Electrical Machine Fundamentals with Numerical Simulation using MATLAB / SIMULINK

Cover\nTitle Page\nCopyright\nContents\nPreface\nAcknowledgements\nChapter 1 Fundamentals of Electrical Machines\n	1.1 Preliminary Remarks\n	1.2 Basic Laws of Electrical Engineering\n		1.2.1 Ohm\'s Law\n		1.2.2 Generalization of Ohm\'s Law\n			1.2.2.1 Derivation of Eq. (1.6)\n		1.2.3 Ohm\'s Law for Magnetic Circuits\n		1.2.4 Kirchhoff\'s Laws for Magnetic Circuits\n		1.2.5 Lorentz Force Law\n		1.2.6 Biot‐Savart Law\n		1.2.7 Ampere Circuital Law\n		1.2.8 Faraday\'s Law\n			1.2.8.1 Motional emf\n		1.2.9 Flux Linkages and Induced Voltages\n		1.2.10 Induced Voltages\n		1.2.11 Induced Electric Fields\n		1.2.12 Reformulation of Faraday\'s Law\n	1.3 Inductance\n		1.3.1 Application of Ampere\'s Law to Find B in a Solenoid\n		1.3.2 Magnetic Field of a Toroid\n		1.3.3 The Inductance of Circular Air‐Cored Toroid\n		1.3.4 Mutual Inductance\n	1.4 Energy\n	1.5 Overview of Electric Machines\n	1.6 Summary\n	Problems\n	References\nChapter 2 Magnetic Circuits\n	2.1 Preliminary Remarks\n	2.2 Permeability\n	2.3 Classification of Magnetic Materials\n		2.3.1 Uniform Magnetic Field\n		2.3.2 Magnetic‐Field Intensity\n	2.4 Hysteresis Loop\n		2.4.1 Hysteresis Loop for Soft Iron and Steel\n	2.5 Eddy‐Current and Core Losses\n	2.6 Magnetic Circuits\n		2.6.1 The Magnetic Circuit Concept\n		2.6.2 Magnetic Circuits Terminology\n			2.6.2.1 Limitations of the Analogy Between Electric and Magnetic Circuits\n		2.6.3 Effect of Air Gaps\n			2.6.3.1 Magnetic Circuit with an Air Gap\n			2.6.3.2 Magnetic Forces Exerted by Electromagnets\n	2.7 Field Energy\n		2.7.1 Energy Stored in a Magnetic Field\n			2.7.1.1 The Magnetic Energy in Terms of the Magnetic Induction B\n			2.7.1.2 The Magnetic Energy in Terms of the Current Density J and the Vector Potential A\n			2.7.1.3 The Magnetic Energy in Terms of the Current I and of the Flux Ψm\n			2.7.1.4 The Magnetic Energy in Terms of the Currents and Inductances\n	2.8 The Magnetic Energy for a Solenoid Carrying a Current I\n	2.9 Energy Flow Diagram\n		2.9.1 Power Flow Diagram of DC Generator and DC Motor\n			2.9.1.1 Power Flow Diagram and Losses of Induction Motor\n			2.9.1.2 Rotational Losses\n	2.10 Multiple Excited Systems\n	2.11 Doubly Excited Systems\n		2.11.1 Torque Developed\n			2.11.1.1 Excitation Torque\n			2.11.1.2 Reluctance Torque\n	2.12 Concept of Rotating Magnetic Field\n		2.12.1 Rotating Magnetic Field due to Three‐Phase Currents\n			2.12.1.1 Speed of Rotating Magnetic Field\n			2.12.1.2 Direction of Rotating Magnetic Field\n		2.12.2 Alternate Mathematical Analysis for Rotating Magnetic Field\n	2.13 Summary\n	Problems\n	References\nChapter 3 Single‐Phase and Three‐Phase Transformers\n	3.1 Preliminary Remarks\n	3.2 Classification of Transformers\n		3.2.1 Classification Based on Number of Phases\n			3.2.1.1 Single‐Phase Transformers\n			3.2.1.2 Three‐Phase Transformers\n			3.2.1.3 Multi‐Phase