __  ​ = X × ​Y​​  −1​​ Y

Y

Subtraction is a special case of Addition . . .

​X − Y = X + (− Y )​

Therefore, the priority of operations is Brackets, Order then Multiplication/Division and finally Addition/ Subtraction. This means that Subtraction has the same importance as Addition, and Division has the same importance as Multiplication.

TRANSPOSITION 8.3 BODMAS defines the order of operations. D A ​B > O > __ ​    ​ > __ ​   ​​  M S

Proficient use of BOMDAS brings the ability to deal with all of the formulas in electrical trade studies. Consider the effect brackets have in this calculation.

TRANSPOSITION 8.4 Importance of Brackets . . . (4 × 3 − 2 + 1) = 11

(1)

4 × 3 − (2 + 1) = 9 (2) ​​    ​  ​  ​  ​  ​​​ 4 × (3 +  2 )  − 1 = 19 (3) 4 × (3 + 2 − 1) = 16

(4)

Not understanding the meaning of the brackets can lead to difficulties. Maths works from left to right, so functions of equal priority are dealt with in order. 457

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Electrical Principles

A formula is like a recipe for how to solve a particular problem. When the method is known, somebody writes a formula so that another person can find the answer by simply putting their own figures into the formula and doing the maths. Named variables are used instead of numbers, so the formula is easier to learn. To avoid writing a new formula for each variation of the same problem, a formula is written for the most common case and is transposed when a different variable needs to be found. For example, the most common formula in the electrician’s trade is Ohm’s Law (see Chapter 1), which can be written as V = IR or E = IR. V is typically used to express voltage (although E is sometimes used to express a source of voltage).

EXAMPLE 8.3 The formula associated with Ohm’s Law is: ​​V​  =​  I × R​ 

(1)​​

Consider the calculation using the values: V = 12

(2)

I=4 (3) ​​​​           ​  ​  ​  ​  ​  ​​​ R=3 (4) ∴ 12 = 4 × 3

(5)​

Transpose the formula to find I: V I = __ ​   ​  (6) R ​​     ​  ​  ​  ​  ​​​ 12 ∴ 4 = ___ ​   ​  (7) 3 Transpose the formula to find R: V R = __ ​   ​  (8) I ​​     ​  ​  ​  ​  ​​​ 12 ___ ∴ 3 = ​   ​  (9) 4 Note that the two sides are equal in each case.

Transposition works by the principle that the two sides are equal and must always remain so. Two common methods of ensuring that they do are:

1. Do the same operation to both sides—if a number is added to one side, it must be added to the other side. The same goes for multiplication, division, substraction, squaring or even using Sine, Cosine and Tangent. 2. Change sides, change signs—meaning, a number can be moved from one side of an equation to the other by taking the inverse of it on both sides. For example, to move +8 from the right to the left hand side, you would subtract 8 from both sides.

Remember, however, to follow the rules of BOMDAS: do not take a number out of a bracket, for example—do the calculation between the brackets first, when possible. In Example 8.4, in line (10) a squared number on the right can be balanced by taking the square root of the left side. Lines 12–15 show the same process for a more complex equation. The end result being that x is left on its own. 458

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Reference section  Chapter 8

EXAMPLE 8.4 The following are examples to demonstrate transposition. In each, find x: Treat each side the same: z = x + y (1) z − y (2)​​​ ​​         ​  =​  x + y − y ​  ​  ​  ∴ z − y = x (3) or change sides—change signs: z = x + y (4) ​​     ​  ​  ​  ​  ​​​ ∴ z − y = x (5) . . . as above . . . z = x × y

(6)

∴ z ÷ y = x × y ÷ y (7) z ___ xy __ (or )   ​    ​​  =​  ​  ​   ​ ​  ​  ​  (8)​​​ ​​             y y z ∴ ​ __  ​ = x (9) y Note: if z = x2 __ ∴√ ​  z ​  = x

______

(10) (11)

√

if z = ​ x  2 + y2 ​  (12) ​​                       ​ 2 ​  ​ 2​  ​ 2 ​  ​​​ ∴ z = x + y (13) ∴ z2 − y2 = x2 ______

√

2

2

∴ ​ ​z  ​​  ​ − ​y​​  ​ ​  =x

(14) (15)

8.5  Energy, work and power Energy, work and power are not the same thing. Energy is the ability to do work, work is the energy that is expended and power is the rate of doing work or expending energy. Work can also be described as the process of converting energy from one form into another. For example, converting the chemical energy of fuel into the heat energy required to drive a steam turbine is a form of work, and the speed with which the heat is generated defines the power. ​energy = work = power × time​ There are many formulas for energy, not just in the electrical and mechanical contexts but also in the chemical and nuclear contexts (and many others). One common mechanical formula calculates the work involved in moving an object a known distance by using a known force. When a body is moved through a distance by a force acting on it, work is done. That is, if a force of F newtons acts through a given distance, then: ​Work = F × d [ joules]​ 459

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Electrical Principles

EXAMPLE 8.5 A force of 100 N is required to move a box 5 m along a horizontal surface. Find the value of work done. ​work = F × d = 100 × 5 = 500 J​ Power is the rate of doing work. It can be found by dividing the work value by the time in seconds and is expressed in units as J/s = W (watts): work  ​power = ____ ​   ​​   time

EXAMPLE 8.6 If the box in Example 8.5 was moved first in 10 s and later in 5 s, calculate the power used in both cases. work  ____ 500  power = ____ ​   ​   = ​   ​  = 50 W  time 10 ​​    ​  ​  ​ ​​ work  ____ 500  power = ____ ​   ​   = ​   ​    = 100 W​  time 5 The potential to do work can be found from power multiplied by its time of application, that is: energy = power × time work but power = ____ ​   ​  time

work ∴ energy = ​ ____ ​   ​ ​ × time ​​                ​  ​  ( time ​ )  ​​ ​ ​​ but work = F × d F×d ∴ energy = ​ _____ ​   ​ ​× time ( time ) ∴ energy = F × d [ joules]

8.5.1 Torque

Torque is a force applied at some distance from the centre of a rotating mass with the effect that the mass will rotate unless an equal and opposite torque is simultaneously applied. Common examples of torque are tightening a nut with a spanner or turning the steering wheel of a car. If insufficient force is applied, these items will not turn, yet a torque has been applied. The actual value of torque is due to two factors—the applied force (newtons) and the lever arm length or radius (metres) from the axis of rotation.

Torque = Force × Radius

Figure 8.1 Torque

​ T = Fr (Nm—newton metres )​ where: T = Torque F = Force in newtons r = distance from the axis of rotation to the point where force is being applied, in metres When the torque does result in rotation, the force is now acting over a distance so work is being done. For mechanical machines where the movement is of a rotational type, the distance covered depends on the radius as well as the speed of rotation. So the distance covered must be calculated from the radius, and this is where the unit ‘radian’ is used. Because the radian is a ratio of the radius to the circumference, the calculation can neglect the radius and use the rotational speed instead. Since speed is a rate

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Reference section  Chapter 8

of rotation or the rate of doing work, power is calculated directly from the rotational speed (n) multiplied by the number of radians in a circle (2π) and torque (T): ​P = 2πnT​

ius

rad

57.3°

rad

Length of arc = radius

ius

but as the rotational velocity is 2πn: ​P = ωT​

In physics, engineering and electrical work, angular velocity is Figure 8.2  The radian expressed in radians per second (rad/s or rad.s−1). A radian is the angle subtended by an arc which is equal in length to the radius, where: ​angle θ = 1 radian​ and r = radius = length of arc. Since the circumference C is found from C = 2πr, it follows that there are 2π radians in one complete revolution: ∴  360° =  2π radians 360°  ​ ​​   ​​ ∴ 1 radian = ​ ____      ​ = ∼57.3°  2π The angular velocity (2πn or 2πf) is often denoted by a lower-case omega, ω: ​∴ ω = 2πn or ω = 2πf​ From this, the rate of doing work (power) for a rotating body is found: ​P = 2πnT = ωT​ where:

P = power in watts n = revolutions per second (r/s) T = torque in newton metres (Nm)

Rotational speed is often given as rpm (r/min) rather than  rad.s−1. Therefore, rpm must be divided by 60 to convert rpm to rad.s−1.

EXAMPLE 8.7 A force of 150 N is applied to the end of a spanner 0.4 m long to tighten a nut. Calculate the torque applied to the nut. ​Torque = Fr = 150 × 0.4 = 60 Nm​

EXAMPLE 8.8 Find the torque exerted by a 3 kW electric motor operating at 1440 rpm. P = ωT = 2πnT ​​    ​  ​   ​​​ 3 kW = 3000 W that is, 3000 = 2 × π × 1400 × T/60 3000 × 60  ​∴ T = ​ _________ ​  = 20.46 Nm​ 2π × 1400 461

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Electrical Principles

8.5.2  Losses in a machine The electric motor in Example 8.8 is rated at 3 kW. The motor is said to have a nominal output of 3 kW, which is not a real indication of the energy delivered to it. In both mechanical and electrical systems, there are losses that can have an important bearing on the operation of the system. The major losses are friction and windage, while other losses such as copper and iron losses must also be accounted for. Extra power has to be supplied to a system to compensate for these losses. Therefore, the power into a system is the sum of the power out plus losses. ​​P​  in​​ = ​P​  out​​  +  Losses​ or ​​P​  out​​ = ​P​  in​​  −  Losses​ This can be expressed as the ratio of the power output to the power input as a percentage, which is called the ‘efficiency’ of the system. The usual symbol for efficiency is η (eta, pronounced ‘eeta’) and is expressed as a number followed by the per cent symbol, e.g. ‘efficiency = 89%’ or ‘η = 89%’. As efficiency is a ratio, it has no units: ​η = (​P​  out​​  ×  100)/ ​P​  in​​%​

EXAMPLE 8.9 If a device has a power input of 160 W and a power output of 120 W, find the efficiency and the loss (W). power output  efficiency = ___________ ​       ​  × 100  power input ​​     ​  ​   ​​​ 120 ∴ efficiency = ____ ​   ​  × 100 = 75% 160 The loss is the difference between the power output and input, and in this example is 160 − 120 = 40 W loss.

