A comprehensive resource providing basic principles and state-of-the art developments in sensorless control technologies for permanent magnet synchronous machine drives Sensorless Control of Permanent Magnet Synchronous Machine Drives highlights the global research achievements over the last three decades and the sensorless techniques developed by the authors and their colleagues, and covers sensorless control techniques of permanent magnet machines, discussing issues and solutions. Many worked application examples are included to aid in practical understanding of concepts. Written by two pioneering authors in the field, Sensorless Control of Permanent Magnet Synchronous Machine Drives covers sample topics such as: Permanent magnet brushless AC and DC drivesSingle three-phase, dual three-phase, and open winding machinesModern control theory based sensorless methods, covering model reference adaptive system, sliding mode observer, extended Kalman filter, and model predictive controlFlux-linkage and back-EMF based methods for non-salient machines, and active flux-linkage and extended back-EMF methods for salient machinesPulsating and rotating high frequency sinusoidal and square wave signal injection methods with current or voltage response, at different reference frames, and selection of amplitude and frequency for injection signalSensorless control techniques based on detecting third harmonic or zero-crossings of back-EMF waveformsParasitic effects in fundamental and high frequency models, impacts on position estimation, and compensation schemes, covering cross-coupling magnetic saturation, load effect, machine saliency and multiple saliencies, inverter non-linearities, voltage and current harmonics, parameter asymmetries, and parameter mismatchesTechniques for rotor initial position estimation, magnetic polarity detection, and transition between low and high speedsDescribing basic principles, examples, challenges, and practical solutions, Sensorless Control of Permanent Magnet Synchronous Machine Drives is a highly comprehensive resource on the subject for professionals working on electrical machines and drives, particularly permanent magnet machines, and researchers working on electric vehicles, wind power generators, household appliances, and industrial automation.

A comprehensive resource providing basic principles and state-of-the art developments in sensorless control technologies for permanent magnet synchronous machine drives

Sensorless Control of Permanent Magnet Synchronous Machine Drives highlights the global research achievements over the last three decades and the sensorless techniques developed by the authors and their colleagues, and covers sensorless control techniques of permanent magnet machines, discussing issues and solutions. Many worked application examples are included to aid in practical understanding of concepts.

Written by two pioneering authors in the field, Sensorless Control of Permanent Magnet Synchronous Machine Drives covers sample topics such as:

Permanent magnet brushless AC and DC drives Single three-phase, dual three-phase, and open winding machines Modern control theory based sensorless methods, covering model reference adaptive system, sliding mode observer, extended Kalman filter, and model predictive control Flux-linkage and back-EMF based methods for non-salient machines, and active flux-linkage and extended back-EMF methods for salient machines Pulsating and rotating high frequency sinusoidal and square wave signal injection methods with current or voltage response, at different reference frames, and selection of amplitude and frequency for injection signal Sensorless control techniques based on detecting third harmonic or zero-crossings of back-EMF waveforms Parasitic effects in fundamental and high frequency models, impacts on position estimation, and compensation schemes, covering cross-coupling magnetic saturation, load effect, machine saliency and multiple saliencies, inverter non-linearities, voltage and current harmonics, parameter asymmetries, and parameter mismatches Techniques for rotor initial position estimation, magnetic polarity detection, and transition between low and high speeds

Describing basic principles, examples, challenges, and practical solutions, Sensorless Control of Permanent Magnet Synchronous Machine Drives is a highly comprehensive resource on the subject for professionals working on electrical machines and drives, particularly permanent magnet machines, and researchers working on electric vehicles, wind power generators, household appliances, and industrial automation.

A comprehensive resource providing basic principles and state-of-the art developments in sensorless control technologies for permanent magnet synchronous machine drives

Sensorless Control of Permanent Magnet Synchronous Machine Drives highlights the global research achievements over the last three decades and the sensorless techniques developed by the authors and their colleagues, and covers sensorless control techniques of permanent magnet machines, discussing issues and solutions. Many worked application examples are included to aid in practical understanding of concepts.