Transformers\n		3.2.2 Classification Based on Operation\n			3.2.2.1 Step‐Up Transformers\n			3.2.2.2 Step‐Down Transformers\n		3.2.3 Classification Based on Construction\n			3.2.3.1 Core‐Type Transformers\n			3.2.3.2 Shell‐Type Transformers\n		3.2.4 Classification Based on Number of Windings\n			3.2.4.1 Single‐Winding Transformer\n			3.2.4.2 Two‐Winding Transformer\n			3.2.4.3 Three‐Winding Transformer\n		3.2.5 Classification Based on Use\n			3.2.5.1 Power Transformer\n			3.2.5.2 Distribution Transformer\n	3.3 Principle of Operation of the Transformer\n		3.3.1 Ideal Transformer\n	3.4 Impedance Transformation\n	3.5 DOT Convention\n	3.6 Real/Practical Transformer\n	3.7 Equivalent Circuit of a Single‐Phase Transformer\n	3.8 Phasor Diagrams Under Load Condition\n	3.9 Testing of Transformer\n		3.9.1 Open‐Circuit Test\n		3.9.2 Short‐Circuit Test\n	3.10 Performance Measures of a Transformer\n		3.10.1 Voltage Regulation\n			3.10.1.1 Condition for Maximum Voltage Regulation\n			3.10.1.2 Condition for Zero Voltage Regulation\n		3.10.2 Efficiency of Transformer\n		3.10.3 Maximum Efficiency Condition\n	3.11 All‐Day Efficiency or Energy Efficiency\n	3.12 Autotransformer\n	3.13 Three‐Phase Transformer\n		3.13.1 Input (Y), Output (Δ)\n		3.13.2 Input Delta (Δ), Output Star (Y)\n		3.13.3 Input Delta (Δ), Output Delta (Δ)\n		3.13.4 Input Star (Y), Output Star (Y)\n	3.14 Single‐Phase Equivalent Circuit of Three‐Phase Transformer\n	3.15 Open‐Delta Connection or V Connection\n	3.16 Harmonics in a Single‐Phase Transformer\n		3.16.1 Excitation Phenomena in a Single‐Phase Transformer\n		3.16.2 Harmonics in a Three‐Phase Transformer\n			3.16.2.1 Star‐Delta Connection with Grounded Neutral\n			3.16.2.2 Star‐Delta Connection without Grounded Neutral\n		3.16.3 Summary\n		3.16.4 Star‐Star with Isolated Neutral\n	3.17 Disadvantages of Harmonics in Transformer\n		3.17.1 Effect of Harmonic Currents\n		3.17.2 Electromagnetic Interference\n		3.17.3 Effect of Harmonic Voltages\n		3.17.4 Summary\n		3.17.5 Oscillating Neutral Phenomena\n	3.18 Open Circuit and Short‐Circuit Conditions in a Three‐Phase Transformer\n	3.19 Matlab/Simulink Model of a Single‐Phase Transformer\n	3.20 Matlab/Simulink Model of Testing of Transformer\n	3.21 Matlab/Simulink Model of Autotransformer\n	3.22 Matlab/Simulink Model of Three‐Phase Transformer\n	3.23 Supplementary Solved Problems\n	3.24 Summary\n	3.25 Problems\n	References\nChapter 4 Fundamentals of Rotating Electrical Machines and Machine Windings\n	4.1 Preliminary Remarks\n	4.2 Generator Principle\n		4.2.1 Simple Loop Generator\n		4.2.2 Action of Commutator\n		4.2.3 Force on a Conductor\n			4.2.3.1 DC Motor Principle\n			4.2.3.2 Motor Action\n	4.3 Machine Windings\n		4.3.1 Coil Construction\n			4.3.1.1 Coil Construction: Distributed Winding\n			4.3.1.2 Coil Construction: Concentrated Winding\n			4.3.1.3 Coil Construction: Conductor Bar\n		4.3.2 Revolving (Rotor) Winding\n		4.3.3 