EXAMPLE 8.10 Find the efficiency of the electric motor in Example 8.8 if the losses are found to be 357 W. input power = 3000 + losses = 3357 W output power = 3000 W (motor rating ) ​​          ​  ​   ​​ ​ ​ 3000  η = _____ ​   ​   × 100 = 89.4%  3357

8.6  Scalar and vector quantities All quantities can be classified as being either ‘scalar’ or ‘vector’, according to these two rules: 1. Scalar quantities are those which have magnitude but no direction (e.g. mass, volume, energy and time). 2. Vector quantities are those which must be expressed in both magnitude and direction (e.g. velocity, acceleration and force). 462

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Reference section  Chapter 8

It is easier to understand the terms ‘scalar’ and ‘vector’ when thinking of mechanical quantities, but these quantities also occur in electrical theory. Vectors, when applied to electrical systems, are called ‘phasors’, but the basic principles are the same as for mechanical vectors.

Point of application Mass (object)

Force Magnitude

Direction and sense

Figure 8.3  Characteristics of a force

8.6.1  Scalar quantities A number and a unit are sufficient to specify many physical quantities. These quantities can be added by ordinary arithmetic. For example, 5 seconds + 3 seconds = 8 seconds, or 1 km + 2.6 km = 3.6 km. Vector quantities acting in the same direction can also be treated as scalar quantities and ordinary arithmetic applies. Scalar quantities may be drawn as a straight line proportional to their magnitude, and negative values may be drawn on the same line but in the opposite direction. For example, a person is given $110, but owes $60 for a speeding fine. They can draw a line 110 mm to the right, and then from the end of that line draw another line 60 mm to the left—they will have 50 mm left, telling them they have $50 available for cheering themselves up after getting the fine. This is a graphical means of calculating the addition of two scalar quantities.

8.6.2  Vector quantities Unlike scalar quantities, vector quantities cannot be satisfactorily described without giving a direction as well as a  quantity and a unit. A vector quantity can be represented by a straight line which, when drawn to a scale, is able  to  represent both magnitude and direction. In mechanics, the vector quantity is often a force. Weight is a special case of force. The unit ‘kilogram’ is used to measure mass, while the unit ‘newton’ is used for force and weight. It is convenient for the purpose of this work to use force as a means of examining methods for solving vector problems. The characteristics of a force are shown in Figure 8.3. The force has both a magnitude and a direction, and also a point of application and a sense of direction.

8.6.3  Forces acting at a point Where more than one force acts on a body simultaneously, the forces can assist or oppose one another. Cyclists are familiar with tail winds and head winds, but the problem is more complicated with a wind blowing from neither of these directions. The cyclist then has to lean ‘against’ the wind to continue on a desired path, a situation usually associated with turning. A similar situation exists with a car in a crosswind. The steering wheel has to be held at an angle to counteract the side forces. In effect, the car is actually being steered across the road to counteract the side force, so that the resultant motion is straight along the road. The resultant value of two forces acting on a body depends on the angle between the directions of the forces, as well as their respective magnitudes. In Figure 8.4(a), F1 is added directly to F2 as a straight arithmetical addition and the resultant force is F1 + F2 (i.e. riding with a tail wind). Similarly, in Figure 8.4(b), the forces are in opposition and the resultant force is F1 − F2 which will act in the direction of the larger force (i.e. riding into a head wind). In Figure 8.4(c), the simple arithmetical process cannot be used. The combination of F1 and F2 gives a resultant force FR acting in a direction between F1 and F2. The strength of the force is a value somewhere between the larger of the two forces and the sum of the two.

8.6.4  Forces acting at 90° In a special case where F1 and F2 are acting at right angles to each other, the value of the resultant force can be derived mathematically by Pythagoras’ theorem. 463

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Electrical Principles

F1

F2

F1

FR

(a)

(b)

F1

FR

F2

(c)

FR

F2

FR

F2

F1

Figure 8.4  Two forces acting on a body

The right angle triangle method can be used to analyse the effects of two forces acting at 90° to each other. One of the best-known examples is the triangle with sides in the ratio of 3:4:5. It can be seen from Figure 8.5 that the square on the Hypotenuse (52 = 25) is equal to the sum of the squares on the other two sides:

Pythagoras’ theorem Hyp2 = A2 + B2 i.e. 52 = 32 + 42

3

5

​​3​​  2​  + ​4​​  2​= 9 + 16 = 25​

4

that is, ​​5​​  2​ = ​3​​  2​  + ​4​​  2​​ ______

Figure 8.5  Pythagoras’ theorem

​or h = √ ​  ​a​​  2​  + ​b​​  2​ ​​  

EXAMPLE 8.11 Two forces (F1 and F2), each of 25 N, act at right angles to each other on a body. Determine the value of the resultant force (FR) acting on the body. ______

√________

​F​  R​​ = ​ ​F   ​  21​ ​  + ​F​  22​ ​​    ​​

√

​ = ​ ​2   5​​  2​  + ​25​​  2​ ​  ________ ​ ​         ​   ​ ​ ​​  =​  ​√625 +    625 ​ _____

​ = ​√1250 ​     ​ = 33.35 N

F1 = 25 N F2 = 25 N

Force diagram

F1

F1

FR

FR

Parallelogram method

Polygon method

F2

F2

Pythagoras’s theorum: FR = F12 + F22 = 35.35 N

Figure 8.6  Force diagrams for Example 8.11

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Reference section  Chapter 8

This method can only be used when the forces act at an angle of 90° to each other.

EXAMPLE 8.12 With the aid of trigonometry and a calculator, solve the unknown values of the sides in this triangle.

Ø = 55°

Ø

adj = 37.6 mm

Adjacent

Hy

po

te

nu

se

Opposite adj & cos 55° = 0.5736 cosØ = ——— hyp By transposition: adj hyp = ————— = 37.6/0.5736 cos 55° = 65.55 mm (hyp) opp & tan 55° = 1.428 tanØ = ——— adj By transposition: opp = tanØ x adj = 1.428 × 37.6 = 53.7 mm (opp)

8.6.5  Parallelogram method In the parallelogram method, the two forces are drawn to scale from a point of application in the direction of application. Lines are drawn from the ends of each force, parallel to the other forces, completing the parallelogram. The resultant force is then drawn from the point of application to the intersection of the parallel lines. This method is also known as the ‘graphical’ or ‘vector diagram method’ of solution. It can be used to solve both the magnitude and direction of resultant forces, irrespective of the direction of the separate forces. The only limitation is the draftsperson’s accuracy of scale and angle. In Figure 8.7, two forces F1 and F2 act on the point O as indicated by their arrowheads. OA and OB are drawn to scale at the appropriate angles to each other. a.c. is drawn parallel to OB and BC is drawn parallel to OA so the two lines cross. The resultant of the two forces is OC, drawn from O to the point C. The value of FR is taken from the scale to which the figure is drawn. Probably the most common method of construction is that of intersecting arcs with the aid of compasses. The compass is set to length OA and an arc is drawn from the tip of arrow OB. Another arc is drawn with the compass at the length of OB and the centre at the tip of OA. For most meaningful engagement with the explanation of this method, access to a scale rule, a set of compasses and a protractor will be useful.

EXAMPLE 8.13 Two forces of 8 N and 5 N act outwards from a point with an angle of 60° between them. Find the resultant force being exerted at the point and the angle at which it acts with respect to the 8 N force. resultant = 11.4 N ​​  angle to OB    ​  =​  22° ​​​ (continued) 465

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Electrical Principles

Scale 1 N = 5 mm

F1 = 5 N O

A

FR

θ = 60° 22° F2 = 8 N

B

Figure 8.7  Force diagram for Example 8.13

EXAMPLE 8.14 Three forces acting at a point are spaced 120° from each other: F1 = 25 N; F2 = 50 N; and F3 = 20 N. Find the resultant force acting at the point. The three forces are drawn to scale in Figure 8.9(a). Commencing at the origin O in Figure 8.9(b), draw vector F1 equal in length and parallel to F1. On the arrowhead end of vector F1, draw F2 equal in length and parallel to F2. On the arrowhead end of F2, add F3 equal in length and parallel to F3. The resultant of the three forces (FR) is the straight line between the origin O and the end of F3. Note that the arrowhead of the resultant is opposite the flow of the arrowheads in the rest of the diagram.

EXAMPLE 8.15 Three forces, all 25 N, acting at a point are spaced 120° from each other. Find the resultant force acting at the point. As in the previous example, the vectors are drawn to scale with due regard to their direction from point O (Figure 8.10(a)). F1 is then drawn parallel to F1 from its origin O, as in Figure 8.10(b). On the end of F1, draw F2 equal in length and parallel to F2. F3 is then added to the end of F2, also equal in length and parallel to F3. The resultant (as in Example 8.14) is the straight line between the origin and the end of F3. In this example, however, F3 joins back to the beginning of F1 at point O. Because the distance between these two ends is zero, the resultant is 0 mm and the system is said to be ‘balanced’ (see Fig. 8.10).

