Natural Variable Modeling and Performance of Interior Permanent Magnet ... Aliyu MEngr Project...

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Natural Variable Modeling and Performance of Interior Permanent Magnet Motor with Concentrated and Distributed Windings

By

Aliyu, Nasiru

PG/M.ENG/12/62492

DEPARTMENT OF ELECTRICAL ENGINEERING

FACULTY OF ENGINEERING

UNIVERSITY OF NIGERIA, NSUKKA

NOV, 2014

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NATURAL VARIABLE MODELING AND PERFORMANCE OF INTERIOR PERMANENT MAGNET MOTOR WITH

CONCENTRATED AND DISTRIBUTED WINDINGS

A PROJECT REPORT SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE AWARD OF MASTERS OF

ENGINEERING DEGREE (M.ENG) IN ELECTRICAL ENGINEERING

BY

ALIYU, NASIRU

PG/M.ENG/12/62492

NOVEMBER, 2014

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BY

ALIYU, NASIRU

PG/M.ENG/12/62492

NOV, 2014

AUTHOR: ……………………… ENGR. NASIRU ALIYU SUPERVISOR: ………………………. ENGR. PROF. E. S. OBE EXTERNAL EXAMINER: ………………………. ENGR. PROF. S. N. NDUBISI HEAD OF DEPARTMENT: ………………………. ENGR. PROF. E. C. EJIOGU

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TITLE PAGE



NOVEMBER, 2014

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CERTIFICATION

Engr. Nasiru Aliyu, a postgraduate student in the Department of Electrical Engineering

with Registration Number, PG/M.ENG/12/62492, has satisfactorily completed the

requirements for the course work and project report for the Degree of Masters of

Engineering in the Department of Electrical Engineering, University of Nigeria Nsukka.

The work contained in this thesis is original and has not been submitted in part or full for

any other diploma or degree of this or any other university to the best of my knowledge.

…………………………… ……………….……………

ENGR. PROF. E. S. OBE ENGR. PROF. E. C. EJIOGU

Supervisor Head of Department

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DEDICATION

This work is dedicated to the unprecedented support of my parents Sheikh Alhaji Aliyu

Babando and Hajiya Aishatu Garba Muri (Asabe) who have been very supportive to me

to fulfill my academic goals.

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ACKNOWLEDGEMENT

I hereby express my sincere gratitude to my supervisor, Engr. Prof. E. S. Obe for giving

me the privilege to benefit from his great intellectual resources, the time devoted to this

work, the material made available and advice he always dished out to me, I appreciate all.

I also use the opportunity to thank the Head of Department, Electrical Engineering. Engr.

Prof. E. C. Ejiogu for his support and pioneering the affairs of this great department well

and Engr. Prof. L. U. Anih for his moral support and encouragement.

My appreciation also goes to Engr. Prof. M. U. Agu, former Head of Department, Engr.

Dr. B. O. Anyaka Engr. Dr. C. I. Ode, and Engr. B. A. Ugochukwu for their support and

encouragement.

Naturally, I thank my family for bringing so much happiness into my life and my loving

wife Rashida and daughter Gumaisa’u for there understanding during this period of my

programme, and my brother Dr. Abubakar Aliyu Babando for downloading some

materials for this project report from Kwazulu Natal University South Africa.

Finally, I wish to appreciate my colleagues for assisting me in one way or another.

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ABSTRACT

Interior Permanent Magnet (IPM) motor is widely used for many industrial applications

and has relatively high torque ripple generated by reluctance torque. Since the

configuration of the stator has great influence on reluctance torque, different stator

configuration is necessary to improve the torque performance of IPM motor. Natural

variable modeling and performance comparison of Interior Permanent Magnet Motor

with Concentrated winding (CW), Short pitched and Full pitched distributed winding

