Electrical Machine Fundamentals with Numerical Simulation using MATLAB / SIMULINK

Dr. Atif Iqbal is a Full Professor in the Department of Electrical Engineering, Qatar University. He is an IET Fellow (UK), IE Fellow (India), and Senior Member of the IEEE, as well as Associate Editor, IEEE Trans. on Industrial Electronics.Dr. Shaikh Moinoddin is a Senior Member of the IEEE, India. He is former Assistant Professor in Electrical Engineering at the University of Polytechnic, Aligarh Muslim University, Aligarh, India.Dr. Bhimireddy Prathap Reddy is currently working as a Post-doc at the Department of Electrical Engineering, Qatar University and is a member of the IEEE.

• Preface xxiAcknowledgements xxiii1 Fundamentals of Electrical Machines 11.1 Preliminary Remarks 11.2 Basic Laws of Electrical Engineering 11.2.1 Ohm’s Law 11.2.2 Generalization of Ohm’s Law 21.2.2.1 Derivation of Eq. (1.6) 21.2.3 Ohm’s Law for Magnetic Circuits 31.2.4 Kirchhoff’s Laws for Magnetic Circuits 31.2.5 Lorentz Force Law 51.2.6 Biot-Savart Law 61.2.7 Ampere Circuital Law 171.2.8 Faraday’s Law 201.2.8.1 Motional emf 241.2.9 Flux Linkages and Induced Voltages 291.2.10 Induced Voltages 291.2.11 Induced Electric Fields 301.2.12 Reformulation of Faraday’s Law 311.3 Inductance 381.3.1 Application of Ampere’s Law to Find B in a Solenoid 391.3.2 Magnetic Field of a Toroid 401.3.3 The Inductance of Circular Air-Cored Toroid 401.3.4 Mutual Inductance 441.4 Energy 471.5 Overview of Electric Machines 491.6 Summary 58Problems 58References 672 Magnetic Circuits 692.1 Preliminary Remarks 692.2 Permeability 692.3 Classification of Magnetic Materials 702.3.1 Uniform Magnetic Field 722.3.2 Magnetic-Field Intensity 722.4 Hysteresis Loop 742.4.1 Hysteresis Loop for Soft Iron and Steel 762.5 Eddy-Current and Core Losses 782.6 Magnetic Circuits 822.6.1 The Magnetic Circuit Concept 822.6.2 Magnetic Circuits Terminology 822.6.2.1 Limitations of the Analogy Between Electric and Magnetic Circuits 862.6.3 Effect of Air Gaps 862.6.3.1 Magnetic Circuit with an Air Gap 862.6.3.2 Magnetic Forces Exerted by Electromagnets 892.7 Field Energy 1002.7.1 Energy Stored in a Magnetic Field 1002.7.1.1 The Magnetic Energy in Terms of the Magnetic Induction B 1012.7.1.2 The Magnetic Energy in Terms of the Current Density J and the Vector Potential A 1022.7.1.3 The Magnetic Energy in Terms of the Current I and of the Flux 𝛹m 1032.7.1.4 The Magnetic Energy in Terms of the Currents and Inductances 1032.8 The Magnetic Energy for a Solenoid Carrying a Current I 1042.9 Energy Flow Diagram 1062.9.1 Power Flow Diagram of DC Generator and DC Motor 1062.9.1.1 Power Flow Diagram and Losses of Induction Motor 1082.9.1.2 Rotational Losses 1092.10 Multiple Excited Systems 1102.11 Doubly Excited Systems 1132.11.1 Torque Developed 1162.11.1.1 Excitation Torque 1172.11.1.2 Reluctance Torque 1222.12 Concept of Rotating Magnetic Field 1262.12.1 Rotating Magnetic Field due to Three-Phase Currents 1262.12.1.1 Speed of Rotating Magnetic Field 1302.12.1.2 Direction of Rotating Magnetic Field 1312.12.2 Alternate Mathematical Analysis for Rotating Magnetic Field 1312.13 Summary 134Problems 135References 1443 Single-Phase and Three-Phase Transformers 1473.1 Preliminary Remarks 1473.2 Classification of Transformers 1493.2.1 Classification Based on Number of Phases 1493.2.1.1 Single-Phase Transformers 1493.2.1.2 Three-Phase Transformers 1493.2.1.3 Multi-Phase Transformers 1503.2.2 Classification Based on Operation 1503.2.2.1 Step-Up