Electrical Machines

Description

Cover Contents Preface Introduction Electromagnetism Direction of Current in a Conductor Direction of Magnetic Flux in a Conductor Flux Distribution of an Isolated Current-carrying Conductor Force Between Two Current-carrying Conductors Force on a Conductor in a Magnetic Field Generation of Induced enf and Current Faraday’s Laws Lenz’s Law Induced emf Dynamically Induced emf Statically Induced emf Magnetic Circuits Magnetomotive Force Magnetic Field Intensity Magnetic Flux Single-phase Circuits Series R-L Circuit Series R-C Circuit Series L-C-R Circuit Power Triangle Complex Power Three-phase Circuits Advantages of Three-phase System Phase Sequence Interconnection of Three Phases Star and Delta Connections Voltages, Currents and Power in Star Connections Voltages, Currents and Power in Delta Connections For Star Connections Measurement of Three-phase Power Principle of Energy Conversion Energy in the Coupling Field Energy in the Field Co-energy Electrical Energy Input to the system Estimation of Mechanical Forces in an Electromagnetic System Case 1: Motion of the Moving Part is Very Slow Case 2: Motion of the Moving Part Instantaneously Estimation of Magnetic Force in Linear Systems Doubly Excited Systems Cylindrical Rotating Machine Case 1: Synchronous Motor/Machine Case 2: ωm = ωs − ωr Chapter 1: Transformers 1.1 Definition 1.2 Basic Principle 1.3 Types of Transformers 1.4 Construction of Single-phase Transformer 1.4.1 Core Type 1.4.2 Shell Type 1.4.3 Spiral Core Type 1.5 Transformer Windings 1.5.1 Concentric Windings 1.5.2 Sandwich Windings 1.6 Terminals and Leads 1.7 Bushings 1.8 Tapping 1.9 Cooling of Transformer 1.10 Transformer Oil 1.11 Conservator and Breather 1.12 Buchholz Relay 1.13 Transformer Tank 1.14 Theory of Transformer 1.15 EMF Equation of a Transformer 1.16 Step-up and Step-down Transformer 1.17 Transformer on no Load 1.18 Transformer on Load 1.19 Equivalent Resistance 1.20 Magnetic Leakage 1.21 Equivalent Reactance 1.22 Transformer with Resistance and Leakage Reactance 1.23 Equivalent Circuit 1.24 Open Circuit Test or No-load Test 1.25 Short Circuit or Impedance Test 1.26 Separation of Core (or Iron) Losses in a Transformer 1.27 Total Approximate Voltage Drop of a Transformer 1.28 Exact Voltage Drop 1.29 Per Unit Resistance, Leakage Reactance and Impedance Voltage Drop 1.30 Voltage Regulation of Transformer 1.30.1 Inherent Voltage Regulation 1.30.2 Voltage Regulation Down 1.30.3 Voltage Regulation Up 1.31 Calculation for Voltage Regulation 1.31.1 Zero Voltage Regulation 1.31.2 Condition for Maximum Voltage Regulation 1.31.3 Kapp’s Regulation 1.32 Losses in a Transformer 1.32.1 Core or Iron Loss 1.32.2 Copper Loss 1.33 Efficiency of a Transformer 1.34 Condition for Maximum Efficiency 1.34.1 Load Current at Maximum Efficiency 1.34.2 kVA Supplied at Maximum Efficiency 1.35 All-day Efficiency 1.36 Polarity Test of a Single-phase Transformer 1.37 Sumpner’s Test 1.38 Parallel Operation of Single-phase Transformer 1.39 Load Sharing by Two Transformers 1.39.1 Equal Voltage Ratios 1.39.2 Unequal Voltage Ratios 1.40 Autotransformers 1.40.1 Construction 1.40.2 Copper Saving in Autotransformer 1.40.3 Conversion of Two-winding Transformer into Single-phase Transformer 1.40.4 Advantages of Autotransformers 1.40.5 Disadvantages of Autotransformers 1.40.6 Applications