8.6.6  Vector polygon method The parallelogram method becomes more cumbersome when three or more forces are involved. The polygon method requires each vector to be drawn to scale and angle with its origin at the end of the previous vector. The vectors can be drawn in any order, provided the requirements of magnitude and direction are met. The resultant is the distance between the origin of the vector diagram and the end of the last vector. A The method is best illustrated with an example. In Figure  8.9(c), the vector addition is repeated F1 but the order is altered, giving a different figure. It should be noted that the two resultants have the FR O C same magnitudes and directions. FR is the value and θ direction of a single force that could replace all three F2 original forces and produce the same effect. In vector diagrams, the resultant can replace all of the vectors. B The resultant starts at the origin and finishes at the Figure 8.8  Parallelogram method of adding vectors arrowhead end of the last vector. 466

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Reference section  Chapter 8

Scale = 1 N = 1 mm

F1

F2 F1

25 N 120°

F3

O

FR = 27.8 N

O

20 N 50 N F2

F3 (a)

(b)

F1 Vector values are often denoted by an ‘overscore’, or a bar above the vector name. For example, in this case...

F3

F2 O FR = 27.8 N

FR = F1 + F2 + F3 but note that FR does not equal F1 + F2 + F3 (c)

Figure 8.9  Polygon method of adding vectors

8.6.7  Vector components

F2

Vectors can be separated into horizontal and F2 vertical components, which can be added in the F1 same way as scalar quantities. Figure 8.11(b) shows O four forces drawn on graph paper, with vertical and F3 O horizontal axes. F1 The dotted lines indicate the horizontal and F3 (a) Scale 1 N = 1 mm (b) vertical components of each of the three forces. Just as two forces can be added by the parallelogram Figure 8.10  Addition of a balanced system of vectors method, a single force can be replaced with two forces. By replacing each force at an odd angle with two forces parallel to the horizontal and vertical axes, forces can be converted into values which can be simply added or subtracted. The forces can be drawn to scale and the horizontal and vertical components measured—or trigonometry used—to calculate the horizontal and vertical values of each force. Once the sum of the horizontal and vertical forces are known, they can be combined using Pythagoras’ theorem to have one single vector resultant.____________________ The angle of the resultant can also be calculated using trigonometry. Using Pythagoras’ theorum, √ ​​     (​(−  27.32  )​​  2​  + ​(−  5.33  )​​  2​ ) ​= 27.83 N​(as before). The direction of the resultant is downwards to the left, which is also the same as that found by the polygon method. Mathematical values of vectors and vector components can be obtained by trigonometry.

8.6.8  Rectangular vs polar A vector has magnitude and direction (angle) and is usually written in polar form—for example, a 40 N force at an angle of 60° is written as 40 N/60°. If it is converted into horizontal and vertical components, it is in a rectangular form and would be written [20,34.6]N. Modern scientific calculators can easily convert between polar and rectangular forms, but without knowing how to do this conversion, it is hard to fully appreciate how and why the methods work.

Table 8.3  Horizontal and vertical components Force

Horizontal

Vertical

F1

+ 4.34

+24.62

F2

−46.98

−17.1

F3

+15.32

−12.85

Totals

−27.32

0–5.33

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Electrical Principles

n io

−X

+Y

Ro t

at

Second Quadrant −X +Y

Vertical Components

+Y

F1 = [5, 10] F2 = [−15,15]

First Quadrant +X+Y

X-axis +X Horizontal Components Fourth Quadrant +X−Y

+X

F3 = [−25,−10] F4 = [15,−15]

Y-axis

Third Quadrant −X−Y

O

−X

−Y (b)

−Y (a)

Figure 8.11  Horizontal and vertical components of vectors

8.7  Trigonometry The component values for the four forces in the above problem could be obtained by graphical means, but were in fact obtained by a branch of mathematics called trigonometry. Trigonometry is based on the measurements of triangles (fortunately, the trigonometry of right angle triangles is relatively simple). Trigonometry can be used to solve the magnitude and direction of vectors with an accuracy greater than that of graphical means.

8.7.1  Ratios of lengths of sides

60° 15 mm

60° 20 mm

60° 25 mm

opp = √3

nit s 2u p= hy

43.3 mm

mm 50

34.7 mm

m 40 m

26 mm

30

mm

The right angle triangles shown in Figure  8.12 are different sizes and have different lengths of sides, but the angles remain constant. Therefore the relationships between the sides remain the same and they have the same trigonometry. As all the corresponding angles are equal, the various figures are called ‘similar triangles’. Further to this, the ratios between the sides remain constant, irrespective of the sizes of the triangles. A check of Figure 8.12 will show that the ratio of the horizontal side to the Hypotenuse for each triangle is 1:2 or h (0.5). Reference to trigonometrical tables shows that the Cosine for 60° is 0.5. What this really means is that, in the right angle triangle, the ratio of the 1 two sides adjacent to a 60° angle will always be 1:2 or __ ​​   ​​ or 0.5 (as it is usually expressed). 2 In any right angle triangle, the longest side is called the ‘Hypotenuse’, the side nearest a given angle is called the ‘Adjacent’ and the side of the triangle opposite the angle is called the ‘Opposite’ side.

60° adj = 1

Figure 8.12  Similar triangles

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Reference section  Chapter 8

There are three ratios of sides for a right angle triangle:

hyp

opp opp

adj

opp

1. Sine of angle  =  Opposite side/Hypotenuse, θ θ adj hyp sin θ = Opposite/Hypotenuse 2. Cosine of angle  =  Adjacent side/Hypotenuse, Figure 8.13  Hypotenuse, Opposite and Adjacent cos θ = Adjacent/Hypotenuse 3. Tangent of angle = Opposite side/Adjacent side, tan θ = Opposite/Adjacent

hyp

adj

θ

These sides are illustrated in Figure 8.13 and apply when the triangle is rotated into any position. Trigonometric tables or scientific calculators can be used to solve triangle problems without the necessity of drawing them to scale.

EXAMPLE 8.16 With the aid of a scientific calculator, find the ratio between the length of the Adjacent side and the Hypotenuse for the following enclosed angles: ​2° ,  20° ,  35° ,  50° ,  34.6° ,  85.2° ,  89.9°​ The ratio Adjacent/Hypotenuse is called the ‘Cosine’ of the enclosed angle: cos 2° = 0.9994, cos   20° = 0.9397, cos  35° = 0.8191, cos   50° = 0.6428, cos   34.6° = 0.8231, cos   85.2° = 0.08368, cos   89.9°  = 0.00174

Note that the value approaches unity for small angles and nears zero for angles approaching 90°. The reverse is true for Sine values: sin 0° = 0 and sin 90° = 1. The Tangent value varies between zero for 0° and very high numbers for angles approaching 90°.

EXAMPLE 8.17 Find the two remaining angles of a right angle triangle, given a Hypotenuse 32.33 m long and the other two sides 28 m and 16.16 m. opp. 28 sin θ = ​​ ____ ​​  = ​​ _____    ​​   = 0.866 hyp. 32.33

.33 32 m

28 m

The problem is how to find the angle whose Sine is 0.866. Mathematically, this is expressed as either arc sin 0.866 or sin −1 0.866. This value has to be found and translated to an angle in degrees. With a calculator that has trigonometrical facilities, it is a matter of using the appropriate buttons. In the case of this example, arc sin (or sin–1) 0.866 = 60°. Since the second angle of the triangle is a right angle (90°) and since there is 180° in a triangle, the remaining angle must be 180° − 90° − 60° = 30°.

16.16 m

Figure 8.14  Diagram for Example 8.17

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Electrical Principles

EXAMPLE 8.18 A lathe operator is required to machine a tapered pin. It has to be 200 mm long with a diameter decreasing from 50 mm to 30 mm. At what angle must the lathe-slide be set? From Figure 8.15, the taper is in the order of 10 mm in 200 mm (shaded area): opp. ____ 10 tan  θ = ____ ​   ​ = ​    ​ = 0.05     ​​  ​  ​  adj. 200 ​ ​​ angle θ = [arc tan  or tan −1]  0.05 = 2.86°

10 mm

θ 200 mm

Figure 8.15  Diagram for Example 8.18

8.7.2  Angles greater than 90°

Whether ‘sine 60°’, ‘sine 120°’, ‘sine 240°’ or ‘sine 300°’ is typed into a calculator, it will respond with ±0.866. The value of Sine goes from 0 at 0° to 1 at 90° and back to 0 at 180°. When converting from a sine value back to an angle, the trick is knowing when the angle is greater than 90°. To ensure that everyone dealing in vectors uses the same language, a vector diagram has a horizontal axis (usually called the ‘X-axis’) and a vertical axis (the ‘Y-axis’). The point where they cross is called the ‘origin’, which is labelled with the letter O. By convention, vector angles increase to the counter-clockwise direction, beginning at the right end of the horizontal axis. Also by convention, angles are always taken as being the angle between the vector and the horizontal or X-axis. So from 0° to 90°, the vector will be above the positive half of the X-axis and to the right of the Y-axis. This is the first quarter of the circle and so it is known as the ‘first NB: quadrant’. From 90° to 180° is known as the ‘second 90° +y X1 = X4 Rotation quadrant’, from 180° to 240° the ‘third quadrant’ and Quadrant 1 X2 = X3 Quadrant 2 y2 y1 from 240° to 360° the ‘fourth quadrant’, as shown in Y1 = Y2 R1 Y3 = Y4 R2 Figure 8.16 150° The quadrants go around the circle in an antix x clockwise direction. This is called the ‘rotation’ of −x +x 30° 30° 2 1 180° 0° x3 x4 Reference 30° 30° the vectors, or the ‘vector rotation’. Axis 210° Figure 8.17 shows the signs for each quadrant. R4 R3 Some angles appear so regularly (for electricians 330ø at least) that the trigonometric values can be y3 y4 Quadrant 3 Quadrant 4 remembered. 270° −y The numbers listed in Table  8.4 will appear surprisingly frequently. Figure 8.16  Four quadrants