Stationary (Stator) Winding\n		4.3.4 DC Armature Windings\n			4.3.4.1 Pole Pitch (Yp)\n			4.3.4.2 Coil Pitch or Coil Span (Ycs)\n			4.3.4.3 Back Pitch (Yb)\n			4.3.4.4 Front Pitch (Yf)\n			4.3.4.5 Resultant Pitch (Y)\n			4.3.4.6 Commutator Pitch (a)\n		4.3.5 Lap Winding\n			4.3.5.1 Lap Multiple or Parallel Windings\n			4.3.5.2 Formulas for Lap Winding\n			4.3.5.3 Multiplex, Single, Double, and Triple Windings\n			4.3.5.4 Meaning of the Term Re‐entrant\n			4.3.5.5 Multiplex Lap Windings\n		4.3.6 Wave Winding\n			4.3.6.1 Formulas for Wave Winding\n			4.3.6.2 Multiplex Wave or Series‐Parallel Winding\n			4.3.6.3 Formulas for Series‐Parallel Winding\n		4.3.7 Symmetrical Windings\n			4.3.7.1 Possible Symmetrical Windings for DC Machines of a Different Number of Poles\n		4.3.8 Equipotential Connectors (Equalizing Rings)\n		4.3.9 Applications of Lap and Wave Windings\n		4.3.10 Dummy or Idle Coils\n			4.3.10.1 Dummy Coils\n		4.3.11 Whole‐Coil Winding and Half‐Coil Winding\n		4.3.12 Concentrated Winding\n		4.3.13 Distributed Winding\n	4.4 Electromotive Force (emf) Equation\n		4.4.1 emf Equation of an Alternator\n			4.4.1.1 Winding Factor (Coil Pitch and Distributed Windings)\n		4.4.2 Winding Factors\n			4.4.2.1 Pitch Factor or Coil Pitch (Pitch Factor (Kp) or Coil Span Factor [Kc])\n		4.4.3 Distribution Factor (Breadth Factor (Kb) or Distribution Factor (Kd))\n			4.4.3.1 Distribution Factor (Kd)\n	4.5 Magnetomotive Force (mmf) of AC Windings\n		4.5.1 mmf and Flux in Rotating Machine\n		4.5.2 Main Air‐Gap Flux (Field Flux)\n		4.5.3 mmf of a Coil\n			4.5.3.1 mmf\n			4.5.3.2 mmf of Distributed Windings\n			4.5.3.3 mmf Space Wave of a Single Coil\n			4.5.3.4 mmf Space Wave of One Phase of a Distributed Winding\n	4.6 Harmonic Effect\n		4.6.1 The Form Factor and the emf per Conductor\n		4.6.2 The Wave Form\n		4.6.3 Problem Due to Harmonics\n		4.6.4 Elimination or Suppression of Harmonics\n			4.6.4.1 Shape of Pole Face\n			4.6.4.2 Use of Several Slots per Phase per Pole\n			4.6.4.3 Use of Short‐Pitch Windings\n			4.6.4.4 Effect of the Y‐ and Δ ‐Connection on Harmonics\n			4.6.4.5 Harmonics Produced by Armature Slots\n	4.7 Basic Principles of Electric Machines\n		4.7.1 AC Rotating Machines\n			4.7.1.1 The Rotating Magnetic Field\n			4.7.1.2 The Relationship between Electrical Frequency and the Speed of Magnetic Field Rotation\n			4.7.1.3 Reversing the Direction of the Magnetic Field Rotation\n			4.7.1.4 The Induced Voltage in AC Machines\n			4.7.1.5 The Induced Voltage in a Coil on a Two‐Pole Stator\n			4.7.1.6 The Induced Voltage in a Three‐Phase Set of Coils\n			4.7.1.7 The rms Voltage in a Three‐Phase Stator\n		4.7.2 The Induced Torque in an AC Machine\n	4.8 Summary\n	Problems\n	References\nChapter 5 DC Machines\n	5.1 Preliminary Remarks\n	5.2 Construction and Types of DC Generator\n		5.2.1 Construction of DC Machine\n		5.2.2 Types of DC Generator\n	5.3 Principle of Operation of DC Generator\n		