(DW) is presented in this project report. Three phase Interior Permanent Magnet Motor

with identical rotor dimensions, air gap length, series turn number, stator outer radius,

and axial length was studied with different stator winding configuration. Basic

parameters and machine performance, such as inductances, copper losses, power density,

efficiency at high and low speed, torque ripple, rotor speed with load torque, phase

currents, electromagnetic torque, controllability and demagnetization tolerance are

compared. As a means of supplementing analysis of the IPM motor, winding function

theory (WFT) is used to analyze the motor. Winding function theory has enjoyed success

with induction, synchronous, and even switched reluctance machines in the past. It is

shown that this method is capable of analyzing IPM motor with different stator

configuration and the simulations were carried out by using Embedded MATLAB

function. It was observed that, the concentrated winding IPM motor has a lower copper

loss of 0.3 kw and 3.7 kw at low and high speed respectively and 133 Nm high peak

torque developed, pull out power of 58 kw, torque ripple of 96 Nm, average torque of

142 Nm, demagnetization tolerance of 60%, amplitude of the fundamental winding is

26.45 and efficiency of 89. the short pitched distributed winding IPM motor has a lower

copper loss of 0.35 kw and 3.6 kw at low and high speed respectively and 116 Nm high

peak torque developed, pull out power of 57 kw, torque ripple of 71 Nm, average torque

of 185 Nm, demagnetization tolerance of 78%, amplitude of the fundamental winding is

27.53 and efficiency of 87. As for full pitched distributed winding IPM motor has a lower

copper loss of 0.35 kw and 3.6 kw at low and high speed respectively and 116 Nm high

peak torque developed, pull out power of 56 kw, torque ripple of 71 Nm, average torque

of 185 Nm, demagnetization tolerance of 78%, amplitude of the fundamental winding is

29.3 and efficiency of 88.