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Reference section  Chapter 8

S A T C

Quadrant 2 sin+ cos− tan−

Quadrant 1 sin+ cos+ tan+

Quadrant 3 sin− cos− tan+

Quadrant 4 sin− cos+ tan−

Figure 8.17  Trigonometrical ratio signs or polarities in four quadrants Table 8.4  Common angle

values

Angle

Sin

Cos

Tan

0°

0

1

0

30°

0.5

0.866

0.577

45°

0.707

0.707

1

60°

0.866

0.5

1.732

90°

1

0

Infinity

EXAMPLE 8.19 Find the horizontal and vertical components for a vector of 29 N acting at an angle of 226.397° to the reference axis. effective angle is 226.397 − 180 = 46.397° − x (= adj.) cos  46.397° = ________ ​   ​     R  hyp. − x that is,     0.689 = ___ ​   ​  29 ​​

∴ − x​  =​  20 N                 ​   ​​ ​ ​ ​ ​ − y opp. sin  46.397° = ___ ​   ​ ​ = ____ ​   ​  ​ R ( adj. ) − y that is,     0.724 = ___ ​   ​  29 ∴ − y = 20 N +y 226.397° −x

+x −y

R −x

−y

Figure 8.18  Diagram for Example 8.19

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Electrical Principles

EXAMPLE 8.20 Find the angle represented by a horizontal component of 45 units and a vertical component of −28 units. What is the length of the rotating vector? − 28 x(= opp.) ____ ​tan  θ  = ​ _______  ​     = ​   ​    = − 0.6222​ 45 y adj. From the tables, this represents an angle of − ​ ​31.89°. The angle from the reference vector is: ​360  − 31.89 = 328.11°​ The length R can be calculated from trigonometrical values or by: ___________

√_________

R = ​ ​4      5​​  2​  + ​(−  28  )​​  2​ ​

​ = ​√2025 +       784 ​ _____ ​​         ​ ​ ​ ​   = ​√2809 ​       ​ ​​​ ​   53 units or     cos  θ = 45/R that is, 0.8490 = 45/R ​∴ R = 53 units​

θ

R

−28

45

Figure 8.19  Diagram for Example 8.20

EXAMPLE 8.21 Evaluate the following: sin 97°, cos 184°, tan 215°, tan 290° and cos 340°. Sin 97°: 83° subtends at horizontal sin 83°  = 0.9925 ​​    ​ ​​ ∴ sin 97°   + 0.9925 Cos 184°: 4° to horizontal cos  4°   = 0.9975 ​​   ​ ​​ ∴ cos   184°   − 0.9975 Tan 215°: 35° to horizontal

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Reference section  Chapter 8

tan 35° = 0.7002 ​​   ​ ​​ ∴ tan 215°   + 0.7002 Tan 290°: 70° to horizontal tan 70°  = 2.7475 ​​   ​ ​​ ∴ tan 290°  −2.7475 Cos 340°: 20° to horizontal        cos 20° = 0.9397 ​∴  cos  340°  = 0.9397​

EXAMPLE 8.22 By means of rectangular components, find the resultant of the following forces. All angles are given according to conventional rotation: F1, 25 N at 80°; F2, 50 N at 135°; F3, 15 N at 215°; and F4, 35 N at 320°. The two components of the resultant can be plotted on a vector diagram (Figure 8.20). Value or magnitude of the resultant: ​ = OA _________________ ​ ​    ​​ = ​ ​(     2​  + ​(28.87)​​  2​ ​​​​  − ​  16.49)​​ 

√

​ = 33.25 N Direction: opp. 28.27 Tan of angle = ​​ ____ ​​ = ______ ​​     ​​  = − 1.75 adj. − 16.49 The angle with a tangent of 1.75 is 60.2°. This is an angle of 60.2° to the horizontal in the second quadrant, so the angle of force is 180 − 60.2 = 119.8°  from the reference line. F2, 50N at 135°

Table 8.5  Rectangular components for Example 8.22 F

/(theta)

R

25 N

    80°

50 N

135°

−35.0

+5.0

15 N

215°

−12.0

−8.6

35 N

320°

26.8

−22.5

33 N

119 °

−16.5

28.9

F1, 25N at 80°

X 4.34

Note: numbers have been rounded for convenience

24.6 Reference

0°

F3, 15N at 215° Vector Diagram (Not necessarily to scale)

F4, 35N at 320°

Figure 8.20  Force diagram for Example 8.22

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7

6

5

4

3

2

1

S1/2

S1/2

2

K

2

S1/2

S1/2

2

S1/2

2

S0

Be

1

S0

1

1

S0

S0

1

S0

1

(226) 2 [Rn]7s 5.2784

Radium

Ra

88

137.327 2 [Xe]6s 5.2117

Barium

Ba

56

87.62 2 [Kr]5s 5.6949

Strontium

S0

1

Sr

38

40.078 2 [Ar]4s 6.1132

Calcium

Ca

20

24.3050 2 [Ne]3s 7.6462

Magnesium

Mg

12

9.012182 2 2 1s 2s 9.3227

Beryllium

4

2 IIA

Cerium

12

Ionization Energy (eV)

140.116 2 [Xe]4f5d6s 5.5387

†

D3/2

2

Scandium

D3/2

88.90585 2 [Kr]4d5s 6.2173

Yttrium

Y

2

44.955910 2 [Ar]3d4s 6.5615

V

Cr

Mn

Fe

Co

Ni

Non-metals Metals

Cu

Zn

P1/2 °

Boron

B

2

Aluminum

Al

2

P1/2 °

10.811 2 2 1s 2s 2p 1 8.2980

13

5

13 IIIA

Carbon

C

P0

3

P0

3

Silicon

Si

14

12.0107 2 2 2 1s 2s 2p 11.2603

6

14 IVA

Nitrogen

N

° S3/2

4

° S3/2

4

P

Phosphorus

15

14.0067 2 2 3 1s 2s 2p 14.5341

7

15 VA

Oxygen

O

P2

3

S

P2

3

Sulfur

16

15.9994 2 2 4 1s 2s 2p 13.6181

8

16 VIA

Fluorine

F

P3/2 °

2

° P3/2 2

Chlorine

Cl

17

18.9984032 2 2 5 1s 2s 2p 17.4228

9

17 VIIA

Helium

He

S0

1

S0

1

Argon

S0

1

Ar

18

20.1797 2 2 6 1s 2s 2p 21.5645

Neon

Ne

10

4.002602 2 1s 24.5874

2

18 VIIIA

D1/2

6

4

F3/2

Tantalum

Ta

73

92.90638 4 [Kr]4d 5s 6.7589

Niobium

Nb

41

50.9415 3 2 [Ar]3d 4s 6.7462

Vanadium

S3

7

5

D0

Tungsten

W

74

95.94 5 [Kr]4d 5s 7.0924

Molybdenum

Mo

42

51.9961 5 [Ar]3d 4s 6.7665

Chromium 2

S5/2

6

6

S5/2

Rhenium

Re

75

(98) 5 2 [Kr]4d 5s 7.28

Technetium

Tc

43

[Ar]3d 4s 7.4340

5

54.938049

Manganese

Iron

5

D4

Osmium

Os

76

[Kr]4d 5s 7.3605

7

101.07

Ruthenium

F5

5

Ru

44

55.845 6 2 [Ar]3d 4s 7.9024

Cobalt

4

F9/2

Ir

F9/2

4

Iridium

77

102.90550 8 1 [Kr]4d 5 s 7.4589

Rhodium

Rh

45

58.933200 7 2 [Ar]3d 4s 7.8810

Nickel

1

S0

Platinum

D3

3

Pt

78

106.42 10 [Kr]4d 8.3369

Palladium

Pd

46

58.6934 8 2 [Ar]3d 4s 7.6398

S1/2

2

S1/2

2

Gold

Au

79

107.8682 10 1 [Kr]4d 5 s 7.5762

Silver

Ag

47

63.546 10 1 [Ar]3d 4s 7.7264

Copper

Zinc

S0

1

S0

1

Mercury

Hg

80

112.411 10 2 [Kr]4d 5s 8.9938

Cadmium

Cd

48

65.409 10 2 [Ar]3d 4s 9.3942

3

F2 ?

2

D3/2

D3/2

2

(227) 2 [Rn]6d7s 5.17

Actinium

Ac

89

138.9055 2 [Xe]5d6s 5.5769

Lanthanum

La

57

(261) 14 2 2 [Rn]5f 6d 7s ? 6.0 ?