of Autotransformers 1.41 Pulse Transformer 1.41.1 Pulse Response Characteristics 1.41.2 Usage of Pulse Transformer 1.42 Welding Transformers 1.42.1 Reactors Used with Welding Transformers 1.43 Current Transformer 1.44 Potential Transformer 1.45 TAP Changing Transformers 1.46 Off-load TAP-changing Transformers 1.47 On-load TAP-changing Transformers 1.48 On-load TAP Changer with Single Primary Winding 1.49 Preventive Autotransformer 1.50 Booster Transformer 1.51 Inrush Phenomenon Additional Solved Problems Significant Points Short Questions and Answers Supplementary Problems Multiple-choice Questions and Answers Chapter 2: Three-phase Transformers 2.1 Advantages of Three-phase Transformers 2.2 Principle of Operation 2.3 Construction of Three-phase Transformers 2.3.1 Core-type Construction 2.3.2 Shell-type Construction 2.4 Three-phase Transformer Connection 2.4.1 Star–Star (γ/γ) Connection 2.4.2 Delta–Delta (Δ/Δ) Connection 2.4.3 Star–Delta (γ/Δ) Connection 2.4.4 Delta–Star (Δ/γ) Connection 2.4.5 Delta–Zig-zag Star Connection 2.5 Open-delta or V–V Connection 2.6 Scott Connection or T–T Connection 2.7 Three-phase to Two-phase Conversion 2.8 Parallel Operations of Transformers 2.9 Three-phase to Six-phase Conversion 2.9.1 Double-star Connection 2.9.2 Double-delta Connection 2.9.3 Six-phase Star Connection 2.9.4 Diametrical Connection 2.10 Three-winding Transformer 2.11 Three-phase Transformer Connections 2.12 Rating of Transformers Additional Solved Problems Significant Points Short Questions and Answers Supplementary Problems Multiple-choice Questions and Answers Chapter 3: Basic Concepts of Rotating Machines 3.1 Electromagnetic Torque 3.2 Reluctance Torque 3.3 Constructional Features of Rotating Electrical Machines 3.4 Construction of DC Machines 3.4.1 Magnetic Frame or Yoke 3.4.2 Pole Cores and Pole Shoes 3.4.3 Pole Coils 3.4.4 Armature Core 3.4.5 Armature Windings 3.4.6 Commutator 3.4.7 Brushes and Bearings 3.5 Ring Windings 3.6 Drum Windings 3.6.1 Number of Coil Sides Per Layer 3.6.2 Coil Span 3.6.3 Winding Pitch 3.6.4 Commutator Pitch 3.6.5 Numbering of Armature Conductors 3.6.6 Difference between Coil Span and Winding Pitch 3.7 Types of DC Windings 3.7.1 Simple Lap Winding 3.7.2 Wave Winding 3.8 Equalizing Connections for LAP Winding 3.9 Uses of Lap and Wave Windings 3.10 Dummy Coils 3.11 Principle of DC Generator 3.12 Operation of a Simple DC Generator with a Two-segment Commutator 3.13 Principle of DC Motor 3.14 Construction of Synchronous Machines 3.14.1 Stator 3.14.2 Rotor 3.14.3 Classifi cation of Synchronous Machines Based on the Prime Mover 3.14.4 Excitation System 3.14.5 Damper Windings 3.14.6 Frequency and Synchronous Speed 3.14.7 Armature Windings 3.15 Polyphase Induction Machines 3.15.1 Squirrel-cage Rotor 3.15.2 Wound Rotor 3.16 Air Gap 3.17 Principle of Operation of Three-phase Induction Motor 3.18 Synchronous Speed and Slip in Induction Motor 3.18.1 Synchronous Speed 3.18.2 Slip in Induction Motor 3.19 Frequency of Rotor Currents 3.20 Speed of the Rotor MMF 3.21 Electrical and Mechanical Degrees 3.22 Pitch Factor 3.23 Distribution Factor 3.24 Winding Factor 3.25 Flux Per Pole 3.26 Generated EMF in Full-pitched Coil 3.27 EMF Generated in AC Machines 3.27.1 Synchronous Machines 3.27.2 Induction Machines 3.27.3 A General Expression for the EMF of Synchronous Generator 3.28 EMF Generated