Written by two pioneering authors in the field, Sensorless Control of Permanent Magnet Synchronous Machine Drives covers sample topics such as:

Permanent magnet brushless AC and DC drives Single three-phase, dual three-phase, and open winding machines Modern control theory based sensorless methods, covering model reference adaptive system, sliding mode observer, extended Kalman filter, and model predictive control Flux-linkage and back-EMF based methods for non-salient machines, and active flux-linkage and extended back-EMF methods for salient machines Pulsating and rotating high frequency sinusoidal and square wave signal injection methods with current or voltage response, at different reference frames, and selection of amplitude and frequency for injection signal Sensorless control techniques based on detecting third harmonic or zero-crossings of back-EMF waveforms Parasitic effects in fundamental and high frequency models, impacts on position estimation, and compensation schemes, covering cross-coupling magnetic saturation, load effect, machine saliency and multiple saliencies, inverter non-linearities, voltage and current harmonics, parameter asymmetries, and parameter mismatches Techniques for rotor initial position estimation, magnetic polarity detection, and transition between low and high speeds

Describing basic principles, examples, challenges, and practical solutions, Sensorless Control of Permanent Magnet Synchronous Machine Drives is a highly comprehensive resource on the subject for professionals working on electrical machines and drives, particularly permanent magnet machines, and researchers working on electric vehicles, wind power generators, household appliances, and industrial automation.

Comprehensive reference delivering basic principles and state-of-the-art parameter estimation techniques for permanent magnet synchronous machines (PMSMs) Parameter Estimation of Permanent Magnet Synchronous Machines reviews estimation techniques of the parameters of PMSMs, introducing basic models and techniques, as well as issues and solutions in parameter estimation challenges, including rank deficiency, inverter nonlinearity, and magnetic saturation. This book is supported by theories, experiments, and simulation examples for each technique covered. Topics explored in this book include: Electrical and mechanical parameter estimation techniques, including those based on current/voltage injection and position offset injection, under constant or variable speed and load for sensored or sensorless controlled PMSMs, accounting for magnetic saturation, cross-coupling, inverter nonlinearity, temperature effects, and moreRecursive least squares, the Kalman filter, model reference adaptive systems, Adaline neural networks, gradient-based methods, particle swarm optimization, and genetic algorithmsApplications of parameter estimation techniques for improvement of control performance, sensorless control, thermal condition monitoring, and fault diagnosisThis book is an essential reference for professionals working on the control and design of electrical machines, researchers studying electric vehicles, wind power generators, aerospace, industrial drives, automation systems, robots, and domestic appliances, as well as advanced undergraduate and graduate students in related programs of study.

Comprehensive reference delivering basic principles and state-of-the-art parameter estimation techniques for permanent magnet synchronous machines (PMSMs)

Parameter Estimation of Permanent Magnet Synchronous Machines reviews estimation techniques of the parameters of PMSMs, introducing basic models and techniques, as well as issues and solutions in parameter estimation challenges, including rank deficiency, inverter nonlinearity, and magnetic saturation. This book is supported by theories, experiments, and simulation examples for each technique covered.

Topics explored in this book include:

Electrical and mechanical parameter estimation techniques, including those based on current/voltage injection and position offset injection, under constant or variable speed and load for sensored or sensorless controlled PMSMs, accounting for magnetic saturation, cross-coupling, inverter nonlinearity, temperature effects, and moreRecursive least squares, the Kalman filter, model reference adaptive systems, Adaline neural networks, gradient-based methods, particle swarm optimization, and genetic algorithmsApplications of parameter estimation techniques for improvement of control performance, sensorless control, thermal condition monitoring, and fault diagnosis

This book is an essential reference for professionals working on the control and design of electrical machines, researchers studying electric vehicles, wind power generators, aerospace, industrial drives, automation systems, robots, and domestic appliances, as well as advanced undergraduate and graduate students in related programs of study.

Comprehensive reference delivering basic principles and state-of-the-art parameter estimation techniques for permanent magnet synchronous machines (PMSMs)

Parameter Estimation of Permanent Magnet Synchronous Machines reviews estimation techniques of the parameters of PMSMs, introducing basic models and techniques, as well as issues and solutions in parameter estimation challenges, including rank deficiency, inverter nonlinearity, and magnetic saturation. This book is supported by theories, experiments, and simulation examples for each technique covered.