Rutherfordium

Rf

104

1

G4°

232.0381 2 2 [Rn]6d 7s 6.3067

Thorium

F2

3

Th

90

140.116 2 [Xe]4f5d6s 5.5387

Cerium

Ce

58

(262)

Dubnium

Db

105

5

I4

4

K11/2

231.03588 2 2 [Rn]5f 6d7s 5.89

Protactinium

Pa

91

1 40.90765 3 2 [Xe]4f 6s 5.473

L6° 5

238.02891 3 2 [Rn]5f 6d7s 6.1941

Uranium

U

92

144.24 4 2 [Xe]4f 6s 5.5250

Praseodymium Neodymium

Nd

60

(264)

° I9/2

4

Pr

59

(266)

Bohrium

Bh

107

Seaborgium

Sg

106

6

H°5/2

62

(268)

7

F0

6

L11/2

(237) 4 2 [Rn]5f 6d7s 6.2657

Neptunium

Np

93

(145) 5 2 [Xe]4f 6s 5.582

Promethium

(244) 6 2 [Rn]5f 7s 6.0260

Plutonium

F0

7

Pu

94

150.36 6 2 [Xe]4f 6s 5.6437

Samarium

8

° S7/2

8

° S7/2

D°2 9

96

D°2 9

157.25 7 2 [Xe]4f 5d6s 6.1498

Gadolinium

Gd

64

(272)

111

(243) 7 2 [Rn]5f 7s 5.9738

Americium

(247) 7 2 [Rn]5f 6d7s 5.9914

Curium

Am Cm

95

151.964 7 2 [Xe]4f 6s 5.6704

Europium

Eu

63

(281)

110

6

H°15/2

6

H°15/2

(247) 9 2 [Rn]5f 7s 6.1979

Berkelium

Bk

97

158.92534 9 2 [Xe]4f 6s 5.8638

Terbium

Tb

65

(285)

Ununbium

112

Mt Uun Uuu Uub Meitnerium Ununnilium Unununium

109

Pm Sm

61

(277)

Hassium

Hs

108

178.49 180.9479 183.84 186.207 190.23 192.217 195.078 196.96655 200.59 14 2 2 14 6 2 14 5 2 14 3 2 14 10 2 14 7 2 14 10 14 9 14 4 2 [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6 s 1 [Xe]4f 5d 6 s 1 [Xe]4f 5d 6s 6.8251 7.5496 7.8640 7.8335 8.4382 8.9670 8.9588 9.2255 10.4375

Hafnium

F2

3

Hf

72

91.224 2 2 [Kr]4d 5s 6.6339

Zirconium

F2

3

Zr

40

47.867 2 2 [Ar]3d 4s 6.8281

Titanium

P1/2 °

2

Ge

Arsenic

As

Se

Selenium

Br

Bromine

Kr

Krypton

Tin

P0

3

Sn

50

° S3/2 4

Antimony

Sb

51

Tellurium

P2

3

Te

52

° P3/2 2

I

Iodine

53

S0

1

Xenon

Xe

54

72.64 74.92160 78.96 79.904 83.798 10 2 2 10 2 3 10 2 4 10 2 5 10 2 6 [Ar]3d 4s 4p [Ar]3d 4s 4p [Ar]3d 4s 4p [Ar]3d 4s 4p [Ar]3d 4s 4p 7.8994 9.7886 9.7524 11.8138 13.9996

Germanium

P1/2 ° 2

5

I8

(251) 10 2 [Rn]5f 7s 6.2817

Californium

Cf

98

162.500 10 2 [Xe]4f 6s 5.9389

Dysprosium

I8

5

Dy

66

6.1082

204.3833 1 [Hg]6p

Thallium

Tl

81

P0

3

° S3/2 4

Er

3

H6 Holmium

4

° I15/2

(252) 11 2 [Rn]5f 7s 6.42

Einsteinium

Es

99

164.93032 11 2 [Xe]4f 6s 6.0215

H6

3

(257) 12 2 [Rn]5f 7s 6.50

Fermium

Fm

100

167.259 12 2 [Xe]4f 6s 6.1077

Erbium

° F7/2 4

Ho

67

2

2

° F7/2

(258) 13 2 [Rn]5f 7s 6.58

Mendelevium

Md

101

168.93421 13 2 [Xe]4f 6s 6.1843

Thulium

Tm

69

(292)

° I15/2

Uuh

Ununhexium (289)

Ununquadium

116

(209) 4 [Hg]6p 8.417 ?

Polonium

P2

3

Po

84

Uuq

68

208.98038 3 [Hg]6p 7.2855

Bismuth

Bi

83

114

207.2 2 [Hg]6p 7.4167

Lead

Pb

82

° P3/2 2

1

S0

S0

1

(259) 14 2 [Rn]5f 7s 6.65

Nobelium

No

102

173.04 14 2 [Xe]4f 6s 6.2542

Ytterbium

Yb

70

(210) 5 [Hg]6p

Astatine

At

85

S0

1

D3/2

2

° ? P1/2 2

(262) 14 2 [Rn]5f 7s 7p? 4.9 ?

Lawrencium

Lr

103

174.967 14 2 [Xe]4f 5d6s 5.4259

Lutetium

Lu

71

(222) 6 [Hg]6p 10.7485

Radon

Rn

86

114.818 118.710 121.760 127.60 126.90447 131.293 10 2 6 10 2 4 10 2 5 10 2 3 10 2 1 10 2 2 [Kr]4d 5s 5p [Kr]4d 5s 5p [Kr]4d 5s 5p [Kr]4d 5s 5p [Kr]4d 5s 5p [Kr]4d 5s 5p 5.7864 7.3439 8.6084 9.0096 10.4513 12.1298

Indium

In

49

69.723 10 2 [Ar]3d 4s 4p 5.9993

Gallium

Ga

26.981538 28.0855 30.973761 32.065 35.453 39.948 4 5 6 7 8 9 10 11 12 2 5 2 6 2 4 2 2 2 1 2 3 [Ne]3s 3p [Ne]3s 3p [Ne]3s 3p [Ne]3s 3p [Ne]3s 3p [Ne]3s 3p IVB VB VIB VIIB VIII IB IIB 5.9858 8.1517 10.4867 10.3600 12.9676 15.7596 ° 32 3P0 33 4S3/2 ° 36 1S0 ° 34 3P2 35 2P3/2 22 3F2 23 4F3/2 24 7S3 25 6S5/2 26 5D4 27 4F9/2 28 3F4 29 2S1/2 30 1S0 31 2P1/2

Ti

Based upon C. ( ) indicates the mass number of the most stable isotope.

3 IIIB

39

G4°

Ce

1

Ground-state Level

58

Electron Configuration

Atomic † Weight

Name

Sc

21

Solid (non-metals) Solid (metals) Liquid Gas Artificia

1 [Rn]7 s 4.0727

(223)

Francium

Fr

87

132.90545 1 [Xe]6 s 3.8939

Cesium

Cs

55

4.1771

85.4678 1 [Kr]5 s

Rubidium

Rb

37

39.0983 [Ar]4s 4.3407

Potassium

19

22.989770 1 [Ne]3 s 5.1391

Sodium

Na

2

6.941 2 1 1s 2 s 5.3917

Lithium

Li

S1/2

2

13.5984

11

3

1.00794 1 1s

Hydrogen

H

Symbol

Atomic Number

Lanthanides

jen21014_ch08_449-476.indd 474 Actinides

Group 1 IA 2 S1/2 1

Electrical Principles

474

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Period

Reference section  Chapter 8

Summary ∙ The SI system of units is a metric system and is, with very few exceptions, a world-wide standard. ∙ There are only seven base units in the system, plus two supplementary. ∙ There are many units derived from the base units, for example, mechanical, electrical and magnetic. ∙ The engineering notation system has standard multiples and sub-multiples with specific names. ∙ Scientific notation is a method for expressing quantities using a mantissa and an exponent value. ∙ Work, power, energy and torque are components of the system. ∙ All machines have losses. Efficiency is the ratio of the input and output values, usually expressed as a percentage. ∙ Scalar values have magnitude only. ∙ Vector (phasor) values have magnitude and direction. ∙ Mechanical forces are expressed as vectors. ∙ Electrical forces are expressed as phasors. ∙ Combinations of forces give rise to a resultant force. ∙ A resultant force can be evaluated graphically by drawing it to scale, with due regard to length and direction. ∙ Polar form is in the form of force and angle. ∙ Rectangular form is in the form of horizontal and vertical components. ∙ Vectors can be converted from polar into rectangular form and then added. ∙ Resultants can be found as the sum of vectors, in rectangular form converted to polar form. ∙ Trigonometry is a mathematical system where angles are expressed in terms of the ratios of the sides of a triangle. ∙ A graph is a pictorial representation of a series of quantities. ∙ Graphs have axes and scales for those axes.