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TABLE OF CONTENTS

TITLE PAGE ……………………………………………………………………………..i

CERTIFICATION ………………………………………………………………………..ii

DEDICATION …………………………………………………………………………...iii

ACKNOWLEDGEMENT …………………….…………………………………………iv

ABSTRACT …………………………………………………………….………………..v

TABLE OF CONTENTS ……………………………………………………..………..vii

LIST OF FIGURES & DIAGRAMS ……………………………………………………x

LIST OF TABLES …………………………………………………………….……….viii

CHAPTER ONE

1.0 Introduction………………….……………………………………………….1

1.1 Overview ………….…………………………………………………………1

1.2 Research Objectives …………………………………………………………6

1.3 Thesis Outline ………………………………………………………………..6

1.4 Study limitation ……………………………………………………………...7

CHAPTER TWO

2.0 Literature Review …. ………………………………………………………..8

2.1 Introduction ………………………………………………………………….8

2.2 Permanent Magnet Materials ………………………………………………...8

2.3 IPM Machine Technology ………………………………………………...... 9

2.4 Winding Function Theory ………………………………………….…….…15

2.5 Why Winding Function Theory ………………………………………… ..17

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CHAPTER THREE

3.0 Analysis of IPM Motor with Winding Function Theory..………………….18

3.1 Introduction ………………………………………………………………..18

3.2 Winding Function Theory and its Modifications …………………….…....18

3.2.1 Basic Winding Function Theory …………………………………18

3.2.2 WFT for machines with salient air gaps …………………………22

3.2.3 WFT Applied to magnetic devices ………………………………28

3.2.4 Verification of a single phase per rotor ………………………….30

3.2.5 Matlab Program for Solving Machine Equations ………………..33

3.2.6 Torque calculated from inductance ………………………………39

3.3 Clock diagram of IPM motor ………………………………………………41

3.4 Total Harmonic Distortion (THD)………………………………………….41

3.5 Winding factor (kw)……..………………….………………………….……42

3.6 Slot-fill factor ………………………………………………………….…...45

3.7 The Voltage Equations ……………………………….…………………….45

3.8 Solution of Equation (3.52) ……………………………………………….48

3.9 Torque Ripple ………………………………………………………………49

3.10 Losses in IPM motor ………………………………………………………49

3.10.1 Core Loss ……………………………………………………….50

3.10.2 Magnet Loss ………………………………………………….....50

3.10.3 Stator Winding Loss …………………………………………….51

3.10.4 Mechanical Losses ………………………………………………51

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CHAPTER FOUR

4.0 Dynamic Simulation in MATLAB Simulink ………………………………52

4.1 Simulation Tools …………………………………………………………...52

4.2 Simulink Simulation of IPM with Short pitched, Full pitched & Concentration

Winding using Embedded MATLAB Function Blocks …………………...52

4.3 Simulation Results …………………………………………………………52

4.4 Discussions ………………………………………………………………...66

CHAPTER FIVE

5.0 Conclusion and Recommendation …………………………………………69

5.1 References …………………………………………………………………70

Appendix 1……………………………………………………………………………77

Appendix 2……………………………………………………………………………78

Appendix 3……………………………………………………………………………80

Appendix 4……………………………………………………………………………82

Appendix 5……………………………………………………………………………83

Appendix 6 …………………………………………………………………………...84

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LIST OF FIGURES AND DIAGRAMS

Figure 1.1: Classification of AC machine types ………………………………………….1

Figure 1.2: Various IPM rotor geometries ………………………………………………..3

Figure 1.3: Various stator winding layouts ……………………………………………….5

Figure 2.1: Flux Density vs Magnetizing Field of Permanent Magnetic Materials …........9

Figure 2.2: Rotor structures of interior IPM type………………………………………..11

Figure 3.1: An idealized machine with conductors in the air gap……………………….19

Figure 3.2: An idealized machine with multiple coils in the air gap…………………….21

Figure 3.3: An idealized machine with a salient rotor and conductors in the air gap……22

Figure 3.4: Fundamental MMF Diagram for Short pitched phase A ………………...….24

Figure 3.5: Fundamental MMF Diagram for Full-Pitched phase A ………………….…24

Figure 3.6: Fundamental MMF Diagram for Concentrated phase A ……………………25

Figure 3.7: Fundamental MMF Diagram for Short pitched Distributed Winding ………25

Figure 3.8: Fundamental MMF Diagram for Full-Pitched Distributed Winding ……….26

Figure 3.9: Fundamental MMF Diagram for Concentrated Winding …………………..26

Figure 3.10: Four Poles magnet flux density ……………………………………………27

Figure 3.11: Airgap ……………………………………………………………………..27

Figure 3.12: Model of a PM which produces an equivalent magnetization vector ……..29

Figure 3.13: IPM with alternating vectors form the basis for a single turns function over

the circumference of the rotor …………………………………………………………..30

Figure 3.14: The turns function modeled with the Fourier series ………………………30

Figure 3.15: An ideal four pole machine ………………………………………………..31

Figure 3.16a: Turns and winding functions for stator phases ……………………….…..32

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Figure 3.16b: WF, from top figure to bottom: winding arrangements in the slots turns

function of winding A, WF of windings A, B and C……………………………………33

Figure 3.17: Self inductance of the stator winding for Short pitched ………………….34

Figure 3.18: Self inductance of the stator winding for Full-Pitched …………………...34

Figure 3.19: Self inductance of the stator winding for Concentrated …………………..34

Figure 3.20: Mutual inductance between stator winding for Short pitched …………….35

Figure 3.21: Mutual inductance between stator winding for Full-pitched ………………35

Figure 3.22: Mutual inductance between stator winding for Concentrated ……………..35

Figure 3.23a: Flowchart for calculated inductances using MWFT in Matlab/Simulink ..36

Figure 3.23b: Flowchart of the iterative procedure for solving machine equations …….37

Figure 3.24: Inverse gap function used for ideal machines in inductance calculations …38

Figure 3.25: Harmonic Order for phase A ………………………………………………38

Figure 3.26: Clock Diagram for Short pitched Distributed Stator winding..……..……..42

Figure 3.27: Clock Diagram for Full pitched Distributed Stator Winding ………….…..43

Figure 3.28: Clock Diagram for Concentrated Stator Winding ………………………....44

Figure 4.1: Stator phase A’s currents …………………………………………………...55

Figure 4.2: d-axis rotor currents …………………………………………………………55

Figure 4.3: q-axis currents ………………………………………………………………56

Figure 4.4: Electromagnetic torques ……………………………………………………56

Figure 4.5: Electromagnetic torques at synchronization ………………………………..57

Figure 4.6: Electromagnetic torques when the load was applied …………………….....57

Figure 4.7: Short pitched Rotor Speeds and its response to a load torque ……………..58

Figure 4.8: Full pitched Speeds during starting and response to a load torque ………..58