Topics explored in this book include:

Electrical and mechanical parameter estimation techniques, including those based on current/voltage injection and position offset injection, under constant or variable speed and load for sensored or sensorless controlled PMSMs, accounting for magnetic saturation, cross-coupling, inverter nonlinearity, temperature effects, and more Recursive least squares, the Kalman filter, model reference adaptive systems, Adaline neural networks, gradient-based methods, particle swarm optimization, and genetic algorithms Applications of parameter estimation techniques for improvement of control performance, sensorless control, thermal condition monitoring, and fault diagnosis

Parameter Estimation of Permanent Magnet Synchronous Machines, is an essential reference for professionals working on the control and design of electrical machines, researchers studying electric vehicles, wind power generators, aerospace, industrial drives, automation systems, robots, and domestic appliances, as well as advanced undergraduate and graduate students in related programs of study.

The electrification of the economy entails the development and optimization of efficient electrical machines. Permanent magnet machines use permanent magnets, rather than windings, for field excitation. They are more efficient than other electrical machine technologies for high-efficiency applications. Multiphase machines, as compared to 3-phase machines, have advantages including lower torque pulsation, higher power density, and better fault tolerance.This book offers concise and systematic coverage of multiphase permanent magnet machines and control techniques. It gives an overview of multiphase machines and control techniques in the context of various electrical machine technologies and presents the advantages of multiphase electrical machines. Applications are covered, including wind turbine generators, electric vehicles, electric ships, and aircraft and train propulsion. Machine topologies, modelling, design, control, pulse-width modulation, fault-tolerance, and reduction of current harmonics and torque ripples are considered.Multiphase Permanent Magnet Synchronous Machines and Drives: Principles, design, and control is written for industrial engineers and researchers, including PhD and post-doctoral research students working on electrical machines and drives, as well as for researchers working on electric vehicles, wind power generators, aerospace, electric ships and trains. Following a general introduction, chapters cover winding configurations, multiphase and dual-three-phase permanent magnet synchronous machines (PMSMs), modelling, design, modulation strategies, field-oriented control, direct torque control, model reference control, sensorless control, and also fault tolerant control for multiphase PMSMs. The logical progression from fundamental concepts to state-of-the-art research outcomes helps readers understand and use multiphase electrical machines.

This book investigates the utilization of harmonics in the permanent magnet (PM) or rotor shape to improve the torque density of PM brushless AC machines including three-phase inner rotor and outer rotor machines, five-phase machines, dual three-phase machines, linear machines, by means of analytical, finite element analyses, and as well as experimental validation. The torque density can be improved while the torque ripple remains low in PM shaping utilizing the 3rd harmonic. In this book, the analytical expression of output torque is derived for PM machines with rotor shape using the 3rd harmonic, and then the optimal 3rd harmonic for maximizing torque is analytically obtained. The book compares the PM shape in surface-mounted PM (SPM) machines and the rotor lamination shape in interior PM (IPM) machines utilizing the 3rd harmonic, and it becomes clear that their shaping methods and amount of torque improvement are different. In a five-phase PM machine, the 3rd harmonic can be utilized in both the current waveform and PM shapes to further improve the output torque. For the dual three-phase SPM machines without deteriorating the torque more than 30% when the optimal 3rd harmonic into both the current and PM shape are injected.The harmonics in airgap flux density have significant influence on the cogging torque, stator iron flux distribution, and radial force between the rotor and stator. These effects has been investigated as well in this book.

This book investigates the utilization of harmonics in the permanent magnet (PM) or rotor shape to improve the torque density of PM brushless AC machines including three-phase inner rotor and outer rotor machines, five-phase machines, dual three-phase machines, linear machines, by means of analytical, finite element analyses, and as well as experimental validation. The torque density can be improved while the torque ripple remains low in PM shaping utilizing the 3rd harmonic. In this book, the analytical expression of output torque is derived for PM machines with rotor shape using the 3rd harmonic, and then the optimal 3rd harmonic for maximizing torque is analytically obtained. The book compares the PM shape in surface-mounted PM (SPM) machines and the rotor lamination shape in interior PM (IPM) machines utilizing the 3rd harmonic, and it becomes clear that their shaping methods and amount of torque improvement are different. In a five-phase PM machine, the 3rd harmonic can be utilized in both the current waveform and PM shapes to further improve the output torque. For the dual three-phase SPM machines without deteriorating the torque more than 30% when the optimal 3rd harmonic into both the current and PM shape are injected.The harmonics in airgap flux density have significant influence on the cogging torque, stator iron flux distribution, and radial force between the rotor and stator. These effects has been investigated as well in this book.

