Design of Brushless Permanent-Magnet Machines. J.R. Hendershot Jr. T.J.E. Miller

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1 Design of Brushless Permanent-Magnet Machines J.R. Hendershot Jr. T.J.E. Miller

Contents 1 GENERAL INTRODUCTION l 1.1 Definitions and types of brushless motor 1 1.2 Commutation,. 4 1.3 Operation of 3-phase brushless DC motor 5 1.3.1 EMF waveform 7 1.3.2 Torque and EMF constants 10 1.

2 Contents 1 GENERAL INTRODUCTION l 1.1 Definitions and types of brushless motor Commutation, Operation of 3-phase brushless DC motor EMF waveform Torque and EMF constants Speed/torque characteristic Sinewave motors and generators, Phasor representation Voltage Practical considerations 23 2 MACHINE TYPES and APPLICATIONS Machine configuration, Reasons for variety Classification Radial-flux machines Interior-rotor surface-magnet machines Interior-rotor interior-magnet machines (IPM) Exterior-rotor machines...,,..,,,, Axial-flux, linear and other machines Gallery 43

xiv CONTENTS 3 BASIC DESIGN CHOICES 65 3.1 Machine and drive configuration 67 3.1.1 Squarewave and sinewave drives 67 3.1.1.1 Squarewave drive 67 3.1.1.2 Sinewave drive 68 3.1.2 Salient-pole and nonsalient-pole machines 68 3.

3 xiv CONTENTS 3 BASIC DESIGN CHOICES Machine and drive configuration Squarewave and sinewave drives Squarewave drive Sinewave drive Salient-pole and nonsalient-pole machines Nonsalient-pole machines Salient-pole machines Number of phases, poles and slots Number of phases Practical considerations Number of phases in electrical systems Number of phases in electrical machines Distribution of coils between phases Number of phases in inverters and rectifiers Numbers of slots and poles Sizing the ABC of electric machine design The output equation Rotor design Length/diameter ratio Airgap length First estimate of magnet dimensions Exploratory selection of magnet grade Magnet overhang Rotor yoke dimensions Stator design Cutting the laminations Choice of core plate Stacking Insulating the slots Slot-fill factor Winding and inserting the phase coils Varnishing Winding with multiple-strand conductors 104

CONTENTS XV 3.5.9 Number of stator slots,,... 105 3.5.10 Stator core dimensions 105 3.5.11 Stator tooth-tips 106 3.5.12 Cogging and skew 107 3.5.13 Management of end-turns, 109 3.

4 CONTENTS XV Number of stator slots,, Stator core dimensions Stator tooth-tips Cogging and skew Management of end-turns, Electrical design of windings Definitions Integral-slot windings Windings for squarewave drive Fractional-slot windings A rule and two examples The 12/10 motor; alternative windings Pitch factor Sinewave and squarewave motors Irregular slotting Systematic analysis of slot/pole ratio and windings Winding resistance Resistance calculation Relationship between resistance and copper weight Variation of resistance with temperature AC resistance Magnet retention FLUX, EMF, AND TORQUE Permanent magnets and magnetic circuits Magnetic equivalent circuits Airgap flux distribution Clearance gap and equivalent magnet Magnet divided by thin bracing bridges Direct solution of Laplace / Poisson equations Finite-element method EMF Formula EMF constant of squarewave motors EMF constant of sinewave motors 180

xvi CONTENTS 4.2.2 BLV waveform method 181 4.2.3 Toothflux waveform method 183 4.3 Torque 185 4.3.1 Torque constants 186 4.3.1.1 Three-phase squarewave motor 186 4.3.1.2 Sinewave motors 187 4.

5 xvi CONTENTS BLV waveform method Toothflux waveform method Torque Torque constants Three-phase squarewave motor Sinewave motors Torque and inductance Salient-pole machines in phase variables Salient-pole machines in dq axes i-psi loop Properties of the elliptical i-psi loop INDUCTANCE Definition of inductance and flux-linkage Alternative definitions di/dt Flux times turns Other necessary laws of electromagnetism Turns squared Important practical effects of inductance Inductance components Airgap inductance of surface-magnet machines Airgap Self Airgap mutual Examples of airgap inductance calculation General case of airgap inductance Slot-leakage inductance End-winding leakage inductance 233

CONTENTS xvii 5.7 Inductances of slotless (airgap) windings 238 5.7.1 Helical windings 241 5.7.2 Lawrenson's method 241 5.8 Equivalent sine-distributed windings 242 5.9 Synchronous inductance. 243 5.