5.3.1 Voltage Build‐Up in a DC Generator\n		5.3.2 Function of Commutator\n	5.4 Commutation Problem and Solution\n		5.4.1 Brush Shifting\n		5.4.2 Commutating Poles\n		5.4.3 Compensating Windings\n	5.5 Types of Windings\n	5.6 emf Equations in a DC Generator\n	5.7 Brush Placement in a DC Machine\n	5.8 Equivalent Circuit of DC Generator\n	5.9 Losses of DC Generator\n	5.10 Armature Reaction\n		5.10.1 No‐Load Operation\n		5.10.2 Loaded Operation\n	5.11 Principle of Operation of a DC Motor\n		5.11.1 Equivalent Circuit of a DC Motor\n	5.12 emf and Torque Equations of DC Motor\n	5.13 Types of DC Motor\n		5.13.1 Separately Excited DC Motor\n		5.13.2 Self‐Excited DC Motor\n			5.13.2.1 Shunt DC Motor\n			5.13.2.2 Series DC Motor\n	5.14 Characteristics of DC Motors\n		5.14.1 Separately Excited and DC Shunt Motor\n		5.14.2 DC Series Motor\n		5.14.3 Compound Motor\n	5.15 Starting of a DC Motor\n		5.15.1 Design of a Starter for a DC Motor\n		5.15.2 Types of Starters\n			5.15.2.1 Three‐Point Starter\n			5.15.2.2 Four‐Point Starter\n	5.16 Speed Control of a DC Motor\n		5.16.1 Separately Excited and DC Shunt Motor\n		5.16.2 DC Series Motor\n	5.17 Solved Examples\n	5.18 Matlab/Simulink Model of a DC Machine\n		5.18.1 Matlab/Simulink Model of a Separately/ Shunt DC Motor\n		5.18.2 Matlab/Simulink Model of a DC Series Motor\n		5.18.3 Matlab/Simulink Model of a Compound DC Motor\n	5.19 Summary\n	Problems\n	Reference\nChapter 6 Three‐Phase Induction Machine\n	6.1 Preliminary Remarks\n	6.2 Construction of a Three‐Phase Induction Machine\n		6.2.1 Stator\n		6.2.2 Stator Frame\n		6.2.3 Rotor\n	6.3 Principle Operation of a Three‐Phase Induction Motor\n		6.3.1 Slip in an Induction Motor\n		6.3.2 Frequency of Rotor Voltage and Current\n		6.3.3 Induction Machine and Transformer\n	6.4 Per‐phase Equivalent Circuit of a Three‐Phase Induction Machine\n	6.5 Power Flow Diagram in a Three‐Phase Induction Motor\n	6.6 Power Relations in a Three‐Phase Induction Motor\n	6.7 Steps to Find Powers and Efficiency\n	6.8 Per‐Phase Equivalent Circuit Considering Stray‐Load Losses\n	6.9 Torque and Power using Thevenin\'s Equivalent Circuit\n	6.10 Torque‐Speed Characteristics\n		6.10.1 Condition for Maximum Torque\n		6.10.2 Condition for Maximum Torque at Starting\n		6.10.3 Approximate Equations\n	6.11 Losses in a Three‐Phase Induction Machine\n		6.11.1 Copper Losses or Resistive Losses\n		6.11.2 Magnetic Losses\n		6.11.3 Mechanical Losses\n		6.11.4 Stray‐Load Losses\n	6.12 Testing of a Three‐Phase Induction Motor\n		6.12.1 No‐Load Test\n		6.12.2 Blocked Rotor Test\n		6.12.3 DC Test\n		6.12.4 Load Test\n		6.12.5 International Standards for Efficiency of Induction Machines\n		6.12.6 International Standards for the Evaluation of Induction Motor Efficiency\n	6.13 Starting of a Three‐Phase Induction Motor\n		6.13.1 Direct‐on‐Line Start\n		6.13.2 Line Resistance Start\n		6.13.3 Star‐Delta Starter\n		6.13.4 Autotransformer Starter\n	6.14 