Transformers 1503.2.2.2 Step-Down Transformers 1513.2.3 Classification Based on Construction 1513.2.3.1 Core-Type Transformers 1513.2.3.2 Shell-Type Transformers 1513.2.4 Classification Based on Number of Windings 1533.2.4.1 Single-Winding Transformer 1533.2.4.2 Two-Winding Transformer 1533.2.4.3 Three-Winding Transformer 1533.2.5 Classification Based on Use 1533.2.5.1 Power Transformer 1533.2.5.2 Distribution Transformer 1543.3 Principle of Operation of the Transformer 1543.3.1 Ideal Transformer 1543.4 Impedance Transformation 1573.5 DOT Convention 1583.6 Real/Practical Transformer 1583.7 Equivalent Circuit of a Single-Phase Transformer 1603.8 Phasor Diagrams Under Load Condition 1663.9 Testing of Transformer 1703.9.1 Open-Circuit Test 1713.9.2 Short-Circuit Test 1723.10 Performance Measures of a Transformer 1753.10.1 Voltage Regulation 1753.10.1.1 Condition for Maximum Voltage Regulation 1773.10.1.2 Condition for Zero Voltage Regulation 1773.10.2 Efficiency of Transformer 1803.10.3 Maximum Efficiency Condition 1813.11 All-Day Efficiency or Energy Efficiency 1853.12 Autotransformer 1863.13 Three-Phase Transformer 1903.13.1 Input (Y), Output (Δ) 1923.13.2 Input Delta (Δ), Output Star (Y) 1943.13.3 Input Delta (Δ), Output Delta (Δ) 1953.13.4 Input Star (Y), Output Star (Y) 1963.14 Single-Phase Equivalent Circuit of Three-Phase Transformer 1973.15 Open-Delta Connection or V Connection 2003.16 Harmonics in a Single-Phase Transformer 2053.16.1 Excitation Phenomena in a Single-Phase Transformer 2083.16.2 Harmonics in a Three-Phase Transformer 2103.16.2.1 Star-Delta Connection with Grounded Neutral 2133.16.2.2 Star-Delta Connection without Grounded Neutral 2143.16.3 Summary 2143.16.4 Star-Star with Isolated Neutral 2143.17 Disadvantages of Harmonics in Transformer 2153.17.1 Effect of Harmonic Currents 2153.17.2 Electromagnetic Interference 2153.17.3 Effect of Harmonic Voltages 2153.17.4 Summary 2163.17.5 Oscillating Neutral Phenomena 2163.18 Open Circuit and Short-Circuit Conditions in a Three-Phase Transformer 2173.19 Matlab/Simulink Model of a Single-Phase Transformer 2193.20 Matlab/Simulink Model of Testing of Transformer 2223.21 Matlab/Simulink Model of Autotransformer 2233.22 Matlab/Simulink Model of Three-Phase Transformer 2233.23 Supplementary Solved Problems 2323.24 Summary 2493.25 Problems 249References 2554 Fundamentals of Rotating Electrical Machines and Machine Windings 2574.1 Preliminary Remarks 2574.2 Generator Principle 2574.2.1 Simple Loop Generator 2574.2.2 Action of Commutator 2594.2.3 Force on a Conductor 2604.2.3.1 DC Motor Principle 2604.2.3.2 Motor Action 2614.3 Machine Windings 2614.3.1 Coil Construction 2614.3.1.1 Coil Construction: Distributed Winding 2614.3.1.2 Coil Construction: Concentrated Winding 2624.3.1.3 Coil Construction: Conductor Bar 2624.3.2 Revolving (Rotor) Winding 2624.3.3 Stationary (Stator) Winding 2624.3.4 DC ArmatureWindings 2624.3.4.1 Pole Pitch (Yp) 2634.3.4.2 Coil Pitch or Coil Span (Ycs) 2634.3.4.3 Back Pitch (Yb) 2634.3.4.4 Front Pitch (Yf) 2644.3.4.5 Resultant Pitch (Y) 2644.3.4.6 Commutator Pitch (a) 2644.3.5 Lap Winding 2654.3.5.1 Lap Multiple or Parallel Windings 2654.3.5.2 Formulas for Lap Winding 2664.3.5.3 Multiplex, Single, Double, and Triple Windings 2674.3.5.4 Meaning of the Term Re-entrant 2684.3.5.5 Multiplex Lap Windings 2684.3.6 WaveWinding 2794.3.6.1 Formulas forWave Winding 2814.3.6.2 MultiplexWave or Series-ParallelWinding 2824.3.6.3 Formulas for Series-Parallel Winding 2834.3.7 