6 CONTENTS xvii 5.7 Inductances of slotless (airgap) windings Helical windings Lawrenson's method Equivalent sine-distributed windings Synchronous inductance Static measurement of synchronous inductance Inductances of salient-pole machines dq-axis inductances from Park's transform Synchronous inductance coefficients Direct calculation of synchronous inductance Differential leakage inductance Static measurement again Inductance from finite-element calculations Magnetization curves beyond inductance Magnetization curves in dqr-axes Saturation in the dq-axis model Demagnetization SQUAREWAVE DRIVE 273 Introduction Three-phase bipolar drives Waveforms and commutation sequences Current regulation Commutation phase squarewave control strategies Accumulations for mean and RMS currents Selection of appropriate switching strategy 289

xviii CONTENTS 6.2 Transient analysis of 3-phase drives, 291 6.2.0.1 Wye connection.,. 293 6.2.0.2 Delta connection 296 6.2.0.3 Regeneration (over-running); no-load speed 301 6.2.0.4 Phase advance 304 6.

7 xviii CONTENTS 6.2 Transient analysis of 3-phase drives, Wye connection., Delta connection Regeneration (over-running); no-load speed Phase advance Dwell control Salient-pole machines with squarewave drive Back-EMF sensing and 2-phase unipolar drives Controller architecture SINEWAVE DRIVE 325 Introduction, The phasor diagram motor operation Torque/angle curves The voltage locus diagram The circle and ellipse diagrams Calculation of the torque/speed characteristic The synchronous reluctance motor Summary calculated characteristics Electronic control The need for current regulation Historical development Overview of controllers Switching representation by voltage vectors Six-step Hysteresis-band current regulator dq_w_cr Sine/triangle ramp comparison Voltage PWM (sine/triangle) The synchronous regulator Space-vector controller Direct torque control (DTC) Summary of voltage capabilities 404

CONTENTS 8 kt AND ke, AND FIGURES-OF-MERIT 405 8.1 Introduction 405 8.2 kt & ke of squarewave and sinewave motor/drives 407 8.2.1 DC commutator motor and drive 407 8.2.2 3-phase squarewave motor and drive 411 8.

8 CONTENTS 8 kt AND ke, AND FIGURES-OF-MERIT Introduction kt & ke of squarewave and sinewave motor/drives DC commutator motor and drive phase squarewave motor and drive phase sinewave motor and drive phase sinewave motor with squarewave drive phase squarewave motor with sinewave drive phase squarewave & sinewave systems compared Example calculations (3-phase) phase squarewave motor and drive phase sinewave motor and drive phase sinewave motor with squarewave drive phase squarewave motor with sinewave drive phase squarewave & sinewave systems compared Figures of merit kt and ke Efficiency and power factor, Torque/Inertia ratio Power rate Speed rate and mechanical time-constant Motor constant The brushless PM motor in control systems Classical transfer function between voltage & speed Brushless DC motor model including inductance Closed-loop feedback system Response of generic second-order system Dynamic braking 449 xix

xx CONTENTS 9 GENERATING 451 9.1 Introduction,,, 451 9.2 Configurations and loads 454 9.2.1 No-load (open-circuit) 455 9.2.2 Steady-state short-circuit 456 9.2.3 Passive impedance load 457 9.2.4 Voltage regulation curves 459 9.

9 xx CONTENTS 9 GENERATING Introduction,,, Configurations and loads No-load (open-circuit) Steady-state short-circuit Passive impedance load Voltage regulation curves Connection to an infinite bus Diode rectifier load Active rectification, Short-circuit faults Classical analysis Transient Magnetic Field by Fourier Transform MULTIPLE-PHASE MACHINES 475 Introduction Polyphase machines Multiplex windings Reasons for using multiplex windings Fault-tolerant machines Analysis of multiplex windings Balance Matrix analysis of the inductances Torque Steady-state operation : phasor diagram Solution method transient Finite-element analysis 496

CONTENTS xxi 11 LINE-START MOTORS 497 11.1 Introduction 497 11.2 History 500 11.3 Analysis of polyphase line-start motors... 503 11.3.1 Steady state 503 11.3.2 Asynchronous operation and starting 506 11.

