General Airgap Field Modulation Theory for Electrical Machines E-Book

Ming Cheng

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 706

Veröffentlichungsjahr: 2022

Beschreibung

General Airgap Field Modulation Theory for Electrical Machines Introducing a new theory for electrical machines Air-gap magnetic field modulation phenomena have been widely observed in electrical machines. This book serves as the first English-language overview of these phenomena, as well as developing systematically for the first time a general theory by which to understand and research them. This theory not only serves to unify analysis of disparate electrical machines, from conventional DC machines, induction machines, and synchronous machines to unconventional flux-switching permanent magnet machines, Vernier machines, doubly-fed brushless machines etc., but also paves the way towards the creation of new electrical machine topologies. General Airgap Field Modulation Theory for Electrical Machines includes both overviews of key concepts in electrical machine engineering and in-depth specialized analysis of the novel theory itself. It works through the applications of the developed theory before proceeding to both qualitative analysis of the theory's operating principles and quantitative analysis of its parameters. Readers will also find: * The collective experience of four award-winning authors with long records of international scholarship on this subject * Three separate chapters covering the principal applications of the theory, with detailed examples * Discussion of potential innovations made possible by this theory General Airgap Field Modulation Theory for Electrical Machines is an essential introduction to this theory for postgraduates, researchers, and electrical engineers.

Leseprobe

Table of Contents

Cover

Title Page

Copyright

Preface

About the Authors

About the Companion Website

1 Introduction

1.1 Review of Historical Development of Electrical Machines

1.2 Limitations of Classical Electrical Machine Theories

1.3 Overview of Magnetic Field Modulation Machines and their Theories

1.4 Scope and Organization of the Book

References

2 Airgap Magnetic Field Modulation Phenomena in Electrical Machines

2.1 Traditional Electrical Machines

2.2 Field Modulation Magnetic Gears

2.3 Magnetically Geared Machines

2.4 PM Vernier Machine

2.5 Linear PMV Machine

2.6 Flux‐switching PM Machine

2.7 Doubly‐Fed Machines

2.8 Uniformity of Machine Operating Principles

References

3 Three Key Elements Model for Electrical Machines

3.1 Introduction

3.2 Classical Winding Function Theory and Its Limitations

3.3 Three Key Elements

3.4 Mathematical Representation of Three Key Elements

3.5 Torque Decomposition

References

4 Analysis of Magnetic Field Modulation Behaviors

4.1 Introduction

4.2 Magnetic Field Modulation Behaviors and Torque Components

4.3 Characterization of Modulation Behaviors in Typical Machine Topologies

4.4 Torque Composition of Typical Machine Topologies

4.5 Magnetic Field Modulation Behaviors of Various Modulators

4.6 Interchangeability of Modulators

References

5 Performance Evaluation of Electrical Machines Based on General Airgap Field Modulation Theory

5.1 Introduction

5.2 Squirrel-Cage IM

5.3 Brushless Doubly‐fed Machines

5.4 SynRM

5.5 FRPM Machine

5.6 Comparison of Representative Machine Topologies

References

6 Innovation of Electrical Machine Topologies

6.1 Innovation Methods

6.2 DSPM Machine with Π‐Shaped Stator Core

6.3 Stator‐PM Variable Reluctance Resolver

6.4 FRPM Machine

6.5 FSPM Machine with Full‐Pitch Windings

6.6 Rotor‐PM FSPM Machine

6.7 Dual‐Rotor Magnetically‐Geared Power Split Machine

6.8 Stator Field‐Excitation HTS Machines

6.9 Brushless Doubly‐Fed Reluctance Machine with an Asymmetrical Composite Modulator

References

7 Other Applications of General Airgap Field Modulation Theory

7.1 Introduction

7.2 Analysis of Radial Forces in Brushless Doubly‐fed Machines

7.3 Design of Suspension Windings for Bearingless Homopolar and Consequent Pole PM Machines

7.4 Loss Calculation

7.5 Optimization of Salient Reluctance Pole Modulators for Typical Field Modulation Electrical Machines

7.6 Airgap‐Harmonic‐Oriented Design Optimization Methodology

References

Appendix A Derivation of Modulation OperatorsDerivation of Modulation Operators

A.1 Derivation of Modulation Operator for Short‐circuited Coils

A.2 Derivation of Modulation Operator for Salient Reluctance Poles

A.3 Derivation of Modulation Operator for Multilayer Flux Barriers

Appendix B Magnetic Force of Current‐Carrying Conductors in Airgap and in SlotsMagnetic Force of Current‐Carrying Conductors in Airgap and in Slots

References

Appendix C Methods for Force and Torque CalculationMethods for Force and Torque Calculation

C.1 Maxwell Stress Tensor Method

C.2 Principle of Virtual Work

References

Index

End User License Agreement

List of Tables

Chapter 1

Table 1.1 Typical theories for electrical machines.

Table 1.2 Comparison of analysis models for IMs and SMs.

Chapter 2

Table 2.1 Comparison between the radially‐magnetized surface‐mounted field ...

Table 2.2 Performance comparison of the three MGMs.

Table 2.3 Comparison of the PMV machine and PMSM.

Table 2.4 Characteristics of no‐load PM airgap flux density harmonics in fl...

Table 2.5 Harmonic characteristic of armature field airgap flux density of ...

Chapter 3

Table 3.1 Typical values of

o

/

t

d

for various electrical machine topologies....

Table 3.2 Specifications of the FRPM prototype.

Table 3.3 Dual objects and parameters between switching converters and elec...

Chapter 4

Table 4.1 Comparison between asynchronous and synchronous modulation behavi...

Table 4.2 Torque composition of typical electrical machine topologies. Only...

Table 4.3 Modes of operation and torque composition of BDFIMs.

Table 4.4 Harmonic components of the source magnetizing MMF before and afte...

Table 4.5 Harmonic components of the source magnetizing MMF before and afte...

Table 4.6 Magnetic field conversion factors of salient reluctance pole modu...

Table 4.7 Magnetic field conversion factors for a BDFRM with a multi‐layer ...

Table 4.8 Magnetic field conversion factors of flux barrier modulators with...

Table 4.9 Magnetic field conversion factors for a BDFRM with the simplest l...

Table 4.10 Magnetic field conversion factors for different short‐circuit wi...

Table 4.11 Magnetic field conversion factors of short‐circuited coil modula...

Table 4.12 Comparison of three modulator types.

Table 4.13 Interchangeability between different modulators.

Table 4.14 Comparison of inductances and magnetic field conversion factors....

Chapter 5

Table 5.1 Specifications of the BDFRM prototype.

Table 5.2 Magnetic field conversion factors and coupling factors of the mul...

Table 5.3 Magnetic field conversion factors and coupling factors of the mult...

Table 5.4 Magnetic field conversion factors and coupling factors of the mult...

Table 5.5 Performance comparison of BDFRMs based on a single and dual power...

Table 5.6 Specifications and key design parameters of the 1.5 kW BDFIM prot...

Table 5.7 Main design parameters of the flux‐reversal PM machine prototype....