Symmetrical Windings 2844.3.7.1 Possible SymmetricalWindings for DC Machines of a Different Number of Poles 2844.3.8 Equipotential Connectors (Equalizing Rings) 2844.3.9 Applications of Lap andWave Windings 2864.3.10 Dummy or Idle Coils 3104.3.10.1 Dummy Coils 3104.3.11 Whole-CoilWinding and Half-CoilWinding 3114.3.12 Concentrated Winding 3124.3.13 Distributed Winding 3124.4 Electromotive Force (emf) Equation 3134.4.1 emf Equation of an Alternator [1] 3134.4.1.1 Winding Factor (Coil Pitch and Distributed Windings) 3134.4.2 Winding Factors 3134.4.2.1 Pitch Factor or Coil Pitch (Pitch Factor (Kp) or Coil Span Factor [Kc]) 3144.4.3 Distribution Factor (Breadth Factor (Kb) or Distribution Factor (Kd)) 3154.4.3.1 Distribution Factor (Kd) 3154.5 Magnetomotive Force (mmf) of ACWindings 3164.5.1 mmf and Flux in Rotating Machine 3164.5.2 Main Air-Gap Flux (Field Flux) 3164.5.3 mmf of a Coil [5] 3164.5.3.1 mmf 3164.5.3.2 mmf of Distributed Windings 3174.5.3.3 mmf SpaceWave of a Single Coil 3174.5.3.4 mmf SpaceWave of One Phase of a Distributed Winding [6] 3194.6 Harmonic Effect [7] 3224.6.1 The Form Factor and the emf per Conductor 3224.6.2 TheWave Form 3234.6.3 Problem Due to Harmonics 3244.6.4 Elimination or Suppression of Harmonics 3244.6.4.1 Shape of Pole Face 3244.6.4.2 Use of Several Slots per Phase per Pole 3244.6.4.3 Use of Short-Pitch Windings 3254.6.4.4 Effect of the Y- and Δ -Connection on Harmonics 3274.6.4.5 Harmonics Produced by Armature Slots 3284.7 Basic Principles of Electric Machines 3304.7.1 AC Rotating Machines 3314.7.1.1 The Rotating Magnetic Field 3314.7.1.2 The Relationship between Electrical Frequency and the Speed of Magnetic Field Rotation 3334.7.1.3 Reversing the Direction of the Magnetic Field Rotation 3354.7.1.4 The Induced Voltage in AC Machines 3354.7.1.5 The Induced Voltage in a Coil on a Two-Pole Stator 3354.7.1.6 The Induced Voltage in a Three-Phase Set of Coils 3374.7.1.7 The rms Voltage in a Three-Phase Stator 3384.7.2 The Induced Torque in an AC Machine 3384.8 Summary 339Problems 339References 3405 DC Machines 3415.1 Preliminary Remarks 3415.2 Construction and Types of DC Generator 3425.2.1 Construction of DC Machine 3425.2.2 Types of DC Generator 3435.3 Principle of Operation of DC Generator 3455.3.1 Voltage Build-Up in a DC Generator 3465.3.2 Function of Commutator 3475.4 Commutation Problem and Solution 3495.4.1 Brush Shifting 3495.4.2 Commutating Poles 3505.4.3 Compensating Windings 3505.5 Types of Windings 3515.6 emf Equations in a DC Generator 3515.7 Brush Placement in a DC Machine 3535.8 Equivalent Circuit of DC Generator 3545.9 Losses of DC Generator 3545.10 Armature Reaction 3605.10.1 No-Load Operation 3615.10.2 Loaded Operation 3615.11 Principle of Operation of a DC Motor 3625.11.1 Equivalent Circuit of a DC Motor 3635.12 emf and Torque Equations of DC Motor 3645.13 Types of DC Motor 3645.13.1 Separately Excited DC Motor 3645.13.2 Self-Excited DC Motor 3655.13.2.1 Shunt DC Motor 3655.13.2.2 Series DC Motor 3665.14 Characteristics of DC Motors 3675.14.1 Separately Excited and DC Shunt Motor 3685.14.2 DC Series Motor 3695.14.3 Compound Motor 3705.15 Starting of a DC Motor 3715.15.1 Design of a Starter for a DC Motor 3725.15.2 Types of Starters 3735.15.2.1 Three-Point Starter 3735.15.2.2 Four-Point Starter 3745.16 Speed Control of a DC Motor 3745.16.1 Separately Excited and DC Shunt Motor 3755.16.2 DC Series Motor 3765.17 Solved Examples 3785.18 Matlab/Simulink Model of a DC Machine 3875.18.1 Matlab/Simulink