Speed Control of Induction Machine\n		6.14.1 By Varying the Frequency of the Supply\n		6.14.2 Pole Changing Method\n			6.14.2.1 Multiple Numbers of Windings\n			6.14.2.2 Consequent Pole Method\n		6.14.3 Stator Voltage Control\n			6.14.3.1 Voltage/Frequency = Constant Control\n			6.14.3.2 Rotor Resistance Variation\n			6.14.3.3 Rotor Voltage Injection Method\n			6.14.3.4 Cascade Connection of Induction Machines\n			6.14.3.5 Pole‐Phase Modulation for Speed Control\n	6.15 Matlab/Simulink Modelling of the Three‐Phase Induction Motor\n		6.15.1 Plotting Torque‐Speed Curve under Steady‐State Condition\n		6.15.2 Dynamic Simulation of Induction Machine\n	6.16 Practice Examples\n	6.17 Summary\n	Problems\n	References\nChapter 7 Synchronous Machines\n	7.1 Preliminary Remarks\n	7.2 Synchronous Machine Structures\n		7.2.1 Stator and Rotor\n	7.3 Working Principle of the Synchronous Generator\n		7.3.1 The Synchronous Generator under No‐Load\n		7.3.2 The Synchronous Generator under Load\n	7.4 Working Principle of the Synchronous Motor\n	7.5 Starting of the Synchronous Motor\n		7.5.1 Starting by External Motor\n		7.5.2 Starting by using Damper Winding\n		7.5.3 Starting by Variable Frequency Stator Supply\n	7.6 Armature Reaction in Synchronous Motor\n	7.7 Equivalent Circuit and Phasor Diagram of the Synchronous Machine\n		7.7.1 Phasor Diagram of the Synchronous Generator\n		7.7.2 Phasor Diagram of the Synchronous Motor\n	7.8 Open‐Circuit and Short‐Circuit Characteristics\n		7.8.1 Open‐Circuit Curve\n		7.8.2 Short‐Circuit Curve\n		7.8.3 The Unsaturated Synchronous Reactance\n		7.8.4 The Saturated Synchronous Reactance\n		7.8.5 Short‐Circuit Ratio\n	7.9 Voltage Regulation\n		7.9.1 Emf or Synchronous Method\n		7.9.2 The Ampere‐Turn or mmf Method\n		7.9.3 Zero‐Power Factor Method or Potier Triangle Method\n			7.9.3.1 Steps for Drawing Potier Triangles\n			7.9.3.2 Procedure to Obtain Voltage Regulation using the Potier Triangle Method\n	7.10 Efficiency of the Synchronous Machine\n	7.11 Torque and Power Curves\n		7.11.1 Real/Active Output Power of the Synchronous Generator\n		7.11.2 Reactive Output Power of the Synchronous Generator\n		7.11.3 Complex Input Power to the Synchronous Generator\n		7.11.4 Real/Active Input Power to the Synchronous Generator\n		7.11.5 Reactive Input Power to the Synchronous Generator\n	7.12 Maximum Power Output of the Synchronous Generator\n	7.13 Capability Curve of the Synchronous Machine\n	7.14 Salient Pole Machine\n		7.14.1 Phasor Diagram of a Salient Pole Synchronous Generator\n		7.14.2 Power Delivered by a Salient Pole Synchronous Generator\n		7.14.3 Maximum Active and Reactive Power Delivered by a Salient Pole Synchronous Generator\n			7.14.3.1 Active Power\n			7.14.3.2 Reactive Power\n	7.15 Synchronization of an Alternator with a Bus‐Bar\n		7.15.1 Process of Synchronization\n	7.16 Operation of a Synchronous Machine Connected to an Infinite Bus‐Bar (Constant Vt and f)\n		