in DC Generator 3.29 Concept of Rotating Magnetic Field 3.29.1 Case 1: ωt = θ = 0° 3.29.2 Case 2: ωt = θ = 60° 3.29.3 Case 3: ωt = θ = 120° 3.29.4 Case 4: ωt = θ = 180° Additional Solved Problems Significant Points Short Questions and Answers Supplementary Problems Multiple-choice Questions and Answers Chapter 4: DC Generators 4.1 Types of DC Machines 4.2 DC Generator 4.3 Brush Drop 4.4 EMF Equation 4.4.1 Shunt Generator 4.4.2 Series Generator 4.4.3 Long-shunt Compound Generator 4.4.4 Short-shunt Compound Generator 4.5 Derivation for Eg 4.6 Losses in DC Generator 4.7 Stray Losses 4.8 Constant or Standing Losses 4.9 Power Stages 4.10 Efficiency 4.11 Condition for Maximum Efficiency 4.12 Armature Reaction in DC Machines 4.13 Demagnetizing and Cross-magnetizing Conductors 4.14 Demagnetizing Ampere-turns Per Pole 4.15 Cross-magnetizing Ampere-turns Per Pole 4.16 Compensating Windings 4.17 Number of Compensating Windings 4.18 Commutation 4.18.1 Linear Commutation 4.18.2 Retarded Commutation 4.18.3 Accelerated Commutation 4.18.4 Sinusoidal Commutation 4.19 Value of Reactance Voltage 4.20 Methods of Improving Commutation 4.20.1 Resistance Commutation 4.20.2 EMF Commutation 4.21 Equalizer Rings 4.22 Characteristics of DC Generators 4.23 Separately Excited Generators 4.23.1 No-load Saturation Characteristic 4.23.2 Internal and External Characteristic (or Load Characteristic) 4.24 No-load Curve for Self-excited Generators 4.25 Advantages and Disadvantages of Separately Excited Generators 4.26 Voltage Build-up of Shunt Generator 4.27 Conditions for Build-up of Shunt Generator 4.28 Reasons for Failure to Build-up of Shunt Generators 4.29 External Characteristic of Shunt Generator 4.30 Voltage Regulation 4.31 Internal or Total Characteristic 4.32 External Characteristic and Internal Characteristic from OCC 4.32.1 Neglecting Armature Reaction 4.32.2 With Armature Reaction 4.33 Effect of Brush Shift on the Terminal Voltage 4.34 Series Generator 4.35 Compound Generator 4.36 Parallel Operations of DC Generators 4.37 Requirements for Paralleling DC Generators 4.38 Parallel Operation of Shunt Generators 4.39 Parallel Operation of Series Generators 4.40 Parallel Operation of Compound Generators 4.41 Uses of DC Generators 4.42 Indications of an Overloaded Generators 4.43 Causes of Overloading 4.44 Causes of Sparking at Brushes of a DC Machine 4.45 Causes of Excessive Heating of Generator on Running 4.46 Causes of Heating of Armature 4.47 Causes for Abnormal Sound in DC Generator 4.48 Reasons for Rapid Brush Wear in a DC Machine Additional Solved Problems Significant Points Short Questions and Answers Supplementary Problems Multiple-choice Questions and Answers Chapter 5: DC Motors 5.1 Voltage Equation 5.2 Back EMF 5.3 Condition for Maximum Mechanical Power 5.4 Armature Torque of a Motor 5.5 Rotational Losses of DC Machines 5.6 Compound Motor 5.7 Relation of Speed (N) with Back EMF (Eb ) and Flux (Φ) 5.8 Characteristics of Shunt or Separately Excited DC Motor 5.9 Characteristics of DC Series Motor 5.10 Characteristics of Compound Motor 5.11 Speed Regulation 5.12 Torque and Speed of DC Series Motor 5.13 Speed Control of DC Motors 5.13.1 Armature Resistance Control 5.13.2 Field Resistance Control 5.14 Ward-Leonard Control (Voltage Control) 5.15 Necessity of a Starter for DC Motors 5.16 Manual Starter 5.16.1 Three-point