A comprehensive resource providing basic principles and state-of-the art developments in sensorless control technologies for permanent magnet synchronous machine drives Sensorless Control of Permanent Magnet Synchronous Machine Drives highlights the global research achievements over the last three decades and the sensorless techniques developed by the authors and their colleagues, and covers sensorless control techniques of permanent magnet machines, discussing issues and solutions. Many worked application examples are included to aid in practical understanding of concepts. Written by two pioneering authors in the field, Sensorless Control of Permanent Magnet Synchronous Machine Drives covers sample topics such as: Permanent magnet brushless AC and DC drivesSingle three-phase, dual three-phase, and open winding machinesModern control theory based sensorless methods, covering model reference adaptive system, sliding mode observer, extended Kalman filter, and model predictive controlFlux-linkage and back-EMF based methods for non-salient machines, and active flux-linkage and extended back-EMF methods for salient machinesPulsating and rotating high frequency sinusoidal and square wave signal injection methods with current or voltage response, at different reference frames, and selection of amplitude and frequency for injection signalSensorless control techniques based on detecting third harmonic or zero-crossings of back-EMF waveformsParasitic effects in fundamental and high frequency models, impacts on position estimation, and compensation schemes, covering cross-coupling magnetic saturation, load effect, machine saliency and multiple saliencies, inverter non-linearities, voltage and current harmonics, parameter asymmetries, and parameter mismatchesTechniques for rotor initial position estimation, magnetic polarity detection, and transition between low and high speedsDescribing basic principles, examples, challenges, and practical solutions, Sensorless Control of Permanent Magnet Synchronous Machine Drives is a highly comprehensive resource on the subject for professionals working on electrical machines and drives, particularly permanent magnet machines, and researchers working on electric vehicles, wind power generators, household appliances, and industrial automation.

A comprehensive resource providing basic principles and state-of-the art developments in sensorless control technologies for permanent magnet synchronous machine drives

Sensorless Control of Permanent Magnet Synchronous Machine Drives highlights the global research achievements over the last three decades and the sensorless techniques developed by the authors and their colleagues, and covers sensorless control techniques of permanent magnet machines, discussing issues and solutions. Many worked application examples are included to aid in practical understanding of concepts.

Written by two pioneering authors in the field, Sensorless Control of Permanent Magnet Synchronous Machine Drives covers sample topics such as:

Permanent magnet brushless AC and DC drives Single three-phase, dual three-phase, and open winding machines Modern control theory based sensorless methods, covering model reference adaptive system, sliding mode observer, extended Kalman filter, and model predictive control Flux-linkage and back-EMF based methods for non-salient machines, and active flux-linkage and extended back-EMF methods for salient machines Pulsating and rotating high frequency sinusoidal and square wave signal injection methods with current or voltage response, at different reference frames, and selection of amplitude and frequency for injection signal Sensorless control techniques based on detecting third harmonic or zero-crossings of back-EMF waveforms Parasitic effects in fundamental and high frequency models, impacts on position estimation, and compensation schemes, covering cross-coupling magnetic saturation, load effect, machine saliency and multiple saliencies, inverter non-linearities, voltage and current harmonics, parameter asymmetries, and parameter mismatches Techniques for rotor initial position estimation, magnetic polarity detection, and transition between low and high speeds

Describing basic principles, examples, challenges, and practical solutions, Sensorless Control of Permanent Magnet Synchronous Machine Drives is a highly comprehensive resource on the subject for professionals working on electrical machines and drives, particularly permanent magnet machines, and researchers working on electric vehicles, wind power generators, household appliances, and industrial automation.

A comprehensive resource providing basic principles and state-of-the art developments in sensorless control technologies for permanent magnet synchronous machine drives

Sensorless Control of Permanent Magnet Synchronous Machine Drives highlights the global research achievements over the last three decades and the sensorless techniques developed by the authors and their colleagues, and covers sensorless control techniques of permanent magnet machines, discussing issues and solutions. Many worked application examples are included to aid in practical understanding of concepts.