Table 5.8 Qualitative comparison of typical “unconventional” machine topolo...

Chapter 6

Table 6.1 Speed and initial phase of airgap flux density harmonics.

Table 6.2 Slot pitch angle based on different dominating harmonics.

Table 6.3 Key dimension parameters of the 12/7 Π‐DSPM machine.

Table 6.4 Armature winding coil connections of the 12/7 Π‐DSPM machine.

Table 6.5 Harmonic orders of PM MMF in FRPM machines with different modes o...

Table 6.6 Spatial harmonics of no‐load airgap flux density.

Table 6.7 Selected harmonic orders of flux density.

Table 6.8 Flux density harmonics contributing to the no‐load back‐EMF.

Table 6.9 Variations of key parameters versus

k

io

.

Table 6.10 Optimal values of key geometric parameters of the 12/7 FSPM mach...

Table 6.11 Break‐down of PM flux linkage harmonics of the rotor‐PM FSPM mac...

Table 6.12 No‐load back‐EMF harmonic contents.

Table 6.13 Inductance characteristics of the rotor‐PM FSPM machine.

Table 6.14 Dq axes inductance with and without considering the PM effect.

Table 6.15 Three commonly used MGPSM working modes (outer rotor rotates cou...

Table 6.16 Design parameters and specifications of the reduced‐power protot...

Table 6.17 Components and rotated angles of the 7th harmonic.

Table 6.18 Main parameters and design specifications of the prototype.

Table 6.19 Main design parameters of DS‐FMSE machine.

Table 6.20 Main parameters of the studied BDFRM with a composite rotor.

Chapter 7

Table 7.1 Radial magnetic force patterns along circumference of airgap of B...

Table 7.2 Radial magnetic force patterns along circumference of airgap of B...

Table 7.3 Radial electromagnetic force patterns along circumference of airg...

Table 7.4 Radial electromagnetic force patterns along circumference of airg...

Table 7.5 Radial forces of different pole‐pair combinations under unsaturat...

Table 7.6 Radial forces of different pole pair combinations under saturated...

Table 7.7 Winding factors of available winding designs.

Table 7.8 Key parameters and specifications of the squirrel‐cage IM under s...

Table 7.9 Magnetic field conversion factors of the rotor cage in the studie...

Table 7.10 Magnetic field conversion factors of the rotor and stator salien...

Table 7.11 Airgap magnetic flux density breakdown.

Table 7.12 Losses produced by main flux density harmonics.

Table 7.13 Measured results of no‐load and rated load tests.

Table 7.14 Geometric parameters of the studied FSPM machine.

Table 7.15 Open‐circuit PM field harmonics in the airgap.

Table 7.16 Armature field harmonics in the airgap, where

m

...

Table 7.17 Airgap magnetic field harmonics introduced by high‐order current...

Table 7.18 Airgap magnetic field harmonics introduced by high‐order current...

Table 7.19 Core loss breakdown with the sinusoidal current source excitatio...

Table 7.20 Core loss breakdown with PWM voltage source excitations.

Table 7.21 Comparison of core loss calculation methods.

Table 7.22 Comparison between the calculated and measured losses under diff...

Table 7.23 Main parameters of the studied MGM and FRPM machines.

Table 7.24 Magnetic field conversion factors of different rotor salient rel...

Table 7.25 Comparison of working airgap magnetic field harmonics produced b...

Table 7.26 Comparison of airgap magnetic field harmonics between Type (2 + ...

Table 7.27 Design specification and basic parameters.

Table 7.28 Sensitivity indexes of design variables.

Table 7.29 Initial values, ranges and optimal values of design variables.

Table 7.30 Performance comparison.

List of Illustrations

Chapter 1

Figure 1.1 Number of publications on “unconventional machines” indexed by IE...

Figure 1.2 Decomposition of armature MMF of would‐field salient‐pole SM into...

Figure 1.3 Magnetic energy

W

m

and magnetic co‐energy

W

m

'

.

Figure 1.4 Two‐axis primitive machine.

Figure 1.5 Dual‐rotor MGM Adapted from [45].

Figure 1.6 Partitioned‐stator FSPM machine [46].

Figure 1.7 PMV machine, (a) cross‐sectional view, (b) linear winding pattern...

Figure 1.8 12/10 FSPM machine.

Figure 1.9 Reluctance vernier machine.

Figure 1.10 Coaxial magnetic gear.

Chapter 2

Figure 2.1 Brushed DCMs. (a) Schematic representation, (b) connections of fi...

Figure 2.2 Volt–ampere characteristics and torque‐speed characteristics of D...

Figure 2.3 MMF in brushed DCMs. (a) Armature‐MMF and flux density distributi...

Figure 2.4 Developed rotor winding of an IM with its flux density and MMF wa...

Figure 2.5 Reactions of a squirrel‐cage rotor in a two‐pole field. (a) Insta...

Figure 2.6 Radial airgap flux density waveform and its amplitude spectrum in...

Figure 2.7 Wound-field non-salient-pole SM.

Figure 2.8 Wound-field salient-pole SM.

Figure 2.9 Cross‐sectional view of a wound-field non-salient-pole SM.

Figure 2.10 MMF distribution created by the field winding in the wound-field...

Figure 2.11 Airgap flux density waveform for a typical wound-field salient-p...

Figure 2.12 Direct‐axis airgap flux density distribution in a salient‐pole S...

Figure 2.13 Quadrature‐axis airgap flux density distribution in a salient‐po...

Figure 2.14 MG with parallel axes and radially‐magnetized magnets.

Figure 2.15 Field modulation co‐axial MG with radially‐magnetized magnets.

Figure 2.16 Field modulation MG variants with: (a) surface‐mounted Halbach P...

Figure 2.17 Fundamental magnetic field generated by the inner and outer roto...

Figure 2.18 Permeance wave of the large airgap region including two physical...

Figure 2.19 Magnetic field modulation behavior of the modulation ring perfor...

Figure 2.20 Radial airgap flux density produced by the outer rotor PMs. (a) ...

Figure 2.21 Radial airgap flux density produced by the inner rotor PMs. (a) ...

Figure 2.22 Tubular linear field modulation MG. The outer tube is stationary...

Figure 2.23 Axial‐flux field modulation MGs. (a) Disk‐type, (b) coaxial.

Figure 2.24 Transverse‐flux MG.

Figure 2.25 Hybrid field modulation MG with axial and transverse fluxes.

Figure 2.26 Reluctance type field modulation MG.

Figure 2.27 Cross‐sectional view of MGMs, (a) with three airgaps, (b) with t...

Figure 2.28 No‐load magnetic field distribution of MGMs. (a) Three‐airgap, (...

Figure 2.29 Radial airgap flux density waveforms of MGMs at the stator outer...

Figure 2.30 Cross‐sectional view of the 18‐slot 28‐pole outer‐rotor PMV mach...

Figure 2.31 Radial airgap flux density distribution of the 18/28 PMV machine...

Figure 2.32 No‐load magnetic field distribution of the 18/28 PMV machine.