475

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Index A acceleration, 14 alternating-current (a.c.) circuits alternator construction, 219 alternators, 217 AS/NZS 3000 requirements, 240 capacitors applications, 236 reactance, 237 in series, 237–238 d.c. voltage, 205 and EMF induced, direction of, 217 loop rotates, 217–218 magnitude of, 217 energy and power requirements Bench–type wattmeters, 291 energy meters, 291 frequency meters, 292 handheld wattmeters, 291 high-frequency wattmeters, 292 power and energy meters, 285–286 power factor improvement, 292 power factor meters, 291 power transmission, 282 SWER distribution, 283 three-phase distribution, 284 three-phase power, 284–290 total harmonic distortion meters, 292 ultra-high-frequency wattmeters, 292 VA and var meters, 291 var measurement, 290 fault loop impedance AS/NZS 3000:2007, 293 resistance and reactance values, 294–295 testers, 296 testing procedure, 296 typical circuits, 295 harmonics AS/NZS 3000:2007, 267, 268 electrical installation, 265 methods and test equipment, 265 parallel circuit resonance, 267 resonance, 265 sawtooth waveform, 263 series-circuit resonance, 265–267 sine waves, 263–264 sources, 264 inductors, in series, 234–236 loop rotating, in magnetic field, 217 Oscilloscope applications, 216 block diagram of, 210 cathode ray oscilloscopes (CRO), 209

cathode-ray tube (CRT), 209 deflection plates, 209–210 dual trace oscilloscopes, 214–215 frequency comparisons, 216 horizontal amplifiers, 210–211 horizontal time base, 212 oscilloscope display, 212–214 phase displacements, 215–216 sweep circuit, 211 trigger circuits, 212 vertical amplifiers, 210 vertical input attenuator, 211 parallel a.c. circuits capacitors in, 247 circuit impedance, 249 inductors in, 248 R-C circuits, 246 R-L-C circuits, 247 R-L circuits, 246 phasor diagrams ‘in-phase,’ ‘out-of-phase,’ ‘phase angle,’ ‘lead’ and ‘lag,’ 225–226 phasor addition by graphical method, 226–232 power in apparent power (S), 252–253 capacitive circuit, 251 inductive circuit, 251 phase angle, 253–254 power factor, 253–263 power losses, 253 reactive power (Q), 253 resistive circuit, 250–251 R-L circuit, 252 single-phase power, energy and demand, 255 true power, 252 resistance in pure or non-inductive resistance, 232–233 in series and parallel, 233 right angle triangle Pythagoras’ theorem, 207–208 sine, cosine and tangent ratios, 206–207 R-L-C series inductors and resistors, characteristics of, 245 total impedance, 242 voltage drop and reactance, 242–245 RMS values, 206 sawtooth wave, 205 series circuit impedance, 239 series R-C circuits, 239–240 series R-L-C circuits, 238 series R-L circuits, 240–241 sinusoidal waveforms, 204–205 average value, 223–224 calculated instantaneous values, 223 electrical frequency, 222–223 graphical method, 222–223

477

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Index alternating-current (a.c.) circuits—Cont. instantaneous values, 219–220 peak-to-peak values, 224 root-mean-square values, 224 voltage and current cycles, 221 square waveform, 206 symmetric wave, 205 three-phase delta connections and interconnected systems limitations and uses, 278–280 phase reversal, effects of, 280 typical power systems, 280–282 three-phase, four-wire systems AS/NZS 3000 requirements, 276 balanced loads, 275–276 broken neutral, effects of, 274–275 neutral conductor, 274 three-phase star connections, 273–274 three-phase systems advantages, 270–271 generation and distribution, efficiency in, 268–269 machine alternator construction, 272 phase sequence, 272 power efficiency and number of phases, 269 sine wave construction, 272 three-phase winding arrangements, 271 triangular wave, 205 two-phase systems, 270 alternating-current (a.c.) motor, speed control of changing frequency, 442 changing number of poles, 441–442 electronic frequency control, 443–444 frequency control, 442 wound-rotor motors, 442–443 alternating-current (a.c.) voltage, 394–395 alternator cooling high speed, 393 low speed, 392–393 alternator ratings, 396–397 alternator voltage, 395–396 ammeters, 22–23, 152–153 analogue instruments characteristics of, 81–82 multimeters, 83 reading techniques, 82–83 anti-lock braking systems (ABS), 155 armature, 160 Australian schemes and initiatives, 188–189 autotransformers, 313–314 auxiliary equipment, 306–307

B Bench–type wattmeter, 291 Bifilar winding inductor, 136, 137 bioenergy, 200 Brackets Order Division, Multiplication, Addition and Subtraction (BODMAS), 456–458 bridge meggers, 91

C capacitance dielectric constants, 97–98 parameters, 96–97 unit of, 95–96 capacitive circuit, 251

capacitors application, 105 ceramic, 94 charged capacitor, dangers of, 101–102 dielectrics drying out, 102 electrolytic, 95 faults, 102 in parallel, 102–103 rolled, 95 in series, 103–105 stacked-plate, 94 testing, 102 variable, 95 carbon-compound resistors, 45 Carbon Farming Initiative, 188 Carbon Neutral Program, 188 cast grid resistors, 44 cathode-ray tube (CRT), 209 cathodic protection, 33–34 ceramic capacitors, 94 circuit diagrams, 16 circuit indicators, 73 circuit labelling, 16 clamp testers, 148 Clean Energy Innovation Fund, 188 Clean Energy Regulator, 190 Climate Change Act 2017, 191 Climate Change Authority (CCA), 190 closed circuit, 18 commercial electronics, 3 computer systems, 3 consumer electronics, 3 contact testing equipment electronic-based voltage detectors, 77 plug-style testers, 77–78 series test lamps, 75–76 single-filament test lamps, 76 vibrating testers, 76–77 control circuit variations interlocks, 416–417 jogging control, 416 ladder diagrams, 417 local or remote operation, 415 push-button switch, 415–416 reversing circuits, 416 two-position control, 415 two-wire control, 415 control devices, types of, 418–419 cooling system air cooling, 319 forced circulation, 319 oil cooling, 319 and rating, 318 core-type transformer, 304 cross-sectional area (CSA), 60 current flow, direction of, 15–16 current testers, 148–149 current transformers, 325–326

D deflection plates, 209–210 Department of the Environment and Energy, 190 dielectric constants, 97–98 digital instruments, 81 direct-current (d.c.) circuit capacitors in, 98 measurement of electrical power, 29–30 time constant, 98–100

478

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Index direct-current (d.c.) excitation, 393–394 direct-current (d.c.) generators equivalent circuit, 166 excitation, 164–166 factors, 165 field flux control, 164 generated and terminal voltage, calculation of, 163–164 load characteristics, 168–169 load test, 169 open circuit characteristics, 167 polarity of, 169 prime movers, energy sources and energy flow, 164 residual magnetism, 166–167 safety risks, 169 speed control, 164 uses, 164 direct-current (d.c.) machine components armature, 160 brush gear and brushes, 161 commutator, 160–161 end-shields and bearings, 159 field coils, 159–160 field frame or yoke, 158 field poles, 159 efficiency, 177–178 energy conversion, 161 fault identification, 162 Fleming’s left-hand rule, 157 Fleming’s right-hand Rule, 156 force and torque, calculation of, 157–158 motor effect, 157 nameplates, 161–162 operating principle, 156 rotating machinery care and maintenance process, 162 safety risk, 162–163 direct-current (d.c.) motors back EMF in, 170 characteristics, 175–176 circuit diagrams, 174 compound motors, 173–174 and energy flow, 169 equivalent circuit, 175 on load or no load, 176 motor reversal, 176 output power of motor, 175 printed circuit motors, 171–172 radius of armature/rotor, 170 safety risk, 176 separately excited motors, 172 series-excited motors, 173 shunt-field motors, 173 direct-current (d.c.) voltage, 205 dissolved gas analysis (DGA), 320 distance and displacement, 13 drip-proof motors, 369 dual trace oscilloscopes, 214–215 duct or force ventilated, 369 dynamometer meter movement, 148, 150

E electrical circuits circuit types, 14 parts of, 14–15 electrical energy, 27–29 electrical instruments

accuracy, 68 A/D or ADC, 81–82 analogue instruments, 81 care and protection, 79–80 category of use, 80 contact testing equipment electronic-based voltage detectors, 77 plug-style testers, 77–78 series test lamps, 75–76 single-filament test lamps, 76 vibrating testers, 76–77 digital instruments, 81 internal impedance, 68 meter ranges, 69 microprocessor-based instruments, 82 needle meters, 81 neon testers light versions, 78 logic probes, 79 neon voltage indicators, 78 screwdrivers, 78 reading position, 69 sensitivity, 68 Type A probes, 69 use of instruments, 89-90 use, selection and category of, 79 electric charge, 12 electric circuits closed circuit, 18 open circuit, 17 short circuit, 18 electric current basic protection, 34 effect of heating, 32 information storage, control and processing, 32 lighting, 32 motion, 32 sound and radio frequencies, 32–33 electrical wiring and machines, 42–43 fault protection, 34 input, output, efficiency or losses, 42 rate of flow of electricity, 12 SI units, 12 electricity AS/NZS 3000:2018, 30–31 early power-distribution systems, 8 electric shock, 30 electrochemical effects, 31 electrostatic effects, 31 heating effects, 31 magnetic effects, 32 modern power-distribution systems, 8–9 utilisation capacitors, 11 electrical components, 9 inductors, 10–11 resistors, 9–10 electric shock, 30 electrochemistry definition, 40 electrochemical energy sources fuel cells, 41 primary cells, 40 secondary cells, 40–41 voltaic cells, 41 electrolytic capacitors, 95 electrolytic corrosion cathodic protection, 33–34

479

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Index electrolytic corrosion—Cont. dissimilar metals, 33 sacrificial anodes, 33 stray electric currents, 33 electromagnetic brake, 134 electromagnetic chuck, 135 electromagnetic clutch, 134 electromagnetic combined detector, 74–75 electromagnetic field detector, 74 electromagnetic induction application electromagnetic brake, 134 electromagnetic chuck, 135 electromagnetic clutch, 134 electromagnetic separator, 135 lifting electromagnet, 135 magnetic relay, 136 EMF conductor length and flux density, 131–132 Faraday’s Law, 132–133 velocity of conductor, 131–132 Fleming’s right-hand rule, 130 Lenz’s Law, 134 principle of, 130 electromagnetic separator, 135 electromagnetism conventions, 118 current, length and distance, effect of, 119 direction of current flow, 118–119 magnetic field, 120 magnetic field pattern, 118 magnetomotive force (MMF), 120 practical applications, 120 electromotive force (EMF), 12 electrochemical sources, 37–38 electromagnetic sources, 35–36 electrostatic sources, 38–39 engine-driven alternators, 37 gas turbine engines, 37 geothermal steam, 36 hydroelectric power, 37 nuclear power, 36–37 photoelectric sources, 38 piezoelectric sources, 39–40 power generation, 36 thermal steam turbines, 36 thermoelectric sources, 39 tidal movements, 37 electronic-based voltage detectors, 77 electrostatic field detector, 74 electrotechnology industry commercial and domestic construction and maintenance subsectors, 2 commercial electronics, 3 computer systems, 3 consumer electronics, 3 data and telecommunications, 3 generation, supply and distribution, 2 industrial and mining, 2 industrial electronics, 3 radio communications, 3 security systems, 3 Emissions Reduction Fund (ERF), 188 energy, 459 conversion of, 43, 161 efficiency measures, 188 storage in capacitor, 100–101 and work, 25 energy meters, 291 Energy Rating Labels, 188 engine-driven alternator

load sizes and alternator capacities, 391 operation of alternators, 391 purchase price, 390 starting methods, 390–391 type of prime mover, 390 Environment Protection and Biodiversity Consideration Act 1999, 191 Environment Protection Authority (EPA), 190, 191

