Electromagnetics for Electrical Machines  book cover
1st Edition

Electromagnetics for Electrical Machines

ISBN 9781498709132
Published March 6, 2015 by CRC Press
439 Pages - 52 B/W Illustrations

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Book Description

Electromagnetics for Electrical Machines offers a comprehensive yet accessible treatment of the linear theory of electromagnetics and its application to the design of electrical machines. Leveraging valuable classroom insight gained by the authors during their impressive and ongoing teaching careers, this text emphasizes concepts rather than numerical methods, providing presentation/project problems at the end of each chapter to enhance subject knowledge.

Highlighting the essence of electromagnetic field (EMF) theory and its correlation with electrical machines, this book:

  • Reviews Maxwell’s equations and scalar and vector potentials
  • Describes the special cases leading to the Laplace, Poisson’s, eddy current, and wave equations
  • Explores the utility of the uniqueness, generalized Poynting, Helmholtz, and approximation theorems
  • Discusses the Schwarz–Christoffel transformation, as well as the determination of airgap permeance
  • Addresses the skin effects in circular conductors and eddy currents in solid and laminated iron cores
  • Contains examples relating to the slot leakage inductance of rotating electrical machines, transformer leakage inductance, and theory of hysteresis machines
  • Presents analyses of EMFs in laminated-rotor induction machines, three-dimensional field analyses for three-phase solid rotor induction machines, and more

Electromagnetics for Electrical Machines makes an ideal text for postgraduate-level students of electrical engineering, as well as of physics and electronics and communication engineering. It is also a useful reference for research scholars concerned with problems involving electromagnetics.

Table of Contents






Field Approach

Domain of Machines

Review of Field Theory

Field Theorems

Uniqueness Theorem

Poynting Theorem

Approximation Theorem

Problem of Slotting

Eddy Current Phenomena

Poly-Phase Induction Machines

Laminated Iron Cores

Un-Laminated Iron Cores

Simulation of Armature Winding

Case Studies

Numerical Techniques

Finite Element Method

Analytical Techniques


Review of Field Equations


Maxwell’s Equations in Integral Form

Maxwell’s Equations in Point Form

General Equations for One Type of Field

Maxwell’s Equations for Fields in Moving Media

Scalar Electric and Magnetic Potentials

Vector Magnetic Potential

Periodic Fields, Field Equations in Phasor Form

Retarded Potentials

Continuity Equation and Relaxation Time

A Rear Window View


Theorems, Revisited


Uniqueness Theorem

Uniqueness Theorem for Laplace and Poisson Equations

Uniqueness Theorem for Vector Magnetic Potentials

Uniqueness Theorem for Maxwell’s Equations

Helmholtz Theorem

Generalised Poynting Theorem

Components of Power Flow

Components of Force

Approximation Theorems

Approximation Theorem for Laplacian Field

Approximation Theorem for Vector Magnetic Potential

Approximation Theorem for Eddy Current Equation


Laplacian Fields


Potential Distribution for Rectangular Double-Slotting

Tooth-Opposite-Tooth Orientation

Tooth-Opposite-Slot Orientation

Arbitrary Orientation of Tooth and Slot

Air-Gap Permeance

Modelling for Aperiodical Field Distributions

Tooth-Opposite-Tooth Orientation

Tooth-Opposite-Slot Orientation

Arbitrary Orientation of Two Teeth

Fringing Flux for Tooth-Opposite-Tooth Orientation with Small Air Gap

Schwarz–Christoffel Transformation

Air-Gap Field of a Conductor Deep Inside an Open Slot

Schwarz–Christoffel Transformation (z-Plane to w-Plane)

Magnetic Field near Armature Winding Overhang

Surface Current Density

Magnetic Field Intensity


Eddy Currents in Magnetic Cores


Eddy Current Machines (Solid Rotor Induction Machines)

