ELECTRIC MACHINES. Steady State, Transients, and Design with MATLAB ION BOLDEA LUCIAN TUTELEA

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1 ELECTRIC MACHINES Steady State, Transients, and Design with MATLAB ION BOLDEA LUCIAN TUTELEA Lop) CRC Press ^ ^ J Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business

Contents Preface xvii Part I Steady State 1 Introduction 3 1.1 Electric Energy and Electric Machines 3 1.2 Basic Types of Transformers and Electric Machines 6 1.3 Losses and Efficiency 13 1.

2 Contents Preface xvii Part I Steady State 1 Introduction Electric Energy and Electric Machines Basic Types of Transformers and Electric Machines Losses and Efficiency Physical Limitations and Ratings Nameplate Ratings Methods of Analysis State of the Art and Perspective Summary Proposed Problems 26 References 27 2 Electric Transformers AC Coil with Magnetic Core and Transformer Principles Magnetic Materials in EMs and Their Losses Magnetization Curve and Hysteresis Cycle Permanent Magnets Losses in Soft Magnetic Materials Electric Conductors and Their Skin Effects Components of Single- and 3-Phase Transformers Cores Windings Flux Linkages and Inductances of Single-Phase Transformers Leakage Inductances of Cylindrical Windings Leakage Inductances of Alternate Windings Circuit Equations of Single-Phase Transformers with Core Losses Steady State and Equivalent Circuit No-Load Steady State (I 2 = 0)/Lab Magnetic Saturation under No Load 70 v

vi Contents 2.9 Steady-State Short-Circuit Mode /Lab 2.2 71 2.10 Single-Phase Transformers: Steady-State Operation on Load/Lab 2.3 74 2.11 Three-Phase Transformers: Phase Connections 78 2.

3 vi Contents 2.9 Steady-State Short-Circuit Mode /Lab Single-Phase Transformers: Steady-State Operation on Load/Lab Three-Phase Transformers: Phase Connections Particulars of 3-Phase Transformers on No Load No-Load Current Asymmetry Y Primary Connection for the 3-Limb Core General Equations of 3-Phase Transformers Inductance Measurement/Lab Unbalanced Load Steady State in 3-Phase Transformers/Lab Paralleling 3-Phase Transformers Transients in Transformers Electromagnetic (R,L) Transients Inrush Current Transients/Lab Sudden Short Circuit from No Load (Vi, =0)/Lab Forces at Peak Short-Circuit Current Electrostatic (C,R) Ultrafast Transients Protection Measures of Anti-Overvoltage Electrostatic Transients Instrument Transformers Autotransformers Transformers and Inductances for Power Electronics Preliminary Transformer Design (Sizing) by Example Specifications Deliverables Magnetic Circuit Sizing Windings Sizing Losses and Efficiency No-Load Current Active Material Weight Equivalent Circuit Summary Proposed Problems 115 References Energy Conversion and Types of Electric Machines Energy Conversion in Electric Machines Electromagnetic Torque Cogging Torque (PM Torque at Zero Current) Passive Rotor Electric Machines Active Rotor Electric Machines DC Rotor and AC Stator Currents AC Currents in the Rotor and the Stator DC (PM) Stator and AC Rotor 129

Contents vii 3.5 Fix Magnetic Field (Brush-Commutator) Electric Machines 131 3.6 Traveling Field Electric Machines 132 3.7 Types of Linear Electric Machines 134 3.8 Summary 139 3.

4 Contents vii 3.5 Fix Magnetic Field (Brush-Commutator) Electric Machines Traveling Field Electric Machines Types of Linear Electric Machines Summary Proposed Problem 140 References 141 Brush-Commutator Machines: Steady State Introduction Stator and Rotor Construction Elements Brush-Commutator Armature Windings Simple Lap Windings by Example: N s = 16, 2 Pl = Simple Wave Windings by Example: N s = 9,2p 1 = Brush-Commutator Airgap Flux Density of Stator Excitation MMF No-Load Magnetization Curve by Example PM Airgap Flux Density and Armature Reaction by Example Commutation Process AC Excitation Brush-Commutation Winding EMF Equivalent Circuit and Excitation Connection DC Brush Motor/Generator with Separate (or PM) Excitation/Lab DC Brush PM Motor Steady-State and Speed Control Methods /Lab Speed Control Methods DC Brush Series Motor/Lab Starting and Speed Control AC Brush Series Universal Motor Testing Brush-Commutator Machines/Lab DC Brush PM Motor Losses, Efficiency, and Cogging Torque Preliminary Design of a DC Brush PM Automotive Motor by Example PM Stator Geometry Rotor Slot and Winding Design Summary Proposed Problems 197 References 201

Vlll Contents 5 Induction Machines: Steady State 203 5.1 Introduction: Applications and Topologies 203 5.2 Construction Elements 204 5.3 AC Distributed Windings 206 5.3.1 Traveling MMF of AC Distributed Windings 206 5.