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Figure 4.9: Concentrated Speeds during starting and its response to a load torque …..58

Figure 4.10: Rotor Speeds during synchronization for Short pitched …………………59

Figure 4.11: Rotor Speeds during synchronization for full pitched. …………………..59

Figure 4.12: Rotor Speeds during synchronization for Concentrated …………………59

Figure 4.13: Rotor Speeds response to a load torque for Short pitched ……………….60

Figure 4.14: Rotor Speeds response to a load torque for Full-pitched..………….…….60

Figure 4.15: Rotor Speeds response to a load torque for Concentrated ………………..60

Figure 4.16: Rotor Speeds with the application of ramp for Short pitched …………….61

Figure 4.17: Rotor Speeds with the application of ramp for Full-pitched ……………...61

Figure 4.18: Rotor Speeds with the application of ramp for Concentrated ……………..61

Figure 4.19: Chorded Torque-Speed characteristic ……………………………………..62

Figure 4.20: Non-Chorded Torque-Speed characteristic ………………………………..62

Figure 4.21: Concentrated Torque-Speed characteristic ………………………………..62

Figure 4.22: Output power against stator current for Short pitched ……………………63

Figure 4.23: Output power against stator current for Full-pitched ……………………..63

Figure 4.24: Output power against stator current for Concentrated …………………….63

Figure 4.25: Stator losses against stator current for Short pitched …………………..…64

Figure 4.26: Stator losses against stator current for Full-pitched ……………….………64

Figure 4.27: Stator losses against stator current for Concentrated ……………….…….64

Figure 4.28: Efficiency against stator current for Short pitched ……………………….65

Figure 4.29: Efficiency against stator current for Full-pitched ………………………...65

Figure 4.30: Efficiency against stator current for Concentrated ………………………..65

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LIST OF TABLES

Table 2.1: Advantages and Disadvantages of different magnet type ………………..…10

Table 4.1: IPM with Short pitched, Full-pitched and Concentrated winding ………..…53

Table 4.2: Summary of the Performance comparison of the each IPM Motor …………54

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CHAPTER ONE

1.0 Introduction

1.1 Overview

Over the years, the application of electric motors has replaced vast numbers of

mechanical rotating devices. From tiny motors used in wristwatches, to very large motors

used for ship propulsion and wind turbines. There are numerous types of electric motors

available for present-day applications, of which the AC types are most commonly used in

high performance applications due to its increased efficiency and excellent dynamic

performance [1]. The classifications of common types of AC motors are shown in Figure

1.1[2].

Figure 1.1: Classification of AC machine types

The Induction, Surface Permanent Magnet (SPM), Inset Permanent Magnet Machine, and

Interior Permanent Magnet (IPM) machine types have already been applied to present

day drive systems. Induction, SPM and inset PM machines usually have a lower power

rating compared to the IPM machine and are most commonly applied as an Integrated

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Motor Assist (IMA) system, where the main driver of the vehicle is the internal

combustion engine while the electric motor assists. On the other hand, the IPM machine

itself produces up to 73kW or more of power and can be driven in full electric mode,

producing zero emissions. [2]

This project report will focus on the IPM machine type, which is generally preferred due

to three main reasons: Firstly, the buried magnets make the rotor structurally stronger,

which make it more capable of withstanding higher speeds. Secondly, the additional

useful reluctance torque, resulting from the salient pole structure, thus giving the motor

greater field-weakening capabilities. Additionally, this saliency allows sensorless control,

properties which the SPM does not offer [3]. Lastly, the possibility of changing the

geometry of buried magnets in the rotor makes it possible to employ flux concentration,

and provides the possibility of saliency ratio optimisation [4].

With the availability of high energy permanent magnet materials and advanced power

electronics, the fields in which IPM machines can be applied to are rapidly broadening.

They include aerospace, nautical, automobile, rail transportation, medical, generation and

industrial process automation [5]. Common magnet geometries include single-piece/pole,

rectangular shaped magnet design (Figure 1.2a), segmented magnet design (Figure 1.2b),

v-shaped magnet design (Figure 1.2c), and the multi-barrier design (Figure 1.2d) [6].