Figure 2.33 Cross‐sectional view of the linear PMV machine.

Figure 2.34 Armature winding layout of the 6/2 linear PMV machine.

Figure 2.35 Four typical mover positions of the linear PMV machine. (a) Posi...

Figure 2.36 Armature field.

Figure 2.37 Radial airgap flux density created by three‐phase armature curre...

Figure 2.38 FSPM machine with 12 stator slots and 10 rotor salient reluctanc...

Figure 2.39 MMF distribution of the FSPM machine over a PM pole pitch.

Figure 2.40 PM MMF distribution of the 12/10 flux‐switching PM machine ignor...

Figure 2.41 Airgap permeance model of flux‐switching PM machines.

Figure 2.42 Open‐circuit airgap flux density waveform and its harmonic spect...

Figure 2.43 Armature MMF distribution of the 12/10 flux‐switching PM machine...

Figure 2.44 Amplitude spectrum of armature MMF in the 12/10 flux‐switching P...

Figure 2.45 Harmonic spectrum of armature field in the 12/10 flux‐switching ...

Figure 2.46 Slip‐ring doubly‐fed machine, (a) cross‐sectional view, (b) stea...

Figure 2.47 Unified description of the operating principle for brushless dou...

Figure 2.48 Unified steady‐state equivalent circuit of cascaded brushless do...

Figure 2.49 Classification of brushless doubly‐fed machines.

Figure 2.50 Evolution of CBDFIM. (a) Cascaded operation of two three‐phase w...

Figure 2.51 Possible rotor windings for BDFIMs. (a) Nested‐loop winding with...

Figure 2.52 Airgap magnetic field modulation phenomenon in the BDFIM with a ...

Figure 2.53 Available rotor structures for BDFRM. (a) Radially‐laminated sal...

Figure 2.54 Radial airgap flux density waveforms and their harmonic spectra ...

Figure 2.55 Radial airgap flux density waveforms and their harmonic spectra ...

Figure 2.56 Magnetic flux patterns of the BDFRM at six time moments in the p...

Figure 2.57 Airgap magnetic field modulation phenomenon in the BDFRM with a ...

Figure 2.58 Hybrid rotors for BDFMs. (a) Combination of multilayer flux barr...

Figure 2.59 Magnetic field modulation behavior in the non‐salient‐pole SM.

Figure 2.60 Magnetic field modualtion behavior in the squirrel‐cage IM.

Figure 2.61 Classification of electrical machines from the perspective of ai...

Figure 2.62 Evolution of electrical machines with rotating excitation source...

Chapter 3

Figure 3.1 Derivation of classical winding function in a doubly cylindrical ...

Figure 3.2 Conductor distribution function.

Figure 3.3 Linear current density distribution function.

Figure 3.4 Airgap MMF distribution function.

Figure 3.5 Airgap flux density distribution function.

Figure 3.6 Classification of electrical machine windings.

Figure 3.7 Influence of short‐circuited coils on the airgap MMF distribution...

Figure 3.8 Influence of salient reluctance poles on the airgap MMF distribut...

Figure 3.9 Influence of multilayer flux barriers on the airgap MMF distribut...

Figure 3.10 Exploded view of a brushless DC PM machine.

Figure 3.11 The cascade of three key elements “excitation source‐modulator‐f...

Figure 3.12 Conductor distribution function, turn function and winding funct...

Figure 3.13 Resultant stator MMF distribution as a function of time and spac...

Figure 3.14 Derivation of induced EMF of a phase winding, (a) coordinate sys...

Figure 3.15 Amplitude spectrums of all the possibilities of three‐phase 12‐s...

Figure 3.16 Equivalent airgap model.

Figure 3.17 Energy flow of electrical machines.

Figure 3.18 Duality of the electrical machine and switching converter.

Figure 3.19 Modulation process in a 1 MHz voltage mode controlled Buck conve...

Figure 3.20 Modulation process in an FRPM machine with six stator teeth and ...

Figure 3.21 Coordinate system for wound‐field salient‐pole SMs.

Figure 3.22 Coordinate system for BDFRMs.

Figure 3.23 Coordinate system for BDFIMs.

Figure 3.24 Coordinate system for the 12/10 FSPM machine.

Figure 3.25 Amplitude spectrums of airgap flux density waveforms of a three‐...

Figure 3.26 Phase spectrums of airgap flux density harmonics with pole pairs...

Figure 3.27 Phase spectrums of airgap flux density harmonics with pole pairs...

Figure 3.28 Phase spectrums of airgap flux density harmonics with pole pairs...

Figure 3.29 Phase spectrums of airgap flux density harmonics with pole pairs...

Figure 3.30 Phase spectrums of airgap flux density harmonics with pole pairs...

Figure 3.31 Amplitude spectrums of airgap flux density waveforms of a three‐...

Figure 3.32 Phase spectrums of airgap flux density harmonics with pole pairs...

Figure 3.33 Phase spectrums of airgap flux density harmonics with pole pairs...

Figure 3.34 Phase spectrums of airgap flux density harmonics with pole pairs...

Figure 3.35 Phase spectrums of airgap flux density harmonics with pole pairs...

Figure 3.36 Amplitude spectrums of airgap flux density waveforms of a three‐...

Figure 3.37 Phase spectrums of airgap flux density harmonics with pole pairs...

Figure 3.38 Phase spectrums of airgap flux density harmonics with pole pairs...

Figure 3.39 Phase spectrums of airgap flux density harmonics with pole pairs...

Figure 3.40 Phase spectrums of airgap flux density harmonics with pole pairs...

Figure 3.41 Average torques contributed by individual airgap flux density ha...

Figure 3.42 Torque decomposition of a three‐phase 12/10 FSPM machine.

T

ff

,

T

Figure 3.43 Coordinate system for the flux‐concentrating field‐modulated PM ...

Figure 3.44 Exploded view of the axial‐flux PMV machine with 16 stator slots...

Figure 3.45 Spectrum of the axial airgap flux density waveform at the mean d...

Figure 3.46 Vector diagram of the studied axial‐flux PMV machine.

Chapter 4

Figure 4.1 Typical example of modulation behaviors, (a) Asynchronous modulat...

Figure 4.2 Production mechanisms of the asynchronous and synchronous torque ...

Figure 4.3 DCM with the synchronous modulation behavior of salient reluctanc...

Figure 4.4 Wound-field salient-pole SM with the synchronous modulation behav...

Figure 4.5 Wound-field non-salient-pole SM and slip‐ring DFIM with the unit ...

Figure 4.6 Squirrel‐cage IM and BDFIM with the asynchronous modulation behav...

Figure 4.7 SynRM and BDFRM with the modulation behavior of flux barrier roto...

Figure 4.8 Surface‐mounted PMSM and FRPM machine. (a) Surface‐mounted PMSM w...

Figure 4.9 Interior PMSM and FSPM machine with the modulation behaviors of s...

Figure 4.10 SRM and vernier machine with the modulation behaviors of salient...

Figure 4.11 MGM and PMV machine with the modulation behaviors of salient rel...