Starter 5.16.2 Four-point Starter 5.17 Automatic Starters 5.17.1 Time Element Starter 5.17.2 Back EMF Starter 5.17.3 Shunt Current-limit Starter 5.17.4 Series Current-limit Starter 5.18 Starters for DC Series Motors 5.19 DC Shunt Motor Starter Design 5.20 Electric Braking 5.21 Electric Braking of Shunt Motors 5.21.1 Rheostatic or Dynamic Braking 5.21.2 Plugging or Reverse Breaking 5.21.3 Regenerative Braking 5.22 Electric Braking of Series Motor 5.22.1 Rheostatic Braking 5.22.2 Plugging or Reverse Current Braking 5.22.3 Regenerative Braking 5.23 Testing of DC Machines 5.24 Brake Test 5.25 Swinburne’s Test 5.25.1 Motoring Mode 5.25.2 Generating Mode 5.26 Hopkinson’s Test (Back-to-Back Test) 5.27 Separation of Losses in a DC Machine 5.28 Retardation or Running Test 5.28.1 To Find 5.28.2 To Find J 5.29 Field’s Test 5.30 Uses of DC Motors 5.31 Special DC Machines 5.31.1 Three-wire Generator 5.31.2 Dynamometer 5.31.3 Cross-field Machines 5.32 Characteristics of Cross-field Generators 5.33 Brushless DC Motor 5.33.1 Unipolar or Half-wave Brushless DC Motor 5.33.2 Bipolar or Full-wave Brushless DC Motor 5.34 Features of Brushless DC Motor Additional Solved Problems Significant Points Short Questions and Answers Supplementary Problems Multiple-choice Questions and Answers Chapter 6: Synchronous Generators 6.1 Parameters of Armature Winding 6.1.1 Armature Resistance 6.1.2 Armature Leakage Reactance (XL) 6.2 Armature Reaction 6.2.1 Unity Power Factor Load 6.2.2 Zero Lagging Power Factor Load 6.2.3 Zero Leading Power Factor Load 6.3 Concept of Synchronous Reactance and Impedance 6.4 Equivalent Circuit of an Alternator 6.5 Voltage Equation of Alternator 6.6 Phasor Diagram of Alternator 6.6.1 Lagging Power Factor 6.6.2 Unity Power Factor 6.6.3 Leading Power Factor 6.7 Voltage Regulation 6.8 Determination of Voltage Regulation 6.8.1 Direct Loading 6.8.2 The emf or Synchronous Impedance Method 6.8.3 Ampere-turn Method 6.8.4 Zero Power Factor Method or Potier Method 6.8.5 ASA Method 6.9 Load Characteristics of Alternators 6.10 Output Power Equation of an Alternator 6.10.1 Real Power Output per Phase of Alternator (Pog) 6.10.2 Reactive Power Output per Phase of Alternator (Qog) 6.10.3 Maximum Power Output per Phase of Alternator 6.10.4 Power Output Equation of Alternator Neglecting Armature Resistance 6.11 Input Power Equation of Alternator 6.11.1 Real Power Input per Phase to Alternator 6.11.2 Reactive Power Input per Phase to Alternator 6.12 Two-reaction Theory 6.13 Two-reaction Theory of Salient-pole Alternator 6.14 Torque-angle Characteristic of Salient-pole Alternator 6.15 Maximum Reactive Power for Salient-pole Alternator 6.16 Losses and Efficiency 6.16.1 Determination of Losses 6.17 Determination of Xd and Xq 6.18 Capability Curves 6.19 Excitation Circle of an Alternator 6.20 Prime Mover Characteristic 6.20.1 Sharing of Powers by Two Alternators 6.21 Infinite Bus 6.22 Need for Parallel Operation of Alternators 6.22.1 Reasons for Paralleling of Alternators 6.22.2 Conditions for Paralleling of Alternators 6.22.3 Identical Voltage Requirement 6.22.4 Identical Phase Sequence 6.22.5 In-phase Requirement 6.22.6 Identical Frequency Requirement 6.22.7 Relation of Prime Mover Torque Speed 6.23 Synchronizing Procedures of Alternator 6.23.1 Voltage Matching 6.23.2 Phase Sequence Matching 6.23.3 Determination of In-phase 6.23.4 