Each of these designs has its advantages and disadvantages: The single-piece/pole

magnet design, for example, is the easiest to manufacture, but has larger magnet losses

compared to the other designs due to the larger magnet pole surface [7]. The segmented

magnet design has lower magnet losses and better field-weakening capability but requires

more magnet pieces. It also results in decreased magnet flux density due to the leakage

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flux in the iron bridges [8]. The v-shaped magnet design provides flux concentration but

also requires more magnet pieces compared to the single-piece/pole design.

(a) rectangular single-piece/pole magnets (b) segmented magnets

(c) v-shaped magnets (d) multi-barrier magnets

Figure 1.2: Various IPM rotor geometries

The multi-barrier magnet design creates a very high saliency ratio, but consequently

results in an increased amount of structural stress on the rotor steel [6]. In practice, there

is no single rotor that can satisfy all applications. The pros and cons of each design as

well as more specific magnet type and shape have to be altered to meet desired

specifications. As magnets are very brittle, there are also practical limits to the

manufacturability of the magnets.

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Before the 21st century, the majority of IPM machines were designed with distributed

stator windings (DW). The use of concentrated winding (CW) was not popular due to a

poor torque to magnetomotive force (MMF) ratio. However in the early 21st century,

Cros and Viarouge [9], Magnussen and Sadarangani [10] proved that by an appropriate

choice of slot and pole combination, the winding factor can be significantly increased,

thus increasing output torque. Additionally it was also shown that with appropriate slot

and pole combination, cogging torque can also be reduced.

Stator windings can either be single-layer or double-layer. The choice depends on the

desired machine performance characteristics. Single-layer CW creates high self-

inductance and low mutual-inductance which leads to better fault-tolerant capability. On

the other hand, double-layer CW has lower airgap MMF harmonic components, thereby

resulting in smaller torque ripples and lower magnet eddy current losses [11]. The

winding layouts for single-layer and double-layer DW are shown in (Figure1.3a) and

(Figure 1.3b), while the layouts for single-layer and double-layer CW are shown in

(Figure1.3c) and (Figure 1.3d) respectively [12].

Finally, the study is primarily concerned with the natural variable modeling and

performance comparison of Interior permanent magnet (IPM) motors with a short pitched

distributed winding, full-pitched distributed winding and concentrated winding. An

Interior permanent magnet (IPM) motor has many advantages such as high power

density, efficiency and wide speed operation. These merits make it particularly suitable

for automotive and other applications where space and energy savings are critical.

However, IPM motor has relatively high torque ripple generated by reluctance torque

which results in noise and vibration [13].

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(a) Single-layer distributed windings (b) Double-layer distributed windings

(c) Single-layer concentrated windings (d) Double-layer concentrated windings

Figure 1.3: Various stator winding layouts

Torque ripple in IPM motor is often a major concern in applications where speed and

position accuracy are great important. Since the component configuration such as a stator

has great impact on reluctance torque, different stator configuration is necessary to

improve the performance of IPM motor [14]. Most previous works to obtain optimal

design for torque ripple reduction have been restricted to size optimization in which

design parameters are known in priori and fixed throughout the optimization process

[15]. The size design variables include slot opening, depth of rotor yoke, angle of one

pole magnet, thickness of permanent magnet and so on.

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1.2 Research Objectives

The general objective of this project report is firstly to present a feasibility study on the

IPM motor with different stator configuration. Subsequently to carryout a natural variable

modeling and performance comparison on a three phase IPM motor with short pitched

distributed winding, full-pitched distributed winding and concentrated winding. Despite

the fact that the machines are now widely in use, there has been considerable interest in a

three phase Interior Permanent Magnet Motor. Finally, the study will help clarify the

advantages and disadvantages of implementing the different stator configuration in IPM

motor, as well as its prospects in industrial applications requiring high efficiency.

1.3. Thesis Outline

In order to conduct the stated project objectives, this project report is outlined as

following:

Chapter I covers overview and some backgrounds on interior permanent magnet motor.

In this chapter the main objectives and motivations of this project, thesis outline and

study limitation are introduced.

Chapter II, this chapter gives the literature reviews on Interior Permanent Magnet

machine technology, permanent magnet materials, winding function theory and why

winding function theory.