Figure 4.12 Definitions of different speeds in BDFIMs.

Figure 4.13 Cross‐sectional view of the BDFM with a hybrid rotor. Common bar...

Figure 4.14 Modulation behavior of the hybrid rotor in BDFMs.

Figure 4.15 Spectrum shift of the BDFM with a hybrid rotor.

Figure 4.16 Torque production mechanism of FSPM machines.

Figure 4.17 Visualization of rotor salient reluctance pole modulator.

Figure 4.18 Modulation behaviors of salient reluctance poles in the 6/8 FRPM...

Figure 4.19 Visualization of the modulation effect of stator teeth on the ma...

Figure 4.20 Amplitude spectrum of the radial airgap flux density waveform in...

Figure 4.21 Modulation process in the 12/10 FSPM machine.

Figure 4.22 Spectrum shift in the 12/10 FSPM machine due to the modulation b...

Figure 4.23 Visualization of the modulation effect of stator teeth on the ma...

Figure 4.24 Amplitude spectrum of the radial airgap flux density waveform in...

Figure 4.25 Modulation process in the 6/8 FRPM machine.

Figure 4.26 Spectrum shift in the 6/8 FRPM machine due to the modulation beh...

Figure 4.27 Modulation process of flux barriers on the unit cosine source ma...

Figure 4.28 Spectrum shift of flux barriers on the unit cosine source magnet...

Figure 4.29 Modulation behavior of

N

SC

independent loops equally spaced alon...

Figure 4.30 Modulation process in the BDFIM with a two‐pole PW and six‐pole ...

Figure 4.31 Spectrum shift in the BDFIM due to the modulation behaviors of s...

Figure 4.32 Winding function of an individual coil...

Figure 4.33 Normalized MMF waveforms of various rotor windings: (a) nested‐l...

Figure 4.34 BDFM variations with (a) the salient reluctance pole rotor, (b) ...

Figure 4.35 BDFM with a nested‐loop rotor, (a) Cross‐sectional view, (b) One...

Figure 4.36 BDFM with a hybrid rotor. The rotor has a salient reluctance pol...

Figure 4.37 Flux lines and flux density distribution of BDFMs when the CW is...

Figure 4.38 Radial airgap flux density waveforms and their amplitude spectru...

Figure 4.39 Cross‐coupling characteristics in voltage control mode. (a) The ...

Figure 4.40 Inductance characteristics of BDFMs with different rotor types. ...

Figure 4.41 Average torque versus CW phase current when CW is excited, and P...

Chapter 5

Figure 5.1 Rotor winding structures and harmonic spectrum. (a) Standard squi...

Figure 5.2 Coordinate system for analysis. The cross and dot denote the curr...

Figure 5.3 Equivalent circuit of the rotor cage. Each bar current denoted by...

Figure 5.4 Performance comparison between IMs with the standard squirrel‐cag...

Figure 5.5 Inductances and rotor currents. (a) Self‐ and mutual inductances ...

Figure 5.6 Visualization of periodicity in squirrel‐cage IMs. (a) Flux patte...

Figure 5.7 Winding function of a single‐phase full‐pitch winding. Only one p...

Figure 5.8 Winding function of a single‐phase double‐layer short‐pitch windi...

Figure 5.9 Winding function of a single‐phase double‐layer short‐pitch distr...

Figure 5.10 Inductances in the CBDFIM.

Figure 5.11 Inductances in the BDFIM with a nested‐loop rotor.

Figure 5.12 Modulation process of the BDFRM with a salient reluctance pole r...

Figure 5.13 Spectrum shift of the BDFRM with a salient reluctance pole rotor...

Figure 5.14 Inductances in the BDFRM with a salient reluctance pole rotor.

Figure 5.15 Inductance of BDFRM with a multilayer flux barrier rotor.

Figure 5.16 Cross‐sectional view of the studied BDFRM.

Figure 5.17 The BDFRM prototype with a modular multiple‐barrier rotor. (a) L...

Figure 5.18 Winding function of stator winding. (a) Waveforms of winding fun...

Figure 5.19 Flux patterns at two instants of time T0 and T1 when SW1 is exci...

Figure 5.20 Airgap flux density at two instants of time T0 and T1 when SW1 i...

Figure 5.21 Flux density distribution of the BDFRM with both SW1 and SW2 exc...

Figure 5.22 The airgap magnetic field distributions of the BDFRM at six inst...

Figure 5.23 The torque compositions of the BDFRM at six instants of time.

Figure 5.24 Waveforms of the flux density in different flux guides of the sa...

Figure 5.25 Waveforms of the flux density in the same flux guide in differen...

Figure 5.26 Torque production mechanism of the BDFRM and SynRM with a multil...

Figure 5.27 Available system configurations of the BDFRM. (a) The single con...

Figure 5.28 Experimental test results. (a) Phase voltage vs. speed. (b) Mutu...

Figure 5.29 Experimental results. (a) Unsaturated inductance waveforms, (b) ...

Figure 5.30 Cross‐sectional view of the studied BDFIM and the coordinate sys...

Figure 5.31 Prototype of the BDFIM with spiral‐loop rotor windings. (a) Roto...

Figure 5.32 Performance of a 1.5‐kW prototype at 1000 r/min with linear and ...

Figure 5.33 Flux patterns with different combinations of SW1 and SW2 MMFs, w...

Figure 5.34 Flux density in rotor core under (a) unsaturated condition, (b) ...

Figure 5.35 Experimental setup for the testing of the 1.5 kW BDFIM prototype...

Figure 5.36 Experimental results. (a) Phase voltage vs. speed, (b) unsaturat...

Figure 5.37 Modulation process in a SynRM with a multi‐layer barrier rotor, ...

Figure 5.38 Inductances in a 6‐pole SynRM prototype with a multilayer barrie...

Figure 5.39 Torque vs. torque angle Γ of a...

Figure 5.40 Cross‐sectional view of the studied FRPM machine and the coordin...

Figure 5.41

FC

v

vs.

ε

.

Figure 5.42 The studied flux‐reversal PM machine prototype with six stator s...

Figure 5.43 No‐load back EMF. (a) Waveforms. (b) Spectrum.

Figure 5.44 Electromagnetic torque with the phase current rms value.

Figure 5.45 Cogging torque waveform.

Chapter 6

Figure 6.1 Conventional 12/10 FSPM machine and the three basic elements. (a)...

Figure 6.2 New stator‐PM machines derived by changing the source excitation ...

Figure 6.3 A new stator‐PM machine derived by changing the source excitation...

Figure 6.4 Other new stator‐PM machine variants derived by changing the stru...

Figure 6.5 Other new stator‐PM machine variants derived by changing armature...

Figure 6.6 New FSPM machine variations derived by changing the position of s...

Figure 6.7 Dual‐rotor PM machine derived by changing the relative motion amo...

Figure 6.8 Cross‐sectional view of the 12/8 E‐DSPM machine. Black arrows den...

Figure 6.9 Cross‐sectional view of the new 12/7...

Figure 6.10 Magnetic field distribution of the new 12/7...