Written by two pioneering authors in the field, Sensorless Control of Permanent Magnet Synchronous Machine Drives covers sample topics such as:

Permanent magnet brushless AC and DC drives Single three-phase, dual three-phase, and open winding machines Modern control theory based sensorless methods, covering model reference adaptive system, sliding mode observer, extended Kalman filter, and model predictive control Flux-linkage and back-EMF based methods for non-salient machines, and active flux-linkage and extended back-EMF methods for salient machines Pulsating and rotating high frequency sinusoidal and square wave signal injection methods with current or voltage response, at different reference frames, and selection of amplitude and frequency for injection signal Sensorless control techniques based on detecting third harmonic or zero-crossings of back-EMF waveforms Parasitic effects in fundamental and high frequency models, impacts on position estimation, and compensation schemes, covering cross-coupling magnetic saturation, load effect, machine saliency and multiple saliencies, inverter non-linearities, voltage and current harmonics, parameter asymmetries, and parameter mismatches Techniques for rotor initial position estimation, magnetic polarity detection, and transition between low and high speeds

Describing basic principles, examples, challenges, and practical solutions, Sensorless Control of Permanent Magnet Synchronous Machine Drives is a highly comprehensive resource on the subject for professionals working on electrical machines and drives, particularly permanent magnet machines, and researchers working on electric vehicles, wind power generators, household appliances, and industrial automation.

Comprehensive reference delivering basic principles and state-of-the-art parameter estimation techniques for permanent magnet synchronous machines (PMSMs) Parameter Estimation of Permanent Magnet Synchronous Machines reviews estimation techniques of the parameters of PMSMs, introducing basic models and techniques, as well as issues and solutions in parameter estimation challenges, including rank deficiency, inverter nonlinearity, and magnetic saturation. This book is supported by theories, experiments, and simulation examples for each technique covered. Topics explored in this book include: Electrical and mechanical parameter estimation techniques, including those based on current/voltage injection and position offset injection, under constant or variable speed and load for sensored or sensorless controlled PMSMs, accounting for magnetic saturation, cross-coupling, inverter nonlinearity, temperature effects, and moreRecursive least squares, the Kalman filter, model reference adaptive systems, Adaline neural networks, gradient-based methods, particle swarm optimization, and genetic algorithmsApplications of parameter estimation techniques for improvement of control performance, sensorless control, thermal condition monitoring, and fault diagnosisThis book is an essential reference for professionals working on the control and design of electrical machines, researchers studying electric vehicles, wind power generators, aerospace, industrial drives, automation systems, robots, and domestic appliances, as well as advanced undergraduate and graduate students in related programs of study.

Comprehensive reference delivering basic principles and state-of-the-art parameter estimation techniques for permanent magnet synchronous machines (PMSMs)

Parameter Estimation of Permanent Magnet Synchronous Machines reviews estimation techniques of the parameters of PMSMs, introducing basic models and techniques, as well as issues and solutions in parameter estimation challenges, including rank deficiency, inverter nonlinearity, and magnetic saturation. This book is supported by theories, experiments, and simulation examples for each technique covered.

Topics explored in this book include:

Electrical and mechanical parameter estimation techniques, including those based on current/voltage injection and position offset injection, under constant or variable speed and load for sensored or sensorless controlled PMSMs, accounting for magnetic saturation, cross-coupling, inverter nonlinearity, temperature effects, and moreRecursive least squares, the Kalman filter, model reference adaptive systems, Adaline neural networks, gradient-based methods, particle swarm optimization, and genetic algorithmsApplications of parameter estimation techniques for improvement of control performance, sensorless control, thermal condition monitoring, and fault diagnosis

This book is an essential reference for professionals working on the control and design of electrical machines, researchers studying electric vehicles, wind power generators, aerospace, industrial drives, automation systems, robots, and domestic appliances, as well as advanced undergraduate and graduate students in related programs of study.

Comprehensive reference delivering basic principles and state-of-the-art parameter estimation techniques for permanent magnet synchronous machines (PMSMs)

Parameter Estimation of Permanent Magnet Synchronous Machines reviews estimation techniques of the parameters of PMSMs, introducing basic models and techniques, as well as issues and solutions in parameter estimation challenges, including rank deficiency, inverter nonlinearity, and magnetic saturation. This book is supported by theories, experiments, and simulation examples for each technique covered.