7.16.1 Motor Operation of Change in Excitation at Fixed Shaft Power\n		7.16.2 Generator Operation for Change in Output Power at Fixed Excitation\n	7.17 Hunting in the Synchronous Motor\n		7.17.1 Role of the Damper Winding\n	7.18 Parallel Operation of Synchronous Generators\n		7.18.1 The Synchronous Generator Operating in Parallel with the Infinite Bus Bar\n	7.19 Matlab/Simulink Model of a Salient Pole Synchronous Machine\n		7.19.1 Results Motoring Mode\n		7.19.2 Results Generator Mode\n	7.20 Summary\n	Problems\n	Reference\nChapter 8 Single‐Phase and Special Machines\n	8.1 Preliminary Remarks\n	8.2 Single‐phase Induction Machine\n		8.2.1 Field System in a Single‐phase Machine\n	8.3 Equivalent Circuit of Single‐phase Machines\n		8.3.1 Equivalent Circuit Analysis\n			8.3.1.1 Approximate Equivalent Circuit\n			8.3.1.2 Thevenin\'s Equivalent Circuit\n	8.4 How to Make a Single‐phase Induction Motor Self Starting\n	8.5 Testing of an Induction Machine\n		8.5.1 DC Test\n		8.5.2 No‐load Test\n		8.5.3 Blocked‐Rotor Test\n	8.6 Types of Single‐Phase Induction Motors\n		8.6.1 Split‐Phase Induction Motor\n		8.6.2 Capacitor‐Start Induction Motor\n		8.6.3 Capacitor‐Start Capacitor‐Run Induction Motor (Two‐Value Capacitor Method)\n	8.7 Single‐Phase Induction Motor Winding Design\n		8.7.1 Split‐Phase Induction Motor\n		8.7.2 Capacitor‐Start Motors\n	8.8 Permanent Split‐Capacitor (PSC) Motor\n	8.9 Shaded‐Pole Induction Motor\n	8.10 Universal Motor\n	8.11 Switched‐Reluctance Motor (SRM)\n	8.12 Permanent Magnet Synchronous Machines\n	8.13 Brushless DC Motor\n	8.14 Mathematical Model of the Single‐phase Induction Motor\n	8.15 Simulink Model of a Single‐Phase Induction Motor\n	8.16 Summary\n	Problems\n	Reference\nChapter 9 Motors for Electric Vehicles and Renewable Energy Systems\n	9.1 Introduction\n	9.2 Components of Electric Vehicles\n		9.2.1 Types of EVs\n			9.2.1.1 Battery‐Based EVs\n			9.2.1.2 Hybrid EVs\n			9.2.1.3 Fuel‐Cell EVs\n		9.2.2 Significant Components of EVs\n			9.2.2.1 Battery Bank\n			9.2.2.2 DC‐DC Converters\n			9.2.2.3 Power Inverter\n			9.2.2.4 Electric Motor\n			9.2.2.5 Transmission System or Gear Box\n			9.2.2.6 Other Components\n	9.3 Challenges and Requirements of Electric Machines for EVs\n		9.3.1 Challenges of Electric Machines for EVs\n		9.3.2 Requirements of Electric Machines for EVs\n	9.4 Commercially Available Electric Machines for EVs\n		9.4.1 DC Motors\n		9.4.2 Induction Motor\n		9.4.3 Permanent Magnet Synchronous Motors (PMSM)\n		9.4.4 Brushless DC Motors\n		9.4.5 Switched Reluctance Motors (SRMs)\n	9.5 Challenges and Requirements of Electric Machines for RES\n	9.6 Commercially Available Electric Machines for RES\n		9.6.1 DC Machine\n		9.6.2 Induction Machines\n		9.6.3 Synchronous Machines\n		9.6.4 Advanced Machines for Renewable Energy\n	9.7 Summary\n	References\nChapter 10 Multiphase (More than Three‐Phase) Machines Concepts and Characteristics\n	10.1 Preliminary Remarks\n	