Figure 6.11 PM flux linkage and no‐load back‐EMF waveforms of DSPM machines....

Figure 6.12 No‐load airgap flux density distribution of the 12/7...

Figure 6.13 PM flux linkage contributed by different dominating harmonics. (...

Figure 6.14 Comparison of phase flux linkages due to different coil connecti...

Figure 6.15 PM flux linkage of the 12/7 Π‐DSPM machine.

Figure 6.16 No‐load back‐EMF of the 12/7 Π‐DSPM machine at 1500 r/min.

Figure 6.17 Comparison of output torque waveforms.

Figure 6.18 Photos of the 12‐7 Π‐DSPM machine...

Figure 6.19 No‐load EMF waveforms and harmonic analysis. (a) Measured and 2D...

Figure 6.20 Experimental setup.

Figure 6.21 Test results of static characteristics.

Figure 6.22 Dynamic performance waveforms. (a) With a constant load toque an...

Figure 6.23 Novel stator‐PM VR resolver. (a) Schematic diagram, (b) Signal l...

Figure 6.24 Structure of a typical stator‐PM VR resolver.

Figure 6.25 EMF waveforms of stator‐PM VR resolver. (a) EMF due to high‐freq...

Figure 6.26 Photo of the stator‐PM VR resolver and its decoding circuit.

Figure 6.27 Decoding diagram for the entire speed range.

Figure 6.28 Measured waveforms of stator‐PM VR resolver prototype. (a) EMF w...

Figure 6.29 Odd‐pole issue in the proposed stator‐PM VR resolver.

Figure 6.30 Odd‐pole structure of stator‐PM VR resolver.

Figure 6.31 FEA results at different rotational speeds. (a) EMF waveform wit...

Figure 6.32 Photo of the 8/3 stator‐PM VR resolver prototype.

Figure 6.33 Measured waveforms of the 8/3 stator‐PM VR resolver. (a) EMF wav...

Figure 6.34 FRPM machines with different magnetization modes. (a) Mode 1 wit...

Figure 6.35 PM MMF distributions of two PRPM machines with different magneti...

Figure 6.36 PM‐MMF distributions of the 6/8 and 12/10 FRPM machines. (a) 6/8...

Figure 6.37 Airgap permeance distribution.

Figure 6.38 PM flux density and harmonic distribution. (a) Flux density (6/8...

Figure 6.39 Winding layouts of the 6/8 FRPM machine. (a) Coil connection 1 f...

Figure 6.40 No‐load back‐EMFs and contributing spatial harmonics in the 6/8 ...

Figure 6.41 Cross‐sectional view of the 12/7 FSPM machine with full‐pitch wi...

Figure 6.42 Magnetic field distribution. (a)

θ

e

 = 0°...

Figure 6.43 No‐load airgap flux density of the 12/7 FSPM machine with full‐p...

Figure 6.44 Slot star diagram of the 12/7 FSPM machine with full‐pitch windi...

Figure 6.45 Definitions of key geometric parameters of the 12/7 FSPM machine...

Figure 6.46 No‐load back‐EMF vs.

k

st

.

Figure 6.47 Torque performance vs.

k

st

.

Figure 6.48 Torque performance vs.

k

io

.

Figure 6.49 Torque performance vs.

k

sy

.

Figure 6.50 Torque performance vs.

h

rt

.

Figure 6.51 Torque performance vs.

k

st

.

Figure 6.52 Comparison of different winding configurations. (a) Flux linkage...

Figure 6.53 Derivation of the rotor‐PM FSPM machine from a 12/10 FSPM machin...

Figure 6.54 Cross‐sectional view of the new three‐phase 24/10 rotor‐PM FSPM ...

Figure 6.55 Flux switching action of the rotor‐PM FSPM machine, (a)

θ

r

 ...

Figure 6.56 PM flux linkage, no‐load back‐EMF and ideal armature current wav...

Figure 6.57 Four specific positions of the 24/10 rotor-PM FSPM machine. (a)

Figure 6.58 No‐load PM magnetic field distributions. (a)

θ

r

...

Figure 6.59 Pole‐to‐pole flux leakage in rotor‐PM FSPM machine.

Figure 6.60 No‐load airgap flux density when

θ

r

 = 0°.

Figure 6.61 Flux linkage waveforms of the 24/10 rotor‐PM FSPM machine.

Figure 6.62 Three‐phase PM flux linkage of the 24/10 rotor‐PM FSPM machine....

Figure 6.63 PM flux linkage harmonic spectrums of the 24/10 rotor‐PM FSPM ma...

Figure 6.64 Single‐phase no‐load back‐EMF waveform of the 24/10 rotor‐PM FSP...

Figure 6.65 No‐load back‐EMF harmonic spectrums of the 24/10 rotor‐PM FSPM m...

Figure 6.66 Definitions of dq axes in rotor‐PM FSPM machines. (a) Position w...

Figure 6.67 PM flux linkage waveforms of the 24/10 rotor‐PM FSPM machine in ...

Figure 6.68 Unsaturated self‐inductance and mutual inductance waveforms.

Figure 6.69 Main flux path of the rotor‐PM FSPM machine.

Figure 6.70 Saturated self‐inductance and mutual inductance waveforms.

Figure 6.71 Unsaturated dq axes inductance waveforms.

Figure 6.72 Saturated dq axes inductance waveforms.

Figure 6.73 Cogging torque of the 24/10 rotor‐PM FSPM machine.

Figure 6.74 Electromagnetic torque of the 24/10 rotor‐PM FSPM machine with

I

Figure 6.75 Input power split hybrid powertrain based on MGPSM.

Figure 6.76 MGPSM. (a) Cross‐sectional view, (b) Key dimensions.

Figure 6.77 Power flow of MGPSM power splitter (Counterclockwise is the posi...

Figure 6.78 Power flowing direction in working mode 1.

Figure 6.79 Power flowing direction in working mode 2.

Figure 6.80 Power flowing direction in working mode 3.

Figure 6.81 Magnetic circuit asymmetry among phases of the MGPSM. (a) Flux l...

Figure 6.82 PM flux linkage and no‐load back‐EMF waveforms at

n

ir

 = 0 r/min ...

Figure 6.83 Definitions of coordinate systems for phase A and phase C airgap...

Figure 6.84 Harmonic analysis of airgap flux density waveforms. (a) Flux den...

Figure 6.85 The influence of spatial harmonics on airgap flux density distor...

Figure 6.86 Description of MGPSM with no‐load operation by simple magnetic c...

Figure 6.87 Schematic diagram of complementary rotor structure.

Figure 6.88 Complementary MGPSM structure and outer airgap flux density wave...

Figure 6.89 Resultant no‐load back‐EMF of phase A.

Figure 6.90 Photos of the 1st prototype. (a) Outer rotor, (b) Inner rotor, (...

Figure 6.91 No‐load back‐EMF waveforms (20 V/div). (a) Inner rotor at 1200 r...

Figure 6.92 Measured cogging torque of the outer rotor in one electrical cyc...

Figure 6.93 Measured steady‐state torque. (a) Torque vs. current density, (b...