10 CONTENTS xxi 11 LINE-START MOTORS Introduction History Analysis of polyphase line-start motors Steady state Asynchronous operation and starting Analysis of synchronization Analysis of single-phase line-start motors Steady state; no rotor cage Symmetrical components Asynchronous and starting performance Advanced topics Winding harmonics Bar-pair-by-bar-pair model of the rotor cage Connection circuits LOSSES and COOLING Introduction Joule losses in stator conductors Core losses..., The nature of core losses Core loss properties of practical materials Calculation of core losses Rotor eddy-current losses Causes of rotor loss Loss mechanisms in the magnets themselves Resistance-or inductance-limited eddy-currents? Hysteresis loss in magnets Harmonic losses in surface-magnet machines Solution of the Complex Diffusion Equation 570

xxii CONTENTS 12.4.2.2 Exterior-rotor machine; 2-region model 574 12.4.2.3 Evaluation of the Exciting Harmonic Current Sheets 580 12.4.2.4 Balanced operation of 3-phase machines 586 12.4.2.5 Unbalanced operation of 3-phase machines 589 12.

11 xxii CONTENTS Exterior-rotor machine; 2-region model Evaluation of the Exciting Harmonic Current Sheets Balanced operation of 3-phase machines Unbalanced operation of 3-phase machines Segmented magnets and finite-length effects Circumferential segmentation., Simplified analysis of double segmentation End-effect; segmentation in the axial direction Russell and Norsworthy's method Alternative analysis of segmented magnets Slot ripple Flux-dip-sweeping analysis of losses in thin can Rotor can losses Harmonic losses in the IPM Losses caused by time-harmonics in the current Losses caused by flux-pulsations (slotting) Subtransient inductance and time-constant Effect of segmentation on subtransient reactance Coupling coefficient of the IPM Rotor time-constant Finite-element calculation of losses Windage, friction and bearing losses Thermal analysis and cooling The need for cooling Cooling and efficiency Responsibility for temperature rise Heat removal Detailed analysis of cooling Conduction Radiation Convection Some rules of thumb Internal temperature distribution Thermal equivalent circuit Some useful tables Intermittent operation 660

CONTENTS xxiü 13 TESTING 667 13.1 Introduction 667 13.2 Objectives of testing 667 13.3 Basic tests and measurements 668 13.3.1 Inertia 668 13.4 Resistance 669 13.5 EMF Testing 670 13.

12 CONTENTS xxiü 13 TESTING Introduction Objectives of testing Basic tests and measurements Inertia Resistance EMF Testing Generator load testing Motor load testing Torque Testing Torque constant kt Cogging torque On-line estimation of torque using the i-psi loop Thermal Testing Thermal equivalent-circuit parameters Inductance Testing APPENDIX Frequently asked questions Machine Design Questions,, How do I decide the shape and size of the machine? How do I choose the number of slots and poles? How do I design the stator teeth and slots? How do I decide the number of turns? How do I decide the type of stator winding? How can I get a fractional number of turns/coil? How can I reduce the wire size? How can I reduce the inductance? How can I increase the inductance? How do I choose between SPM and IPM? 686

xxiv CONTENTS 14.1.1.11 How do I choose between exterior or interior rotor? 688 14.1.1.12 When should I consider an axial-flux machine? 688 14.1.1.13 How do I decide the rotor geometry? 689 14.1.1.14 How can I reduce the inertia?

13 xxiv CONTENTS How do I choose between exterior or interior rotor? When should I consider an axial-flux machine? How do I decide the rotor geometry? How can I reduce the inertia? How can I improve the torque linearity? How can I reduce torque ripple? How do I design a PM synchronous generator? How do I test a PM synchronous machine? Why isn't my measured ke equal to kt? How do I calculate the machine temperature? What are the main effects of temperature? How can I prevent demagnetization? How can I reduce the noise level? How can I reduce the motor cost? How about EMF ripple? How about a sine-emf motor with squarewave drive? Performance and Control Questions How can I increase efficiency? How can I increase power-factor? How can I get smooth rotation at low speed? How can I make the motor go faster? How can I get a more sinusoidal EMF waveform? How can I get a more sinusoidal current waveform? How do I avoid first-turn insulation failure? How do I avoid bearing currents? What causes machines to fail? Saliency Half turns Series and parallel inductances Gearing Units of inertia Calculation of inertia 721 Symbols, Abbreviations, and Explanatory Notes 723 Bibliography 737 Index 755

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