10.2 Necessity of Multiphase Machines\n		10.2.1 Evolution of Multiphase Machines\n		10.2.2 Advantages of Multiphase Machines\n			10.2.2.1 Better Space Harmonics Profile\n			10.2.2.2 Better Torque Ripple Profile\n			10.2.2.3 Improved Efficiency\n			10.2.2.4 Fault Tolerant Capability\n			10.2.2.5 Reduced Ratings of Semiconductor Switches and Better Power/Torque Distribution\n			10.2.2.6 Torque Enhancement by Injecting Lower‐Order Harmonics into Stator Currents\n		10.2.3 Applications of Multiphase Machines\n	10.3 Working Principle\n		10.3.1 Multiphase Induction Machine\n		10.3.2 Multiphase Synchronous Machine\n	10.4 Stator‐Winding Design\n		10.4.1 Three‐Phase Windings\n			10.4.1.1 Single‐Layer Full‐Pitch Winding\n			10.4.1.2 Single‐Layer Short‐Pitch Winding\n			10.4.1.3 Double‐Layer Full‐Pitch Winding\n			10.4.1.4 Double‐Layer Short‐Pitch Winding\n			10.4.1.5 Fractional‐Slot Winding\n		10.4.2 Five‐Phase Windings\n		10.4.3 Six‐Phase Windings\n			10.4.3.1 Symmetrical Winding of Six‐Phase Machine\n			10.4.3.2 Asymmetrical Winding\n		10.4.4 Nine‐Phase Windings\n	10.5 Mathematical Modelling of Multiphase Machines\n		10.5.1 Mathematical Modelling of Multiphase Induction Machines in Original Phase‐Variable Domain\n		10.5.2 Transformation Matrix for Multiphase Machines\n		10.5.3 Modelling of Multiphase Induction Machines in Arbitrary Reference Frames\n		10.5.4 Commonly used Reference Frames\n		10.5.5 Modelling of a Multiphase Synchronous Machine\n	10.6 Vector Control Techniques for Multiphase Machines\n		10.6.1 Indirect Field‐Oriented Control or Vector‐Control Techniques for Multiphase Induction Machines\n		10.6.2 Vector Control for Multiphase Synchronous Machines\n	10.7 Matlab/Simulink Model of Multiphase Machines\n		10.7.1 Dynamic Model of the Nine‐Phase Induction Machine\n		10.7.2 Dynamic Model of the Nine‐Phase Synchronous Machine\n	10.8 Summary\n	Problems\n	References\nChapter 11 Numerical Simulation of Electrical Machines using the Finite Element Method\n	11.1 Introduction\n	11.2 Methods of Solving EM Analysis\n		11.2.1 Analytical Techniques\n		11.2.2 Numerical Techniques\n			11.2.2.1 Finite Difference Method\n			11.2.2.2 Finite Element Method\n			11.2.2.3 Solution of Laplace Equation Using the Finite Element Method\n	11.3 Formulation of 2‐Dimensional and 3‐Dimensional Analysis\n		11.3.1 Maxwell Equations\n			11.3.1.1 Gauss Law\n			11.3.1.2 Gauss Law of Magnetism\n			11.3.1.3 Ampere\'s Integral Law\n			11.3.1.4 Faraday\'s Integral Law\n			11.3.1.5 Differential Form of Maxwell Equations\n		11.3.2 FEM Adaptive Meshing\n		11.3.3 FEM Variation Principle\n	11.4 Analysis and Implementation of FEM Machine Models\n		11.4.1 RMxprt Design to Implement a Maxwell Model of Machine\n		11.4.2 Power Converter Design in Simplorer\n		11.4.3 Integration of Power Converter with a Maxwell Model for Testing Drive\n	11.5 Example Model of Three‐Phase IM in Ansys Maxwell 2D\n	11.6 Summary\n	References\nIndex\nEULA