Figure 6.94 Dynamic response. (a) Simulation results, (b) Measured results (...

Figure 6.95 Photos of the 2nd MGPSM Prototype. (a) 3D drawing, (b) Rotor ass...

Figure 6.96 Complementary MGPSM prototype test platform.

Figure 6.97 Measured torque and current waveforms. (torque 25 Nm/div, curren...

Figure 6.98 Torque response at a constant speed. (Torque 25 Nm/div, speed 50...

Figure 6.99 Measured efficiency map of the MGPSM (η

sys

).

Figure 6.100 Classification of SC electrical machines.

Figure 6.101 Configuration of stator SC excitation flux switching machine.

Figure 6.102 SC field winding and Dewar. (a) Schematics, (b) Photos.

Figure 6.103 Prototype and its experimental system. (a) Prototype assembly, ...

Figure 6.104 Measured no‐load back‐EMF of prototype (n = 200 r/min). (a) Fie...

Figure 6.105 Structure of the double‐stator field modulation SC excitation m...

Figure 6.106 Composite d electromagnetic shielding layer. (a) Composite elec...

Figure 6.107 No‐load back‐EMF of SC coil in rated working conditions without...

Figure 6.108 No‐load back‐EMF of SC coil in rated working conditions with th...

Figure 6.109 Flux density in the direction parallel to the SC winding in rat...

Figure 6.110 Flux density in the direction perpendicular to the SC winding i...

Figure 6.111 10 kW DS‐FMSE machine prototype. (a) Inner stator with SC magne...

Figure 6.112 Topology and no‐load flux lines/density distribution of the 4/2...

Figure 6.113 Spatial phase distribution. (a) Control winding excited and pow...

Figure 6.114 Schematic of modulated p‐pole‐pair harmonic superposition for t...

Figure 6.115 Torque improvement of the 4/2 BDFRM. (a) Topology diagram: alon...

Figure 6.116 Torque waveforms comparison of the 4/2 BDFRM with symmetrical a...

Figure 6.117 Modulated harmonic distributions. (a) Harmonic spectrum compari...

Figure 6.118 Prototype machines. (a) Symmetrical modulator, (b) Asymmetrical...

Figure 6.119 Measured cross‐coupling characteristics (excitation phase volta...

Figure 6.120 Inductance characteristics. (a) BDFRM with a symmetrical compos...

Figure 6.121 Torque performance. (a) Torque versus current, (b) Torque versu...

Chapter 7

Figure 7.1 Radial force distribution on the top of the stator teeth for brus...

Figure 7.2 Resultant radial force under different pole‐pairs corresponding t...

Figure 7.3 Resultant radial force under different pole‐pair corresponding to...

Figure 7.4 FEA‐predicted radial airgap flux density waveforms and associated...

Figure 7.5 FEA‐predicted radial airgap flux density waveforms and associated...

Figure 7.6 The torque winding (

Q

 = 36,

p

 = 4,...

Figure 7.7 The derivation of the conductor distribution of the suspension wi...

Figure 7.8 The derivation of the conductors distribution of the suspension w...

Figure 7.9 Fourier transforms of the suspension winding I (Fourier coefficie...

Figure 7.10 Fourier transforms of the suspension winding II (Fourier coeffic...

Figure 7.11 The derivation of the conductors distribution of the suspension ...

Figure 7.12 The derivation of the conductors distribution of the suspension ...

Figure 7.13 Fourier transforms of the suspension winding III (Fourier coeffi...

Figure 7.14 Fourier transforms of the suspension winding IV (Fourier coeffic...

Figure 7.15 Stray load loss calculation.

Figure 7.16 Cross‐sectional view and winding layout of the squirrel‐cage IM ...

Figure 7.17 Influence of lamination material permeability on the airgap magn...

Figure 7.18 2D FEA model for stator core loss calculation. Rotor slots are f...

Figure 7.19 2D FEA model for rotor core loss calculation. Stator slots are f...

Figure 7.20 Calculation process for stray load loss.

Figure 7.21 Experiment setup.

Figure 7.22 Total loss from no‐load test vs. voltage squared for loss separa...

Figure 7.23 Measured stray load loss vs. torque squared. The rated load oper...

Figure 7.24 Cross‐sectional view of the FSPM machine under study. (a) Full c...

Figure 7.25 Simplified model for the source magnetizing MMF.

Figure 7.26 Source magnetizing MMF distribution.

Figure 7.27 Calculation process for PM operating point.

Figure 7.28 The radial airgap flux density distribution when the stator/roto...

Figure 7.29 No‐load airgap flux density distribution. (a) Waveforms, (b) Amp...

Figure 7.30 Armature‐reaction airgap flux density distributions, (a) Wavefor...

Figure 7.31 Stator core loss calculation model.

Figure 7.32 Rotor core loss calculation model.

Figure 7.33 Workflow for core loss calculation with the current excitation f...

Figure 7.34 Amplitude spectrums of PWM voltage sources used in the study. (a...

Figure 7.35 Amplitude spectrums of current waveforms from PWM voltage source...

Figure 7.36 Core loss calculation process based on the GAFMT.

Figure 7.37 Amplitude distribution of the airgap magnetic flux density. (a) ...

Figure 7.38 Experimental setup.

Figure 7.39 Rotor salient reluctance pole structures under study and shapes ...

Figure 7.40 Cross‐sectional view and flux lines distribution of the MGM unde...

Figure 7.41 Variations of the fundamental harmonic (12th) amplitude vs.

ε

...

Figure 7.42 Torque performance vs.

ε

out

and

ε

...

Figure 7.43 Comparison of torque performance for different rotor salient pol...

Figure 7.44 The optimum combination of

ε

out

and...

Figure 7.45 Cross‐sectional view and flux lines of the 6/8 FRPM machine with...

Figure 7.46 Modulated harmonic distributions (the fundamental harmonic: 6th)...

Figure 7.47 Torque performance for Type (2 + 4). (a) Average torque, (b) Tor...

Figure 7.48 The optimum solution for FRPM machines with different pole‐slot ...

Figure 7.49 FRPM porotypes with different pole‐slot combinations. (a) The 6/...

Figure 7.50 Open‐circuit back‐EMF and inductance characteristics of the 6/8 ...

Figure 7.51 Torque performance. (a) Average torque vs. current density, (b) ...

Figure 7.52 Relationship between the three chained key elements and the perf...

Figure 7.53 3D geometry of the V‐FMPM machine under study.

Figure 7.54 Workflow of the airgap‐harmonic‐orientated design optimization m...

Figure 7.55 Implementation of the airgap‐harmonic‐oriented design optimizati...

Figure 7.56 Visualization of geometric parameters.

Figure 7.57 The contribution of airgap field harmonics to the torque perform...

Figure 7.58 Sensitivity analysis for the selected airgap filed harmonics. (a...

Figure 7.59 Representative surface responses. (a) Output torque produced by ...

Figure 7.60 Comparisons of torque performance contributions in the initial a...

Figure 7.61 Flux lines and flux density distributions of the V‐FMPM machine....