F Faraday’s Law, 132–133 fault loop impedance AS/NZS 3000:2018, 293 resistance and reactance values, 294–295 testers, 296 testing procedure, 296 typical circuits, 295 field flux control, 164 flame-proof motor, 370 Fleming’s left-hand rule, 157 Fleming’s right-hand rule, 130, 156 flux shunt welding transformer, 315 force, 25 frequency meters, 291 fuel cells, 41

G galvanometers, 22 gas turbine engines, 37 geothermal energy, 199 geothermal steam, 36

H Hall effect devices, 155 handheld wattmeters, 290–291 heating effects, 31 HFC Refrigerant Levy, 192 high-frequency wattmeters, 292 hi-pot testing, 91–92 horizontal amplifiers, 210–211 horizontal time base, 212 hydraulics, 15 hydroelectric power, 37 hydro energy, 199

I inductance air cores, 138 angle of the conductor path, 137 Australian Standard circuit diagram symbol, 136–137 Bifilar winding inductor, 136, 137 conductor length, 137 iron cores, 138 iron-powder cores, 138 loop, 139 magnetic field density, 137 magnetic inductance, 140 multi coil transformer, 139 mutual inductance, 140–141, 143–145 self-inductance, 139–145

480

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Index solenoid coil-air-core, 139 solenoid coil-magnetic core, 139 straightline type, 138–139 time constant, 145–148 toroidal core, 139 velocity of motion, of conductor, 137 inductive circuit, 251 industrial electronics, 3 industrial instruments, 90 insulation resistance (IR), 90, 93, 308 interfacial tension (IFT) test, 320 internal impedance, 68 isolation transformers, 314

K Kyoto Protocol, 189

L lamp and sound annunciators, 73–74 Lenz’s Law, 134 lifting electromagnet, 135 liquid resistor starters, 427–428 loaded transformer, 312 losses, in machine, 462

M magnetic circuits air gap, effects of, 129 B/H magentisation curves, 123 electrical losses, 124 flux density, 128 magnetic flux, 124–125 magnetic leakage and fringing, 129–130 magnetic materials hysteresis loops, 123–124 hysteresis losses, 124 magnetisation curve for, 121 and non-magnetic materials, reluctance and permeability, 125–127 magnetic saturation, 121–123 magnetising force, 128–129 MMF unit, 127–128 non-magnetic materials, 121 permeability, 125 types, 129 magnetic devices arc current and magnetic field, 154 armature relay, 153–154 contactor, 154 Hall effect devices, 155 magnetic sensing devices, 155 magnetostriction equipment, 155 magnetic effects, 32 magnetic field density, 137 magnetic inductance, 140 magnetic levitation, 66 magnetic relay, 136 magnetic resonance imaging (MRI), 66 magnetism attraction and repulsion, 115 definition, 114 magnetic and nonmagnetic materials, 115–116 magnetic field pattern, of bar and horse-shoe magnets, 114–115 magnetic screening and applications, 116–117 practical applications, 117

reed switches, 117 see also electromagnetism magnetomotive force (MMF), 120 metallic resistor starters liquid resistor starters, 433 primary resistance, 427 secondary resistance, 432–433 Minimum Energy Performance Standards (MEPS), 188 motor protection circuit breakers, 371 combined thermal-magnetic over-current relays, 373 direct current motor protection, 376 electronic overloads, 376 environmental protection, 368–370 field discharge protection, 376–377 field failure protection, 376 fuses, 370–371 high humidity, 368 hot-spot allowance, 367–368 locked rotor, 365 magnetic trip circuit breakers, 372 microtherm devices, 374–375 over-current relays, 372 overload current, 364 over-voltage protection, 366, 377 protection devices, 370 repetitive starts, 366 reverse-phase sequence protection, 375 short-circuit current, 364 short-duration overload, 365 single-phasing protection, 375 sustained overload, 365 temperature rise, 367 thermal overloads, 372–373 under-voltage protection, 365–366 moving-coil meters application of, 150 suspension system, 147 moving-iron meters, 147–148, 150 multi coil transformer, 139 mutual inductance, 140–141, 143–145

N nameplate for transformer, 308 National Greenhouse and Energy Reporting (NGER), 188 needle meters, 81 neon testers light versions, 78 logic probes, 79 neon voltage indicators, 78 screwdrivers, 78 non-contact testing equipment, 74 non-contact testing instruments current testers, 88 current transformer, 88 modern versions, 88–89 repulsion-type movement (AC and DC), 88 voltage testers, 88 non-renewable energy sources, 7 nuclear power, 36–37

O ocean energy tidal energy, 199 wave energy, 199

481

jen21014_idx_477-486.indd 481

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Index ohmmeters parallel ohmmeters, 70 series ohmmeters, 69–70 Ohm’s law, 20–21, 458 open circuit, 17 open circuit characteristics (OCC), 167 open motors, 369 Oscilloscope applications, 216 block diagram of, 210 cathode ray oscilloscopes (CRO), 209 cathode-ray tube (CRT), 209 deflection plates, 209–210 dual trace oscilloscopes, 214–215 frequency comparisons, 216 horizontal amplifiers, 210–211 horizontal time base, 212 oscilloscope display, 212–214 phase displacements, 215–216 sweep circuit, 211 trigger circuits, 212 vertical amplifiers, 210 vertical input attenuator, 211 output power, 29 Ozone Protection and Synthetic Greenhouse Gas Management Act 1989, 191

P parallel circuit applications, 55 current in, 56, 57 faults in, 57 power in, 56–57 resistance in, 56, 57 voltage in, 55 parallelogram method, 465–466 parallel ohmmeters, 70 Paris Agreement, 190 particle accelerators, 66 phase displacements, 215–216 photoelectric sources, 38 piezoelectric sources, 39–40 plug-style testers, 77–78 pneumatics, 15 power definition, 25 electrical power electrical calculations, 26–28 Ohm’s Law and rules of transposition, 26 generation of, 36 power losses in conductor, 48 in transformer copper loss, 317 hysteresis, 316–317 iron losses, 316 no-load or open-circuit test, 317 test results, 318 transformer short-circuit test, 317 power ratings of resistor, 47–48 power transmission, 282 precision instruments, 90 prefixes and multipliers, 19–20 primary cells, 40 prime movers high speed, 391–392 low speed, 391 programmable relays

connecting, checking and troubleshooting, 422 features and advantages, 422–423 graphical user interfaces (GUI), 421 logic control program, 420 microprocessor programs, 422 safety, 423 solid-state circuitry, 420 protected motors, 369 Pythagoras’ theorem, 207–208

R radio communications, 3 rectangular forms, 467 relay circuit block diagrams, 409–410 circuit diagrams, 404 components arrangement of, 406 connections to symbols, 406 parallel components, 406 schematic circuit diagrams, 406–408 contactors drawing contactors, 413–414 operating components, 412 thermal overload contactor, 413 timing mechanism, 412 typical contactor, 412 conventions, in line work joins in, 405 line identification, 406 line types, 406 straight lines, 405 electric symbols, 404–405 low-cost/low-powered switches, 403 one-line diagram, 410 wiring diagram, 410–411 renewable energy sources, 7 Renewable Energy Target (RET), 1 87–188 renewable energy technologies bioenergy, 200 definition, 198 geothermal energy, 199 hydro energy, 199 ocean energy, 199 solar energy, 198 wind energy, 198–199 repulsion-type movement, 149 residual magnetism, 166–167 resistance, 12 battery-powered insulation testers (IR testers), 90–91 bridge meggers, 91 continuity testing, 91, 93 in current-carrying capacity, 66 factors cross-sectional area (CSA), 60 length, 60 in parallel circuit, 56, 57 in series circuit, 52 superconductors, 65–66 temperature, 62–65 type of material (resistivity), 60–62 voltage and current, 23–24 hi-pot testing, 91–92 insulation resistance, 90, 93 low-value resistance and continuity testers, 92–93

482

jen21014_idx_477-486.indd 482

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Index measurement of parallel ohmmeters, 70 series ohmmeters, 69–70 volt-ammeter testing, 70–71 Wheatstone bridge circuit, 71–73 usage care of, 92 voltage drop in conductors, 67 resistors carbon-compound resistors, 45 cast grid resistors, 44 co-axial sheathed elements, 44 power ratings of resistor, 47–48 preferred resistor values, 49–50 reading resistors, 48–49 resistance, 43–44 resistor colour-coding, 48 selection of, 51 variable resistors see variable resistors wire-wound resistors, 44–45 rolled capacitors, 95