5 Vlll Contents 5 Induction Machines: Steady State Introduction: Applications and Topologies Construction Elements AC Distributed Windings Traveling MMF of AC Distributed Windings Primitive Single-Layer Distributed Windings (q > 1, Integer) Primitive Two-Layer 3-Phase Distributed Windings (q = Integer) MMF Space Harmonics for Integer q (Slots/Pole/Phase) Practical One-Layer AC 3-Phase Distributed Windings Pole Count Changing AC 3-Phase Distributed Windings Two-Phase AC Windings Cage Rotor Windings Induction Machine Inductances Main Inductance Leakage Inductance Rotor Cage Reduction to the Stator Wound Rotor Reduction to the Stator Three-Phase Induction Machine Circuit Equations Symmetric Steady State of 3-Phase IMs Ideal No-Load Operation/Lab Zero Speed Operation (S = 1)/Lab No-Load Motor Operation (Free Shaft)/Lab Motor Operation on Load (1 > S > 0)/Lab Generating at Power Grid (n >f 1 /p l,s < 0)/Lab Autonomous Generator Mode (S < 0)/Lab Electromagnetic Torque and Motor Characteristics Deep-Bar and Dual-Cage Rotors Parasitic (Space Harmonics) Torques Starting Methods Direct Starting (Cage Rotor) Reduced Stator Voltages Additional Rotor Resistance Starting Speed Control Methods Wound Rotor IM Speed Control Unbalanced Supply Voltages One Stator Phase Open by Example One Rotor Phase Open Capacitor Split-Phase Induction Motors Linear Induction Motors End and Edge Effects in LIMs 277

I Contents ix 5.25 Regenerative and Virtual Load Testing of IMs/Lab 5.7... 280 5.26 Preliminary Electromagnetic IM Design by Example 282 5.26.1 Magnetic Circuit 283 5.26.2 Electric Circuit 287 5.26.3 Parameters 287 5.

6 I Contents ix 5.25 Regenerative and Virtual Load Testing of IMs/Lab Preliminary Electromagnetic IM Design by Example Magnetic Circuit Electric Circuit Parameters Starting Current and Torque Breakdown Slip and Torque Magnetization Reactance, X m, and Core Losses, piron No-Load and Rated Currents, 1Q and I Efficiency and Power Factor Final Remarks Summary Proposed Problems 298 References 300 Synchronous Machines: Steady State Introduction: Applications and Topologies Stator (Armature) Windings for SMs Nonoverlapping (Concentrated) Coil SM Armature Windings SM Rotors: Airgap Flux Density Distribution andemf PM Rotor Airgap Flux Density Two-Reaction Principle via Generator Mode Armature Reaction and Magnetization Reactances, X dm and X qm Symmetric Steady-State Equations and Phasor Diagram Autonomous Synchronous Generators No-Load Saturation Curve/Lab Short-Circuit Curve: (I sc (J F ))/Lab Load Curve: V s (I s )/Lab Synchronous Generators at Power Grid/Lab Active Power/Angle Curves: P e (5 V ) V-Shaped Curves Reactive Power Capability Curves Basic Static- and Dynamic-Stability Concepts Unbalanced Load Steady State of SGs/Lab Measuring X d, X q, Z_, andx 0 /Lab Large Synchronous Motors Power Balance PM Synchronous Motors: Steady State Load Torque Pulsations Handling by Synchronous Motors /Generators 349

x Contents 6.14 Asynchronous Starting of SMs and Their Self-Synchronization to Power Grid 352 6.15 Single-Phase and Split-Phase Capacitor PM Synchronous Motors 353 6.15.1 Steady State of Single-Phase Cageless-Rotor PMSMs 354 6.