Model of a Separately/ Shunt DC Motor 3875.18.2 Matlab/Simulink Model of a DC Series Motor 3875.18.3 Matlab/Simulink Model of a Compound DC Motor 3885.19 Summary 392Problems 392Reference 3996 Three-Phase Induction Machine 4016.1 Preliminary Remarks 4016.2 Construction of a Three-Phase Induction Machine 4026.2.1 Stator 4026.2.2 Stator Frame 4036.2.3 Rotor 4036.3 Principle Operation of a Three-Phase Induction Motor 4046.3.1 Slip in an Induction Motor 4066.3.2 Frequency of Rotor Voltage and Current 4076.3.3 Induction Machine and Transformer 4086.4 Per-phase Equivalent Circuit of a Three-Phase Induction Machine 4086.5 Power Flow Diagram in a Three-Phase Induction Motor 4156.6 Power Relations in a Three-Phase Induction Motor 4166.7 Steps to Find Powers and Efficiency 4176.8 Per-Phase Equivalent Circuit Considering Stray-Load Losses 4206.9 Torque and Power using Thevenin’s Equivalent Circuit 4216.10 Torque-Speed Characteristics 4246.10.1 Condition for Maximum Torque 4276.10.2 Condition for Maximum Torque at Starting 4296.10.3 Approximate Equations 4296.11 Losses in a Three-Phase Induction Machine 4336.11.1 Copper Losses or Resistive Losses 4336.11.2 Magnetic Losses 4346.11.3 Mechanical Losses 4346.11.4 Stray-Load Losses 4346.12 Testing of a Three-Phase Induction Motor 4356.12.1 No-Load Test 4356.12.2 Blocked Rotor Test 4366.12.3 DC Test 4376.12.4 Load Test 4386.12.5 International Standards for Efficiency of Induction Machines 4416.12.6 International Standards for the Evaluation of Induction Motor Efficiency 4426.13 Starting of a Three-Phase Induction Motor 4436.13.1 Direct-on-Line Start 4466.13.2 Line Resistance Start 4476.13.3 Star-Delta Starter 4486.13.4 Autotransformer Starter 4496.14 Speed Control of Induction Machine 4516.14.1 By Varying the Frequency of the Supply 4516.14.2 Pole Changing Method 4526.14.2.1 Multiple Numbers of Windings 4536.14.2.2 Consequent Pole Method 4536.14.3 Stator Voltage Control 4546.14.3.1 Voltage/Frequency = Constant Control 4556.14.3.2 Rotor Resistance Variation 4566.14.3.3 Rotor Voltage Injection Method 4566.14.3.4 Cascade Connection of Induction Machines 4566.14.3.5 Pole-Phase Modulation for Speed Control 4586.15 Matlab/Simulink Modelling of the Three-Phase Induction Motor 4616.15.1 Plotting Torque-Speed Curve under Steady-State Condition 4646.15.2 Dynamic Simulation of Induction Machine 4646.16 Practice Examples 4696.17 Summary 482Problems 482References 4897 Synchronous Machines 4917.1 Preliminary Remarks 4917.2 Synchronous Machine Structures 4927.2.1 Stator and Rotor 4927.3 Working Principle of the Synchronous Generator 4967.3.1 The Synchronous Generator under No-Load 4987.3.2 The Synchronous Generator under Load 4987.4 Working Principle of the Synchronous Motor 5017.5 Starting of the Synchronous Motor 5027.5.1 Starting by External Motor 5027.5.2 Starting by using Damper Winding 5037.5.3 Starting by Variable Frequency Stator Supply 5037.6 Armature Reaction in Synchronous Motor 5037.7 Equivalent Circuit and Phasor Diagram of the Synchronous Machine 5067.7.1 Phasor Diagram of the Synchronous Generator 5087.7.2 Phasor Diagram of the Synchronous Motor 5107.8 Open-Circuit and Short-Circuit Characteristics 5147.8.1 Open-Circuit Curve 5147.8.2 Short-Circuit Curve 5167.8.3 The Unsaturated Synchronous Reactance 5177.8.4 The Saturated Synchronous Reactance 5177.8.5 Short-Circuit Ratio 5187.9 Voltage Regulation 5207.9.1 Emf or Synchronous Method 5217.9.2 The Ampere-Turn or mmf Method 5227.9.3 Zero-Power Factor Method