S sacrificial anodes, 33 scalar quantities, 463 scientific calculators, 20 secondary cells, 40–41 security systems, 3 self-inductance, 139–145 series circuit complex circuits, 58 compound circuits, 58 current in, 52 definition, 51 equivalent resistance, 58 faults in, 53 nodes and loops, 59 power in, 53 resistance in, 52 simple circuit analysis, 59 uses, 51–52 voltage drops, 53–55 voltage in, 52 series ohmmeters, 69–70 series test lamps, 75–76 short circuit, 18 simple circuits, 21–22 single-filament test lamps, 76 single-phase motor abnormal operating conditions frequency variation, 354 frequent starting, 355 overheating, 354 overloading, 354–355 voltage fluctuation, 354 advantages and disadvantages, 362 capacitor-start/capacitor-run motor, 356–358 capacitor-start motor, 356 negative torque, 350 permanent split capacitor (PSC) motor, 358 shaded pole motor, 358–359 universal motor application, 361 construction, 360 operating principles, 360 operation, 360–361 SI units, 12–13 base quantities and units, 452–454 base units

angular area, 451 electric current, 451 kilogram, 450 luminance, 451 metre, 450 plane angle, 451 temperature, 451 time, 451 electrical derived units, 454–455 engineering notation, 455 magnetic derived units, 455 mechanical derived units angular velocity, 452 energy and work, 452 force, 452 power, 452 pressure, 452 temperature, 452 volume, 451 multiples and sub-multiples, 456 scientific notation, 455 solar communities program, 188 solar energy, 198 solenoid coil—air-core, 139 solenoid coil—magnetic core, 139 speed and velocity, 13–14 split-phase motors running, 352–353 starting, 351–352 stacked-plate capacitors, 94 standby power supplies, 388–389 static and current electricity current (dynamic) electricity, 7 electrical energy, 3 natural electricity, 4 static electricity electrical charge, production of, 4–5 electrical potential, 5 partial charge, 5–6 stray electric currents, 33 superconductors, 65–66 current flowing, 66 magnetic levitation, 66 magnetic resonance imaging (MRI), 66 particle accelerators, 66 sustainable work practices domestic, commercial and industrial strategies copper, 195 electricity, 195–196 oil and gas, 196 economic benefits of HFC Refrigerant Levy, 192 environmental awareness, 184 greenhouse effect and carbon-produced energy, 192–194 causes, 186 consequences, 186–187 definition, 186 international and national greenhouse imperatives Australian schemes and initiatives, 188–189 Clean Energy Innovation Fund, 188 Emissions Reduction Fund (ERF), 188 Kyoto Protocol, 189 National Greenhouse and Energy Reporting (NGER), 188 Paris Agreement, 190 Renewable Energy Target (RET), 187–188 UNFCCC, 189 legislative requirements Climate Change Act 2017, 191 Environment and Protection Authority (EPA), 191

483

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Index sustainable work practices—Cont. Environment Protection and Biodiversity Consideration Act 1999, 191 Ozone Protection and Synthetic Greenhouse Gas Management Act 1989, 191 neglecting of, 185–186 recycle, 185 reduce, 184 renewable energy technologies, 198–200 renewable power sources and low-emission fuel sources, 184 repair, 185 reuse, 185 role of regulators Clean Energy Regulator, 190 Climate Change Authority (CCA), 190 Department of the Environment and Energy, 190 Environment Protection Authority (EPA), 190 and international bodies, 190 trade-related retrofits, 197–198 trade-related technologies and methods, 196–197 sweep circuit, 211 SWER distribution, 283

T tapped windings, 313 terminal block arrangements squirrel cage motors, 339–340 wound-rotor motors, 340 thermal steam turbines, 36 thermoelectric sources, 39 three-phase distribution, 284 three-phase induction motors abnormal operating conditions, 346 continuity tests, 340–341 direction of rotation and reversal, 334–335 dismantling, 342 electrical tests, 340 insulation test between windings, 341 insulation-to-earth test, 341 motor enclosures, 339 operational parameters, 345–346 overloading, 347 phase reversal, 346 rate of rotation and factors, 333–334 rotating magnetic fields, 332–333 rotor frequency, 336–337 single phasing, 346–347 slip, 335–336 specialised test equipment, 341–342 squirrel cage motors cast aluminium rotor bars, 344 double cage rotor, 344 high-resistance rotor bars, 344 low starting torque rotor, 343 speed and torque, 342–343 standard rotor bars, 344 terminal block arrangements, 339–340 squirrel cage rotor, 337–338 stator, 337 torque, 335 visual inspection, 341 wound-rotor motors circuit resistance, 338 operating characteristics, 345 starting resistance, 339 terminal block arrangements, 340 three-phase induction motor starters autotransformer contactor starter circuit, 435 autotransformer starters, 428–430

direct-on-line contactor starter circuit, 433 direct-on-line (DOL) startings, 425 limitation of, 424 primary resistance applications, 428 liquid resistor starters, 427–428 metallic resistor starters, 427 primary resistance contactor starter circuit, 434–435 requirements of, 424 secondary resistance, 432–433 secondary resistance contactor starter circuit, 435–436 soft start, 430–432 solid state reduced-voltage starter, 436 speed-torque relationships, 424–425 star-delta contactor starter circuit, 434 star-delta starting, 426 three-phase motor reversal dynamic braking, 438–439 eddy-current disc braking, 438 mechanical braking, 437–438 plug braking, 439–440 regenerative braking, 439 three-phase motor braking, 437 three-phase power bench-type wattmeters, 291 delta connection, 285 electronic three-phase power meter, 289–290 energy meters, 291 four-wire system, 286, 289 frequency meters, 292 handheld wattmeters, 291 high-frequency wattmeters, 292 power factor improvement, 292 power factor meters, 291 star connection, 284–285 three-wire system, 286–289 total harmonic distortion meters, 292 ultra-high-frequency wattmeters, 292 VA and var meters, 291 volt-ampere reactive (var) measurement, 290 three-phase synchronous machine auxiliary motors, 387 construction, 384 effect of load, 385 field excitation, 385–386 hunting effect, 383, 386 hysteresis motors, 387 load sharing, 381–383 operating principle, 384 power factor correction, 386 reluctance motors, 387 rotor low speed, 380 parallel operation of alternators, 380–381 single-phase synchronous motors, 387 stator, 380 tidal energy, 199 tidal movements, 37 time constant, 98–100, 145–147 toroidal core, 139 torque, 460–461 totally enclosed fan-cooled motor, 369 transformer, 149 application of, 308 AS/NZS3000, 315, 324 autotransformers, 313–314, 323 auxiliary equipment, 306–307 cooling system air cooling, 319 forced circulation, 319

484

jen21014_idx_477-486.indd 484

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Index oil cooling, 319 and rating, 318 core-type transformer, 304 current transformers, 325–326 flux shunt welding transformer, 315 high-reactance or flux leakage transformers, 314–315 induced voltage, in transformer winding, 309 insulation resistance (IR), 308 isolation transformers, 314 loaded transformer, 312 low-and high-voltage transformers, 306 with multiple secondary, 312–313 mutual induction, principle of, 309 nameplate, 308 no-load conditions, 311 parallel operation conditions/restrictions, 321 consequences/effects, incorrect connection, 322–323 single-phase transformer, 322 unidentified single-phase double wound transformer, 321 power losses in copper loss, 317 hysteresis, 316–317 iron losses, 316 no-load or open-circuit test, 317 test results, 318 transformer short-circuit test, 317 secondary voltage and current, 309–310 shell-type construction, 304 tapped windings, 313 three-phase core type, 305 three-phase cruciform stepped core, 305 three-phase shell type, 305 three-phase toroidal, 305 toroidal core, 304 transformer oil, 319-320 transformer tank construction, 306 variac transformers, 314 voltage regulation, 320 voltage transformers, 324–325 welding transformers, 315 winding arrangement, 305–306 winding identification test, 308 transposition BODMAS, 456–458 working principles, 458 trigger circuits, 212 trigonometry angles greater than 90°, 470–474 ratios of lengths of sides, 468–470 Type A probes, 69

U ultra-high-frequency wattmeters, 292 unification theory, 114 The United Nations Framework Convention on Climate Change (UNFCCC), 189

V variable capacitors, 95 variable resistors light-dependent (LDR) resistors, 47 liquid resistors, 47 low temperature coefficient resistors, 46 negative temperature coefficient (NTC) resistors, 46 non-inductive resistors, 47 non-linear resistors, 46 positive temperature coefficient (PTC) resistors, 46 voltage-dependent resistors (VDRs), 46–47 variac transformers, 314 var measurement, 290 vector components, 467–468 horizontal and vertical components, 468 quantities, 463 velocity of conductor, 131–132 vertical amplifiers, 210 vertical input attenuator, 211 vibrating testers, 76–77 voltage current and resistance determination, 23–24 graphical relationships, 24 fluctuation, 354 and potential difference, 12 regulation, 164, 320, 396 testers, 148 voltage transformers AS/NZS1243 specification, 324 factors, 324 potential transformer burden, 325 safe working procedures, 325 voltaic cells, 41 volt-ammeter testing, 70–71 voltmeters, 23 ammeter section, 83–84 analogue multimeters, 83, 87 digital multimeters, 86–87 digital reading meters, 85–86 digital voltmeters, 86, 87 meter’s components, 85 ohmmeter section, 84 range of, 150–152 readout display, 86 Sanwa 460-ED multimeter, 85 voltmeter section, 83

W wave energy, 199 welding transformers, 315 Wheatstone bridge circuit, 71–73 wind energy, 198–199 winding arrangement, 305–306 winding identification test, 308 wire-wound resistors, 44–45

485

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Notes

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