Figure 7.62 No‐load back‐EMF waveforms.

Figure 7.63 Torque performance of the initial and optimal designs. (a) Coggi...

Figure 7.64 Stress distribution of the V‐FMPM machine at 5000 r/min.

Figure 7.65 Parts of the V‐FMPM machine prototype. (a) Stator and rotor lami...

Figure 7.66 Experimental setup for testing the V‐FMPM machine prototype.

Figure 7.67 Measured machine performance. (a) Back‐EMF waveforms. (b) THD of...

Figure 7.68 Torque versus phase current.

Figure 7.69 Transient waveforms. (a) Staring performance. (b) Transient vari...

Appendix A

Figure A.1 Graphical derivation of the modulation operator for short‐circuit...

Figure A.2 Graphical derivation of the modulation operator for salient reluc...

Figure A.3 Derivation of the multilayer flux barrier modulation operator.

Figure A.4 Graphical derivation of the modulation operator for multilayer fl...

Appendix B

Figure B.1 Flux density distributions in the airgap and along the armature s...

Figure B.2

F

d

versus

d

/

g

and

b

s

/

g

, where

b

s

...

Appendix C

Figure C.1 Representation of an electrical machine with

m

electrical ports a...

Figure C.2 Magnetic stored energy and co‐energy when

m

 = 1.

Guide

Cover Page

Table of Contents

Series Page

Title Page

Copyright

Preface

About the Authors

About the Companion Website

Begin Reading

Appendix A Derivation of Modulation Operators

Appendix B Magnetic Force of Current‐Carrying Conductors in Airgap and in Slots

Appendix C Methods for Force and Torque Calculation

Index

Wiley End User License Agreement

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IEEE Press

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Jeffrey Reed

Thomas Robertazzi

Diomidis Spinellis

Ahmet Murat Tekalp

General Airgap Field Modulation Theory for Electrical Machines

Principles and Practice

Ming Cheng

Southeast UniversityNanjing, China

Peng Han

Ansys, Inc.Irvine, USA

Yi Du

Jiangsu UniversityZhenjiang, China

Honghui Wen

Southeast UniversityNanjing, China

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Preface

Electrical machines are devices that convert mechanical energy into electrical energy or vice versa. They were invented in the 1800s and have a history of nearly 200 years. Other inventions of similar ages, such as the Watt steam engine, telegraph, incandescent light bulb, etc., have been outdated by emerging technologies. By contrast, the electrical machine shows great tenacity and vitality, becoming a living fossil of the Industrial Revolution.

Demand for high‐performance electrical machines is increasing day by day with the rapid development of our social economy. Application areas of electrical machines have extended from conventional industrial drive to aerospace, transportation, numerical control machine tools, robots, and other high‐tech fields, ranging from deep below the surface of the earth to deep space, from the furthest depths of the ocean to the surfaces of land and sea.

The diversity in performance requirements for different applications leads to the invention of novel electrical machine topologies with different performance advantages, especially those having multiple working spatial harmonics, such as the magnetically geared machine (MGM), permanent magnet vernier (PMV) machine, brushless doubly fed machines, just to name a few.

These new machine topologies show significant magnetic field modulation effects, posing great challenges to existing theories for the analysis of electrical machines. The operation of some emerging electrical machines, such as the PMV machine with dissimilar numbers of stator winding pole pairs and magnet polarities, can hardly be explained directly by the well‐established theory for induction machines and synchronous machines. In addition, most theories and methods for the analysis of electrical machines were developed and therefore valid for only certain machine types.

Based on the extensive scientific and industrial research for high‐performance electrical machines and drive technologies conducted by the Jiangsu Electrical Machines & Power Electronics League (JEMPEL), Southeast University, Nanjing, China, over the past decades, the authors noticed the generality of airgap magnetic field modulation phenomena in electrical machines and its instrumental role in improving performance of electrical machines. The discoveries were further examined against almost all the known electrical machine topologies, and then theorized to develop the general airgap field modulation theory.

The book is organized into seven chapters and three appendices, as outlined below:

Chapter 1

reviews the historical development of electrical machines and their theories.

Chapter 2

analyzes the airgap magnetic field modulation phenomena in common machine topologies, aiming to reveal the ubiquity of magnetic field modulation phenomena in electrical machines.

Chapter 3

abstracts a unit machine with one stator, one rotor and one layer of airgap as a cascade of three key elements, based on which generalized mathematical models for the three elements are proposed, forming the general airgap field modulation theory framework for electrical machines.

Chapter 4

analyzes the relationship between different modulation behaviors and their torque compositions.

Chapter 5

applies the general airgap magnetic field modulation theory to multiple representative machine topologies to show its application in qualitative analysis and quantitative calculation of machine performance.

Chapter 6

covers the innovation of machine topology with the guidance of the general airgap field modulation theory.

Chapter 7

presents more application examples of the developed theory.

Appendix A

shows the mathematical derivation of the three typical modulation operators.

Appendix B

clarifies the relationship between electromagnetic forces/torques on conductors placed in the airgap and in-slot conductors.

Appendix C

presents the Maxwell Stress Tensor method and principle of virtual work, which are the basis of force/torque analysis using the general airgap field modulation theory.

The contents presented in this book are a selected collection of scientific and industrial research work conducted by the JEMPEL and its extended research groups during the past decades. The authors are very grateful to all the JEMPEL members, especially Prof. Xiaoyong Zhu, Prof. Yubin Wang, Dr. Le Sun, Dr. Xinkai Zhu, Dr. Jingxia Wang, Dr. Yu Zeng for their dedicated assistance in preparing the manuscript, and Dr. Gan Zhang, Mr. Zhengzhou Ma, Ms. Chenchen Zhao for their tremendous help in the preparation of main figures.

The authors would also like to express their sincere gratitude to Prof. Wei Hua, Prof. Jianzhong Zhang, Prof. Wenxiang Zhao, Prof. Xianglin Li, Dr. Qiang Sun, Dr. Hongyun Jia, Dr. Feng Yu, Dr. Feng Li, Dr. Lingyun Shao, Dr. Peng Su, Dr. Minghao Tong, Dr. Xiaofeng Zhu and Dr. Peixin Wang for their excellent research outcomes, which are essential ingredients of this book.

We are deeply indebted to our colleagues and friends worldwide for their continuous support, encouragement, and discussion on the subject matter over the years, especially Prof. Ayman EL‐Refaie, Prof. C.C. Chan, Prof. Dan M. Ionel, Prof. Hossein Torkaman, Prof. Ion Boldea, Prof. Iqbal Husain, Prof. James Kirtley, Prof. Jianguo Zhu, Prof. K.T. Chau, Prof. Longya Xu, Prof. W.N. Fu, Prof. Ying Fan, Prof. Z.Q. Zhu, Prof. Zhe Chen, Prof. Zheng Wang, Dr. Arijit Banerjee, Dr. Baoyun Ge, Dr. Hao Huang, Dr. Jianning Dong, Dr. Kaiyuan Lu, Dr. Ming Xu, Dr. Sa Zhu, Dr. Shengyi Liu, Dr. Ying Pang, Ms. Xiaoping Li, for their valuable feedback on this theory.