Topics explored in this book include:

Electrical and mechanical parameter estimation techniques, including those based on current/voltage injection and position offset injection, under constant or variable speed and load for sensored or sensorless controlled PMSMs, accounting for magnetic saturation, cross-coupling, inverter nonlinearity, temperature effects, and more Recursive least squares, the Kalman filter, model reference adaptive systems, Adaline neural networks, gradient-based methods, particle swarm optimization, and genetic algorithms Applications of parameter estimation techniques for improvement of control performance, sensorless control, thermal condition monitoring, and fault diagnosis

Parameter Estimation of Permanent Magnet Synchronous Machines, is an essential reference for professionals working on the control and design of electrical machines, researchers studying electric vehicles, wind power generators, aerospace, industrial drives, automation systems, robots, and domestic appliances, as well as advanced undergraduate and graduate students in related programs of study.

The electrification of the economy entails the development and optimization of efficient electrical machines. Permanent magnet machines use permanent magnets, rather than windings, for field excitation. They are more efficient than other electrical machine technologies for high-efficiency applications. Multiphase machines, as compared to 3-phase machines, have advantages including lower torque pulsation, higher power density, and better fault tolerance.This book offers concise and systematic coverage of multiphase permanent magnet machines and control techniques. It gives an overview of multiphase machines and control techniques in the context of various electrical machine technologies and presents the advantages of multiphase electrical machines. Applications are covered, including wind turbine generators, electric vehicles, electric ships, and aircraft and train propulsion. Machine topologies, modelling, design, control, pulse-width modulation, fault-tolerance, and reduction of current harmonics and torque ripples are considered.Multiphase Permanent Magnet Synchronous Machines and Drives: Principles, design, and control is written for industrial engineers and researchers, including PhD and post-doctoral research students working on electrical machines and drives, as well as for researchers working on electric vehicles, wind power generators, aerospace, electric ships and trains. Following a general introduction, chapters cover winding configurations, multiphase and dual-three-phase permanent magnet synchronous machines (PMSMs), modelling, design, modulation strategies, field-oriented control, direct torque control, model reference control, sensorless control, and also fault tolerant control for multiphase PMSMs. The logical progression from fundamental concepts to state-of-the-art research outcomes helps readers understand and use multiphase electrical machines.

This book investigates the utilization of harmonics in the permanent magnet (PM) or rotor shape to improve the torque density of PM brushless AC machines including three-phase inner rotor and outer rotor machines, five-phase machines, dual three-phase machines, linear machines, by means of analytical, finite element analyses, and as well as experimental validation. The torque density can be improved while the torque ripple remains low in PM shaping utilizing the 3rd harmonic. In this book, the analytical expression of output torque is derived for PM machines with rotor shape using the 3rd harmonic, and then the optimal 3rd harmonic for maximizing torque is analytically obtained. The book compares the PM shape in surface-mounted PM (SPM) machines and the rotor lamination shape in interior PM (IPM) machines utilizing the 3rd harmonic, and it becomes clear that their shaping methods and amount of torque improvement are different. In a five-phase PM machine, the 3rd harmonic can be utilized in both the current waveform and PM shapes to further improve the output torque. For the dual three-phase SPM machines without deteriorating the torque more than 30% when the optimal 3rd harmonic into both the current and PM shape are injected.The harmonics in airgap flux density have significant influence on the cogging torque, stator iron flux distribution, and radial force between the rotor and stator. These effects has been investigated as well in this book.

This book investigates the utilization of harmonics in the permanent magnet (PM) or rotor shape to improve the torque density of PM brushless AC machines including three-phase inner rotor and outer rotor machines, five-phase machines, dual three-phase machines, linear machines, by means of analytical, finite element analyses, and as well as experimental validation. The torque density can be improved while the torque ripple remains low in PM shaping utilizing the 3rd harmonic. In this book, the analytical expression of output torque is derived for PM machines with rotor shape using the 3rd harmonic, and then the optimal 3rd harmonic for maximizing torque is analytically obtained. The book compares the PM shape in surface-mounted PM (SPM) machines and the rotor lamination shape in interior PM (IPM) machines utilizing the 3rd harmonic, and it becomes clear that their shaping methods and amount of torque improvement are different. In a five-phase PM machine, the 3rd harmonic can be utilized in both the current waveform and PM shapes to further improve the output torque. For the dual three-phase SPM machines without deteriorating the torque more than 30% when the optimal 3rd harmonic into both the current and PM shape are injected.The harmonics in airgap flux density have significant influence on the cogging torque, stator iron flux distribution, and radial force between the rotor and stator. These effects has been investigated as well in this book.