Two-Dimensional Model

Eddy Currents in Large Plates Due to Alternating Excitation Current

Single-Phase Excitation

Poly-Phase Excitation

Eddy Currents in Cores with Rectangular Cross-Sections

Eddy Currents in Cores with Triangular Cross-Sections

Eddy Currents in Cores with Regular Polygonal Cross-Sections

Cores with Triangular Cross-Sections

Cores with Hexagonal Cross-Sections

Cores with Octagonal Cross-Sections

Eddy Currents in Circular Cores

Distribution of Current Density in Circular Conductors

Eddy Currents in Laminated Rectangular Cores


Laminated-Rotor Polyphase Induction Machines


Two-Dimensional Fields in Anisotropic Media

Cage or Wound Rotor Induction Machines

Rotor Parameters

Induction Machines with Skewed Rotor Slots

Air-Gap Field

Fields in the Anisotropic Rotor Region

Determination of Arbitrary Constants


Un-Laminated Rotor Polyphase Induction Machines


Tooth-Ripple Harmonics in Solid-Rotor Induction Machines

Physical Description

Field Distribution in Stator Slots

Field Distribution in the Air Gap

Field Distribution in the Solid Rotor

Machine Performances

Three-Dimensional Fields in Solid- Rotor Induction Machines

Idealised Model

Field Distributions

Effects of Finite Machine Length

Effect of Different Rotor and Stator Lengths

Performance Parameters


Case Studies


Slot Leakage Inductance for Conductors in Open Slots

Physical Configuration

Current Density Distribution

Vector Magnetic Potential

Flux Density


Leakage Inductance of Transformers

Physical Configuration

Current Density Distribution

Vector Magnetic Potential

Magnetic Flux Density

Arbitrary Constants

Leakage Inductance

Field Theory of Hysteresis Machines

Simplifying Assumptions

Field Distributions

Induction Machine Action

Hysteresis Machine Action

Impact of Different Parameters

Single-Phase Induction Motors with Composite Poles

Simplifying Assumptions

Idealised Machine Structure

Field Distribution

Transient Fields in Plates Due to Type 2 Impact Excitations

Current Impact Excitation

Voltage Impact Excitation


Numerical Computation


Numerical Analysis

Computational Errors

Numerical Stability

Domain of Numerical Analysis

Values of Functions

Equations and Systems of Equations

Eigen-Value or Singular Value Problems

Optimisation Problem

Differential Equations

Numerical Integration


Types of Equations

Relations without Summation or Integration

Relations Involving Simple Summations

Summations Leading to Simultaneous Linear Algebraic Equations

Further Reading


Hilbert Transform

Evaluation of Integrals Involved in Equations 4.52 and 4.54

Evaluation of Integrals Involved in Equations 4.61 through 4.63

Evaluation of Integrals Involved in Equations 4.76a, 4.82b and 4.83b

Evaluation of Arbitrary Constants Involved in Section 5.9

Current Sheet Simulation of Stator Winding

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Saurabh Kumar Mukerji obtained his B.Sc from Aligarh Muslim University (AMU), India, and M.Tech and Ph.D from the Indian Institute of Technology Bombay, Mumbai. He has more than 50 years of teaching experience at Madhav Engineering College, Gwalior, India; AMU; SRMS College of Engineering and Technology, Bareilly, India; Multimedia University, Melaka, Malaysia; and Alfatha University, Misurata, Libya. Currently, he is a senior guest professor at Mangalayatan University, Aligarh, India. He has published more than 40 research papers in various journals and conference proceedings, as well as served on multiple journal review boards and as executive editor with Thomson George Publishing House, Malaysia.

Ahmad Shahid Khan has more than 42 years of teaching, research, and administrative experience. He obtained his B.Sc, M.Sc, and Ph.D from Aligarh Muslim University (AMU), India. He is currently a visiting professor at Mewat Engineering College (Wakf) Palla, Nuh, India. Previously, he served at AMU as professor and chairman of the Department of Electronics Engineering, registrar, and estate officer (gazetted). He also served as director of the International Institute of Management and Technology, Meerut, India; director of the Vivekananda College of Technology and Management, Aligarh, India; director of the Jauhar College of Engineering and Technology, Rampur, India; and professor at the Krishna Institute of Engineering and Technology and the Institute of Management Studies, both in Ghaziabad, India. Widely published, he is a recipient of the Pandit Madan Mohan Malviya Memorial Gold Medal.

Yatendra Pal Singh has more than 7 years of teaching experience. He obtained his graduate, postgraduate, and Ph.D degrees from Aligarh Muslim University (AMU), India. He is currently working as an assistant professor in the Department of Applied Physics at the Institute of Engineering and Technology, Mangalayatan University, Aligarh, India. He has published more than 25 papers in international conference proceedings and peer-reviewed journals, including the Journal of Geophysical Research, Astronomy & Astrophysics, Solar Physics, Journal of Atmospheric and Solar-Terrestrial Physics, and Planetary and Space Science. Dr. Singh is also a reviewer of research papers for Progress in Electromagnetic Research and Astrophysics and Space Science.


"… unravels intricacies of the subject in a simple and systematic manner. … one of few books which cover a difficult subject through inquisition and using programmed concept for learning. The authors have spent considerable time in formulating the structure of the book and its contents. I think they have been successful in their attempt. There have been several books on electromagnetic fields, each one having its own flavor. However, the present book is a different attempt to teach the concept of electromagnetic field theory (EMFT), and its application to the theory and design of electrical machines. The contributions of the authors of this book in various research and scientific areas are outstanding. They are academicians who have devoted themselves to the task of educating young minds and inculcating scientific temper amongst them. I must heartily congratulate the authors for the magnificent job they have done."
— Brig. (Dr.) Surjit Pabla, Vice Chancellor, Mangalayatan University, Aligarh, India

"The authors of this book set out to achieve the goal of presenting electromagnetics for electrical machines in a simple and systematic manner. I think they achieve that goal. They reduce Maxwell’s equations to Laplace’s equation, Poisson’s equation, wave equation, and eddy current equation and apply them to electrical machines."
— Matthew Sadiku, Prairie View A&M University

"I particularly value the approach taken of developing accurate theoretical electromagnetic models for several electrical machine structures. Traditional approaches of using lumped element models for machine parts, and then trying to modify the resulting equivalent network by taking into account the effect of these elements having non-zero physical size in a piece-meal fashion do not develop the user’s basic comprehensive insight into all aspects of the electromagnetic fields which can have some effect on machine behavior."
— Philip H. Alexander, Electrical and Computer Engineering, University of Windsor