We also much appreciate the reviewers of this book for their thoughtful and constructive comments, and Editors of John Wiley & Sons for their professional and timely support in the review and production process.

Last but not least, we thank our families for nurturing and unconditionally supporting the writing of this book.

About the Authors

Ming Cheng received his B.Sc. and M.Sc. degrees from Southeast University, Nanjing, China, in 1982 and 1987, respectively, and his Ph.D. degree from the University of Hong Kong, Hong Kong, in 2001, all in electrical engineering. Since 1987, he has been with Southeast University, where he is currently an Endowed Chair Professor at the School of Electrical Engineering and the Director of the Research Center for Wind Power Generation.

He is a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and the Institution of Engineering and Technology (IET) and was a Distinguished Lecturer of the IEEE Industry Applications Society for 2015/2016. He has served as editor‐in‐chief, editor and editorial board member of various international journals, as well as chair and organizing committee member of many international conferences, especially in the area of Electrical Machines and Power Electronics.

His teaching and research interests include electrical machines, motor drives for EV, renewable energy generation, and servo motor & control. In these areas, he has published over 500 refereed technical papers and 7 books and holds over 150 invention patents.

He has received many awards, including Second Prize in the State Technological Invention Awards (given by the State Council of the People's Republic of China); First Prize in China's Ministry of Education's Natural Science Awards; First Prize in Jiangsu Provincial Government's Science and Technology Award; the IET Achievement Award; and the Environmental Excellence in Transportation Award for Education, Training, and Public Awareness by SAE International.

Peng Han received B.Sc. and Ph.D. degrees in electrical engineering from the School of Electrical Engineering, Southeast University, Nanjing, China, in 2012 and 2017, respectively.

From November 2014 to November 2015, he was a Guest Ph.D. student at the Department of Energy Technology, Aalborg University, Aalborg, Denmark, where he focused on brushless doubly fed machines' application in wind energy conversion and high‐power drives. He is currently with Ansys, Inc., USA, as a Senior Application Engineer. Before joining Ansys, he was a Postdoctoral Researcher with the Center for High Performance Power Electronics (CHPPE) Department of Electrical and Computer Engineering, The Ohio State University, and later the SPARK Laboratory, Department of Electrical and Computer Engineering, University of Kentucky. His current research interests include electrical machines, machine drives, power electronics, and renewable energy.

He is an IEEE Senior Member and an Associate Editor for IEEE Transactions on Industrial Electronics, IEEE Transactions on Industry Applications and Journal of Power Electronics. He received two best paper/poster awards from IEEE conferences, and Third Prize in the IEEE IAS Student Thesis Contest in 2018.

Yi Du received B.Sc. and M.Sc. degrees in electrical engineering from Jiangsu University, Zhenjiang, China, in 2002 and 2007, respectively, and a Ph.D. degree in electrical engineering from Southeast University, Nanjing, China, in 2014.

He has been with Jiangsu University since 2002, where he is currently a Professor in the School of Electrical and Information Engineering. From 2018 to 2019, he was a Visiting Professor with the Department of Electronic & Electrical Engineering, The University of Sheffield, Sheffield, UK. His research interests include design and analysis of electrical machine systems with low‐speed and high‐torque outputs, and with wide‐speed range.

Honghui Wen received B.Sc. and Ph.D. degrees in electrical engineering from the School of Electrical Engineering, Southeast University, Nanjing, China, in 2016 and 2021, respectively.

Since January 2022, he has been with the College of Electrical and Information Engineering, Hunan University, Changsha, China, where he is currently an Assistant Professor. His teaching and research interests include the design, analysis, and optimization of magnetic field electrical machines. In these areas, he has published one book and over 10 peer‐reviewed technical papers.

About the Companion Website

This book is accompanied by a companion website:

www.wiley.com/go/genairgapfieldmodulationtheory

The website includes models and scripts.

1Introduction

1.1 Review of Historical Development of Electrical Machines

Electrical machines are electromagnetic devices to achieve electromechanical energy conversion. Since Jacobi invented the DC machine (DCM) in 1834 and Tesla invented the induction machine (IM) in 1880s, electrical machine technology has developed rapidly, and its application has become more and more extensive. Electrical machines have become one of the most important energy and power technologies to support the national economy. Various types of machines with power levels ranging from several milliwatts to hundreds of megawatts, especially the three traditional machine topologies, namely the DCM, AC induction (asynchronous) machine, and AC synchronous machine (SM), have made great contributions to the development of human society [1, 2].

It is worth mentioning that the steam engine, telegraph, incandescent lamp, etc., which appeared at virtually the same time as electrical machines, have been replaced by emerging technologies and have gradually faded into disuse. By contrast, the electrical machine presents a tenacious vitality, and can be considered a surviving fossil of the modern industrial revolution, one which constantly renews its life. Correspondingly, the development and innovation of electrical machine theories and technologies have never stopped.

With the proliferation of electrification and automation technologies, the application of electrical machines has expanded from conventional industrial drive to aerospace, transportation, CNC equipment, robotics and other high‐tech fields, and from ground to deep space, deep sea, and deep earth. The performance requirements of machines for different applications are constantly refined, and the traditional brushed DCMs, IMs, and SMs are difficult to meet the demanding requirements of new fields and applications. Meanwhile, the rapid development of material technology, processing and manufacturing technology, and control technology, combined with new application requirements, has given rise to various new electrical machines with different constructions, different working principles, and different performance advantages, such as: synchronous reluctance machines (SynRMs) [3–5], permanent magnet (PM) brushless machines [6, 7], vernier machines [8], brushless doubly‐fed induction machines (BDFIMs) [9–11], brushless doubly‐fed reluctance machines (BDFRMs) [12, 13], transverse flux machines [14], switched reluctance machines (SRMs) [15, 16], stator‐PM brushless machines [17–20], PM vernier (PMV) machines [21, 22], magnetically‐geared machines (MGMs) [23–26], dual‐mechanical‐port (DMP) machines [27, 28], etc.

In order to provide an overview of the relevant research on electrical machines, a bibliometric analysis was performed in IEEE Xplore digital library database at the end of 2021. The results summarized in Figure 1.1 show the diversity of machine topologies and soaring numbers of publications on these “unconventional” machines.

As representative traditional electrical machines, IMs and wound‐field salient‐pole SMs have experienced the longest history of research. Considerable research work had been done before the

field‐oriented control

(

FOC

) method was invented by F. Blaschke in 1971. Research on IMs grows steadily and peaked at 2014–2015. In contrast, research on wound‐field salient‐pole SMs was interrupted in the 1970s and 1980s and resumed later, but it is much less popular than that of IMs.

High‐energy‐product PM materials were introduced into the manufacturing and performance improvement of electrical machines in the late 1970s, after which the research on PM brushless machines began to grow steadily, with a dramatic increase in 2010. Afterwards, the research on PM machines decreased due to the large price fluctuation of PM materials, but still stayed at a high level.