Electrical Machine Fundamentals with Numerical Simulation using MATLAB / SIMULINK

Description

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