Frequency Synchronization 6.23.5 Synchroscope Synchronization 6.24 Distribution of Load 6.24.1 Effect of Change in Excitation 6.24.2 Effect of Change of Steam Supply 6.25 Synchronizing Power and Synchronizing Torque Coefficient 6.26 Units of Synchronizing Power Coefficient 6.27 Significance of Synchronizing Power Coefficient 6.28 Hunting 6.28.1 Causes of Hunting 6.28.2 Effects of Hunting 6.28.3 Reduction of Hunting 6.29 Oscillations of Synchronous Machines 6.30 Sudden Short Circuit of Synchronous Generator 6.31 Short-circuit Ratio 6.32 Protection of Generators Additional Solved Problems Significant Points Short Questions and Answers Supplementary Problems Multiple-choice Questions and Answers Chapter 7: Synchronous Motors 7.1 Principles of Operation 7.2 Armature Reaction in Synchronous Motors 7.3 Phasor Diagram of Synchronous Motor 7.3.1 Effect of Loading Synchronous Motor 7.3.2 Lagging Power Factor Load 7.3.3 Leading Power Factor Load 7.3.4 Unity Power Factor Load 7.4 Operation at a Constant Load with Variable Excitation 7.5 V Curves and Inverted V Curves 7.6 Complex Power Input of Synchronous Motor 7.7 Complex Power Output of a Synchronous Motor 7.8 Maximum Output Power 7.9 Power Output when Armature Resistance Is Negligible 7.10 Input Reactive Power when Armature Resistance Is Negligible 7.11 Motor Characteristics, Performance and Circle Diagram of a Synchronous Motor 7.11.1 Current Locus for Constant Power Input 7.11.2 Current Locus for Constant Power Developed (Pom ) 7.11.3 Current Locus for Constant Excitation (E f ) 7.12 Torque of a Synchronous Motor 7.13 Salient-pole Synchronous Motor—Two-reaction Model 7.13.1 Lagging Power Factor 7.13.2 Leading Power Factor 7.13.3 Unity Power Factor 7.14 Power Developed by a Salient-pole Synchronous Motor 7.14.1 Stability and Maximum Load Angle 7.15 Damper Windings 7.16 Damping Effect 7.17 Hunting/Surging of Synchronous Motors 7.18 Periodicity of Hunting 7.19 Methods of Starting of Synchronous Motors 7.20 Applications of Synchronous Motor 7.21 Synchronous Condensers Additional Solved Problems Significant Points Short Questions and Answers Supplementary Problems Multiple-choice Questions and Answers Chapter 8: Polyphase Induction Motors 8.1 Rotor Current 8.2 Rotor Power 8.3 Expression for Torque 8.4 Starting Torque 8.4.1 Starting Torque of a Squirrel-cage Motor 8.4.2 Starting Torque of Slip-ring Motor 8.5 Effect of Change in Supply Voltage on Starting Torque 8.6 Effect of Change in Supply Voltage on Torque and Slip 8.7 Condition for Maximum Torque 8.8 Torque-slip and Torque-speed Characteristics 8.9 Relation Between Full-load Torque and Maximum Torque 8.10 Relation Between Starting Load Torque and Maximum Torque 8.11 Condition for the Starting Torque to be Equal to the Maximum Torque 8.12 Effect of Variation of Rotor Resistance and Rotor Reactance on Maximum Torque, Efficiency and Power Factor of an Induction Motor 8.12.1 Effect of Rotor Resistance on Maximum Torque 8.12.2 Effect of R2 and X 2 on the Power Factor of an Induction Motor 8.12.3 Effect of R2 and X 2 on the Efficiency of an Induction Motor 8.13 Effect of Change in Supply Voltage on Torque and Speed 8.14 Effect of Change in Supply Frequency on Torque and Speed 8.15 Losses 8.16 Power Stages 8.17 Efficiency 8.18 Synchronous Watt 8.19 Measurement of Slip 8.19.1 Electromechanical Counter 8.19.2 Mechanical