7 x Contents 6.14 Asynchronous Starting of SMs and Their Self-Synchronization to Power Grid Single-Phase and Split-Phase Capacitor PM Synchronous Motors Steady State of Single-Phase Cageless-Rotor PMSMs Preliminary Design Methodology of a 3-Phase PMSM by Example Summary Proposed Problems 366 References 370 Part II Transients 7 Advanced Models for Electric Machines Introduction Orthogonal (dq) Physical Model Pulsational and Motion-Induced Voltages in dq Models dq Model of DC Brush PM Motor (cu b = 0) Basic dq Model of Synchronous Machines (cut, = ш г) Basic dq Model of Induction Machines (шь = 0,iu r,a>i) Magnetic Saturation in dq Models Frequency (Skin) Effect Consideration in dq Models Equivalence between dq Models and AC Machines Space Phasor (Complex Variable) Model High-Frequency Models for Electric Machines Summary Proposed Problems 396 References Transients of Brush-Commutator DC Machines Introduction Orthogonal (dq) Model of DC Brush Machines with Separate Excitation Electromagnetic (Fast) Transients Electromechanical Transients Constant Excitation (PM) Flux, dr Variable Flux Transients DC Brush Series Motor Transients Basic Closed-Loop Control of DC Brush PM Motor DC-DC Converter-Fed DC Brush PM Motor Parameters from Test Data/Lab Summary 417

Contents xi 8.9 Proposed Problems 418 References 419 9 Synchronous Machine Transients 421 9.1 Introduction 421 9.2 Phase Inductances of SMs 422 9.3 Phase Coordinate Model 423 9.

8 Contents xi 8.9 Proposed Problems 418 References Synchronous Machine Transients Introduction Phase Inductances of SMs Phase Coordinate Model dqo Model Relationships of 3-Phase SM Parameters Structural Diagram of the SM dqo Model pu dqo Model of SMs Balanced Steady State via the dqo Model Laplace Parameters for Electromagnetic Transients Electromagnetic Transients at Constant Speed Sudden 3-Phase Short Circuit from a Generator at No Load/Lab Asynchronous Running of SMs at a Given Speed Reduced-Order dqo Models for Electromechanical Transients Neglecting Fast Stator Electrical Transients Neglecting Stator and Rotor Cage Transients Simplified (Third-Order) dq Model Adaptation for SM Voltage Control Small-Deviation Electromechanical Transients (in PU) Large-Deviation Electromechanical Transients Asynchronous Starting and Self-Synchronization of DC-Excited SMs/Lab Asynchronous Self-Starting of PMSMs to Power Grid Line-to-Line and Line-to-Neutral Faults Transients for Controlled Flux and Sinusoidal Current SMs Constant d-axis (i ^) Flux Transients in Cageless SMs Vector Control of PMSMs at Constant л1> ао (ко = const) Constant Stator Flux Transients in Cageless SMs at cosi[>i = Vector Control of SMs with Constant Flux (i ) s ) and cos cp s = Transients for Controlled Flux and Rectangular Current SMs Model of Brushless DC Motor Transients DC-Excited Cage Rotor SM Model for Rectangular Current Control 468

xii Contents 9.17 Switched Reluctance Machine Modeling for Transients 469 9.18 Split-Phase Cage Rotor SMs 475 9.19

9 xii Contents 9.17 Switched Reluctance Machine Modeling for Transients Split-Phase Cage Rotor SMs Standstill Testing for SM Parameters/Lab Saturated Steady-State Parameters, L^m and Lq m, from Current Decay Tests at Standstill Single Frequency Test for Subtransient Inductances, I/j and Ц Standstill Frequency Response Tests Linear Synchronous Motor Transients Summary Proposed Problems 489 References Transients of Induction Machines Three-Phase Variable Model dq (Space Phasor) Model of IMs Three-Phase IM-dq Model Relationships Magnetic Saturation and Skin Effects in the dq Model Space Phasor Model Steady State: Cage and Wound Rotor IMs Electromagnetic Transients Three-Phase Sudden Short Circuit/Lab Transient Current at Zero Speed Small-Deviation Electromechanical Transients Large-Deviation Electromechanical Transients/Lab Reduced-Order dq Model in Multimachine Transients Other Severe Transients m/n r Actual Winding Modeling of IMs with Cage Faults Transients for Controlled Magnetic Flux and Variable Frequency Complex Eigenvalues of IM Space Phasor Model Cage Rotor Constant Stator Flux Transients and Vector Control Basics Cage-Rotor Constant Rotor Stator Flux Transients and Vector Control Basics Constant Rotor Flux Transients and Vector Control Principles of Doubly Fed IMs Doubly Fed IM as a Brushless Exciter for SMs Parameter Estimation in Standstill Tests/Lab Standstill Flux Decay for Magnetization Curve Identification: W^ (I m ) 538

Contents xiii 10.15.2 Identification of Resistances and Leakage Inductances for Standstill Flux Decay Tests 540 10.15.3 Standstill Frequency Response Tests 541 10.