or Potier Triangle Method 5267.9.3.1 Steps for Drawing Potier Triangles 5267.9.3.2 Procedure to Obtain Voltage Regulation using the Potier Triangle Method 5267.10 Efficiency of the Synchronous Machine 5297.11 Torque and Power Curves 5337.11.1 Real/Active Output Power of the Synchronous Generator 5347.11.2 Reactive Output Power of the Synchronous Generator 5357.11.3 Complex Input Power to the Synchronous Generator 5367.11.4 Real/Active Input Power to the Synchronous Generator 5367.11.5 Reactive Input Power to the Synchronous Generator 5377.12 Maximum Power Output of the Synchronous Generator 5377.13 Capability Curve of the Synchronous Machine 5417.14 Salient Pole Machine 5457.14.1 Phasor Diagram of a Salient Pole Synchronous Generator 5477.14.2 Power Delivered by a Salient Pole Synchronous Generator 5527.14.3 Maximum Active and Reactive Power Delivered by a Salient Pole Synchronous Generator 5557.14.3.1 Active Power 5557.14.3.2 Reactive Power 5557.15 Synchronization of an Alternator with a Bus-Bar 5587.15.1 Process of Synchronization 5607.16 Operation of a Synchronous Machine Connected to an Infinite Bus-Bar (Constant Vt and f ) 5627.16.1 Motor Operation of Change in Excitation at Fixed Shaft Power 5627.16.2 Generator Operation for Change in Output Power at Fixed Excitation 5657.17 Hunting in the Synchronous Motor 5707.17.1 Role of the DamperWinding 5727.18 Parallel Operation of Synchronous Generators 5727.18.1 The Synchronous Generator Operating in Parallel with the Infinite Bus Bar 5747.19 Matlab/Simulink Model of a Salient Pole Synchronous Machine 5817.19.1 Results Motoring Mode 5857.19.2 Results Generator Mode 5857.20 Summary 586Problems 587Reference 5918 Single-Phase and Special Machines 5938.1 Preliminary Remarks 5938.2 Single-phase Induction Machine 5938.2.1 Field System in a Single-phase Machine 5948.3 Equivalent Circuit of Single-phase Machines 5978.3.1 Equivalent Circuit Analysis 5998.3.1.1 Approximate Equivalent Circuit 6008.3.1.2 Thevenin’s Equivalent Circuit 6018.4 How to Make a Single-phase Induction Motor Self Starting 6028.5 Testing of an Induction Machine 6088.5.1 DC Test 6098.5.2 No-load Test 6098.5.3 Blocked-Rotor Test 6108.6 Types of Single-Phase Induction Motors 6128.6.1 Split-Phase Induction Motor 6128.6.2 Capacitor-Start Induction Motor 6128.6.3 Capacitor-Start Capacitor-Run Induction Motor (Two-Value Capacitor Method) 6138.7 Single-Phase Induction Motor Winding Design 6148.7.1 Split-Phase Induction Motor 6178.7.2 Capacitor-Start Motors 6188.8 Permanent Split-Capacitor (PSC) Motor 6218.9 Shaded-Pole Induction Motor 6228.10 Universal Motor 6228.11 Switched-Reluctance Motor (SRM) 6248.12 Permanent Magnet Synchronous Machines 6248.13 Brushless DC Motor 6258.14 Mathematical Model of the Single-phase Induction Motor 6268.15 Simulink Model of a Single-Phase Induction Motor 6278.16 Summary 633Problems 633Reference 6379 Motors for Electric Vehicles and Renewable Energy Systems 6399.1 Introduction 6399.2 Components of Electric Vehicles 6419.2.1 Types of EVs 6419.2.1.1 Battery-Based EVs 6429.2.1.2 Hybrid EVs 6439.2.1.3 Fuel-Cell EVs 6469.2.2 Significant Components of EVs 6499.2.2.1 Battery Bank 6499.2.2.2 DC-DC Converters 6619.2.2.3 Power Inverter 6629.2.2.4 Electric Motor 6639.2.2.5 Transmission System or Gear Box 6639.2.2.6 Other Components 6639.3 Challenges and Requirements of Electric Machines for EVs 6639.3.1 Challenges of Electric Machines for EVs 6649.3.2 Requirements of Electric Machines for EVs 6649.4 Commercially Available