Differential Counter 8.19.3 Stroboscopic Method 8.20 Equivalent Circuit 8.20.1 Stator Equivalent Circuit 8.20.2 Rotor Equivalent Circuit 8.21 Thevenin’s Equivalent Circuit of an Induction Motor 8.22 Starting of Induction Motors 8.23 Starting of Squirrel-cage Motors 8.23.1 Direct-on-line Starting of Induction Motors 8.23.2 Stator Resistor (or Reactor) Starting 8.23.3 Autotransformer Starting 8.23.4 Star-delta Starter 8.24 Starting of Slip-ring Induction Motors 8.25 No-load Test or Open-circuit Test 8.26 Blocked-rotor or Short-circuit Test 8.27 Direct Testing of Induction Motors 8.28 Circle Diagram 8.29 Speed Control of Induction Motor 8.29.1 Speed Control from Rotor Side 8.29.2 Speed Control of Induction Motors from Stator Side 8.30 Comparison Between Wound-rotor and Cage-rotor Induction Motors 8.31 Crawling 8.32 Magnetic Locking (Cogging) 8.33 Deep-cage Rotors 8.34 Double-cage Rotors 8.35 Applications 8.36 Comparison Between Synchronous and Induction Motors 8.37 Factors Governing the performance of Induction Motors 8.38 Effects of Operating Conditions 8.39 Ratings of Induction Motor 8.40 Common Faults in Three-phase Induction Motors 8.41 Most Probabale Reasons for which Three-phase Induction Motors Fail to Start 8.42 Most Probabale Reasons for Which Three-phase Induction Motors Fail to Carry Load 8.43 Schrage Motor 8.44 Power Factor Compensation 8.45 Linear Induction Motor 8.46 Induction Generator 8.47 Electrical Braking of Polyphase Induction Motors 8.47.1 Regenerative Braking 8.47.2 Plugging or Counter-current Braking 8.47.3 Dynamic Braking 8.48 Synchronous-induction Motor Additional Solved Problems Signifi cant Points Short Questions and Answers Supplementary Problems Multiple-choice Questions and Answers Chapter 9: Single-phase Motors and Special Machines 9.1 Classification of Single-phase Induction Motors 9.2 Production of Rotating Field 9.3 Working Principle of Single-phase Induction Motor 9.4 Double Revolving Field Theory 9.5 Rotor Slip with Respect to Two Rotating Fields 9.6 Equivalent Circuit of Single-phase, Single-winding Induction Motor 9.7 Power Developed and Losses of Single-phase, Single-winding Induction Motor 9.8 Determination of Equivalent Circuit Parameters 9.8.1 Blocked Rotor Test 9.8.2 No-load Test 9.9 Split-phase Induction Motors 9.10 Capacitor Motors 9.10.1 Capacitor-start Motors 9.10.2 Capacitor-start Capacitor-run Motors 9.11 Permanent Split Capacitor Motors 9.12 Shaded Pole Motor 9.13 Single-phase Synchronous Motors 9.13.1 Reluctance Motors 9.13.2 Hysteresis Motor 9.14 Series Motor or Universal Motor 9.14.1 Circuit Model and Phasor Diagram 9.14.2 Torque 9.14.3 Phasor Diagram and Performance Characteristics 9.15 Stepper Motor 9.15.1 Variable Reluctance Stepper Motor 9.15.2 Permanent Magnet Stepper Motor 9.15.3 Hybrid Stepper Motor 9.16 Characteristics of Stepper Motors 9.17 DC Servomotors 9.17.1 Excitation of DC Servomotors 9.17.2 Armature-controlled DC Servomotor 9.17.3 Field-controlled DC Servomotors 9.18 AC Servomotors 9.19 Servomechanism 9.19.1 Positional Servomechanism 9.19.2 Rate Servomechanism 9.19.3 Damping by Derivative Feedback Significant Points Short Questions and Answers Supplementary Problems Multiple-choice Questions and Answers Appendix A Appendix B Appendix C Appendix D Appendix E Appendix F Appendix G Appendix H Multiple Choice Questions References Index