10 Contents xiii Identification of Resistances and Leakage Inductances for Standstill Flux Decay Tests Standstill Frequency Response Tests Split-Phase Capacitor IM Transients/Lab Phase Variable Model dq Model Linear Induction Motor Transients Summary Proposed Problems 553 References 557 Part III FEM Analysis and Optimal Design 11 Essentials of Finite Element Method in Electromagnetics Vectorial Fields Coordinate Systems Operations with Vectors Line and Surface (Flux) Integrals of a Vectorial Field Differential Operations Integral Identities Differential Identities Electromagnetic Fields Electrostatic Fields Fields of Current Densities Magnetic Fields Electromagnetic Fields: Maxwell Equations Visualization of Fields Boundary Conditions Dirichlet's Boundary Conditions Neumann's Boundary Conditions Mixed Robin's Boundary Conditions Periodic Boundary Conditions Open Boundaries Problem Truncation Asymptotical Boundary Conditions Kelvin Transform Finite Element Method Residuum (Galerkin's) Method Variational (Rayleigh-Ritz) Method Stages in Finite Element Method Application Domain Discretization Choosing Interpolation Functions 584

xiv Contents 11.5.3.3 Formulation of Algebraic System Equations 584 11.5.3.4 Solving Algebraic Equations 584 11.6 2D FEM 584 11.7 Analysis with FEM 586 11.7.1 Electromagnetic Forces 589 11.7.1.1 Integration of Lorenz Force 589 11.

11 xiv Contents Formulation of Algebraic System Equations Solving Algebraic Equations D FEM Analysis with FEM Electromagnetic Forces Integration of Lorenz Force Maxwell Tensor Method Virtual Work Method Loss Computation Iron Losses 591 References FEM in Electric Machines: Electromagnetic Analysis Single-Phase Linear PM Motors Preprocessor Stage Postprocessor Stage Summary Rotary PMSMs (6/4) BLDC: Preprocessor Stage BLDC Motor Analysis: Postprocessor Stage Summary The 3-Phase Induction Machines Induction Machines: Ideal No Load Rotor Bar Skin Effect Summary 649 References Optimal Design of Electric Machines: The Basics Electric Machine Design Problem Optimization Methods Optimum Current Control Modified Hooke-Jeeves Optimization Algorithm Electric Machine Design Using Genetic Algorithms 670 References Optimization Design of Surface PMSMs Design Theme Electric and Magnetic Loadings Choosing a Few Dimensioning Factors A Few Technological Constraints Choosing Magnetic Materials Dimensioning Methodology Rotor Sizing PM Flux Computation 686

Contents XV 14.6.3 Weights of Active Materials 692 14.6.4 Losses 693 14.6.5 Thermal Verification 694 14.6.6 Machine Characteristics 694 14.7 Optimal Design with Genetic Algorithms 694 14.7.1 Objective (Fitting) Function 696 14.

12 Contents XV Weights of Active Materials Losses Thermal Verification Machine Characteristics Optimal Design with Genetic Algorithms Objective (Fitting) Function PMSM Optimization Design Using Genetic Algorithms: A Case Study Optimal Design of PMSMs Using Hooke-Jeeves Method Conclusion 710 References Optimization Design of Induction Machines Realistic Analytical Model for Induction Machine Design Design Theme Design Variables Induction Machine Dimensioning Rotor Design Stator Slot Dimensions Winding End-Connection Length Induction Machine Parameters Induction Motor Optimal Design Using Genetic Algorithms Induction Motor Optimal Design Using Hooke-Jeeves Algorithm Machine Performance Conclusion 750 References 751 Index 753

Contents. Review of Electric Circuitd. Preface ;

Contents. Review of Electric Circuitd. Preface ; Preface ; Chapter 1 Review of Electric Circuitd 1.1 Introduction, 1 1.2 Direct Circuit Current, 1 1.2.1 Voltage, 3 1.2.2 Power, 3 1.2.3 Ohm's Law, 5 1.2.4 KirchhofTs Laws, 5 1.2.4.1 Kirchhoff s Current