Electric Machines for EVs 6679.4.1 DC Motors 6679.4.2 Induction Motor 6679.4.3 Permanent Magnet Synchronous Motors (PMSM) 6689.4.4 Brushless DC Motors 6689.4.5 Switched Reluctance Motors (SRMs) 6699.5 Challenges and Requirements of Electric Machines for RES 6699.6 Commercially Available Electric Machines for RES 6719.6.1 DC Machine 6719.6.2 Induction Machines 6719.6.3 Synchronous Machines 6749.6.4 Advanced Machines for Renewable Energy 6759.7 Summary 676References 67710 Multiphase (More than Three-Phase) Machines Concepts and Characteristics 67910.1 Preliminary Remarks 67910.2 Necessity of Multiphase Machines 67910.2.1 Evolution of Multiphase Machines 68010.2.2 Advantages of Multiphase Machines 68310.2.2.1 Better Space Harmonics Profile 68310.2.2.2 Better Torque Ripple Profile 68410.2.2.3 Improved Efficiency 68610.2.2.4 Fault Tolerant Capability 68610.2.2.5 Reduced Ratings of Semiconductor Switches and Better Power/Torque Distribution 68810.2.2.6 Torque Enhancement by Injecting Lower-Order Harmonics into Stator Currents 68810.2.3 Applications of Multiphase Machines 68910.3 Working Principle 69110.3.1 Multiphase Induction Machine 69110.3.2 Multiphase Synchronous Machine 69110.4 Stator-Winding Design 69210.4.1 Three-PhaseWindings 69510.4.1.1 Single-Layer Full-Pitch Winding 69510.4.1.2 Single-Layer Short-Pitch Winding 69810.4.1.3 Double-Layer Full-PitchWinding 69910.4.1.4 Double-Layer Short-Pitch Winding 69910.4.1.5 Fractional-Slot Winding 70110.4.2 Five-PhaseWindings 70110.4.3 Six-Phase Windings 70610.4.3.1 Symmetrical Winding of Six-Phase Machine 70710.4.3.2 Asymmetrical Winding 71010.4.4 Nine-PhaseWindings 71010.5 Mathematical Modelling of Multiphase Machines 71510.5.1 Mathematical Modelling of Multiphase Induction Machines in Original Phase-Variable Domain 71510.5.2 Transformation Matrix for Multiphase Machines 71810.5.3 Modelling of Multiphase Induction Machines in Arbitrary Reference Frames 72010.5.4 Commonly used Reference Frames 72210.5.5 Modelling of a Multiphase Synchronous Machine 72310.6 Vector Control Techniques for Multiphase Machines 72510.6.1 Indirect Field-Oriented Control or Vector-Control Techniques for Multiphase Induction Machines 72610.6.2 Vector Control for Multiphase Synchronous Machines 73010.7 Matlab/Simulink Model of Multiphase Machines 73110.7.1 Dynamic Model of the Nine-Phase Induction Machine 73110.7.2 Dynamic Model of the Nine-Phase Synchronous Machine 73410.8 Summary 741Problems 741References 74211 Numerical Simulation of Electrical Machines using the Finite Element Method 74511.1 Introduction 74511.2 Methods of Solving EM Analysis 74711.2.1 Analytical Techniques 74911.2.2 Numerical Techniques 75011.2.2.1 Finite Difference Method 75211.2.2.2 Finite Element Method 75311.2.2.3 Solution of Laplace Equation Using the Finite Element Method 75311.3 Formulation of 2-Dimensional and 3-Dimensional Analysis 75811.3.1 Maxwell Equations 75911.3.1.1 Gauss Law 75911.3.1.2 Gauss Law of Magnetism 76011.3.1.3 Ampere’s Integral Law 76111.3.1.4 Faraday’s Integral Law 76111.3.1.5 Differential Form of Maxwell Equations 76111.3.2 FEM Adaptive Meshing 76311.3.3 FEM Variation Principle 76411.4 Analysis and Implementation of FEM Machine Models 76511.4.1 RMxprt Design to Implement a Maxwell Model of Machine 76511.4.2 Power Converter Design in Simplorer 77611.4.3 Integration of Power Converter with a Maxwell Model for Testing Drive 77611.5 Example Model of Three-Phase IM in Ansys Maxwell 2D 77811.6 Summary 793References 793Index 795