Chapter III gives the analysis of Interior Permanent Magnet Motor with winding function

theory and its modifications which include basic winding function theory, winding

function theory for machines with salient air gaps, winding function theory applied to

magnetic devices, verification of a single phase per rotor and Torque calculated from

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inductance. It also include the clock diagram of IPM motor, Total Harmonic Distortion

(THD), winding factor (kw), Slot-fill Factor, the Voltage Equations, Torque Ripple and

Losses in IPM motor which includes the core loss, magnet loss, stator winding loss and

mechanical losses

Chapter IV is a set performance, simulation and results.

Chapter V is a Conclusions and Recommendations.

1.4 Study Limitations

A major limitation encountered in this project report thesis occurred during the modeling

of the different stator configuration of the machines and only the first harmonics was

used since third harmonic would be eliminated if the motor is connected in star.

Eventually, certain assumptions deemed necessary.

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CHAPTER TWO

2.0 Literature Review

2.1 Introduction

Distributed Winding IPM machines have been widely used in high performance

industrial applications over decades. Concentrated Winding IPM machines on the other

hand have only more recently found their way into industrial markets. This section

reviews permanent magnet materials and well established work in IPM machine

technology as well as recent research in winding function theory for AC machines.

2.2 Permanent Magnet Materials

The properties of the permanent magnet material will affect directly the performance of

the motor and proper knowledge is required for the selection of the materials and for

understanding PM motors.

The earliest manufactured magnet materials were hardened steel. Magnets made from

steel were easily magnetized. However, they could hold very low energy and it was easy

to demagnetize. In recent years other magnet materials such as Aluminum Nickel and

Cobalt alloys (ALNICO), Strontium Ferrite or Barium Ferrite (Ferrite), Samarium Cobalt

(First generation rare earth magnet) (SmCo) and Neodymium Iron-Boron (Second

generation rare earth magnet) (NdFeB) have been developed and used for making

permanent magnets. The rare earth magnets are categorized into two classes: Samarium

Cobalt (SmCo) magnets and Neodymium Iron Boride (NdFeB) magnets. SmCo magnets

have higher flux density levels but they are very expensive. NdFeB magnets are the most

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common rare earth magnets used in motors these days. A flux density versus magnetizing

field for these magnets is illustrated in Figure 2.1 [16].

Figure 2.1 Flux Density versus Magnetizing Field of Permanent Magnetic Materials

NdFeB magnets are the preferred choice in present day applications due to its reasonable

cost, high coercivity and high remanent flux density. However, NdFeB magnets have

comparatively low operating temperatures. Table: 2.1 shows the advantages and

disadvantages of different magnet types [17].

2.3 IPM Machine Technology

A permanent magnet synchronous motor (PMSM) is a motor that uses permanent

magnets to produce the air gap magnetic field rather than using electromagnets. These

motors have significant advantages, attracting the interest of researchers and industry for

use in many applications.

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Table: 2.1

Advantages and disadvantages of different magnet types

Magnet type Advantages Disadvantages

Ferrite Least expensive magnet

material

High operating

temperature up to 300oC

Hard and brittle

Lowest remanent flux

density of up to 0.42T

Alnico High operating

temperature up to 520 ºC

Lowest temperature

coefficient (0.02%/ºC)

Extremely hard and

brittle

Can be easily

demagnetised

Samarium-cobalt High remanent flux


Extremely resistant to

corrosion

High resistance to

demagnetisation

High operating

temperature of up to

350ºC

Low temperature


High coercivity

Extremely hard and

brittle

Most expensive

magnetic material

Neodymiumiron-boron Highest remanent flux


High resistance to

demagnetisation

Least brittle

Lower cost compared to

SmCo

High coercivity

Low operating

temperature up to 200ºC

High temperature


Susceptible to corrosion

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The recent development of improved ferrites and rare earth cobalt magnet materials has

caused a renewed interest in permanent magnet machine design. These materials have

straight-line BH characteristics in the second quadrant so that demagnetization is of a

lesser concern than with the earlier Alnicos. Such machines have their permanent

magnets inserted below a rotor squirrel cage winding and are known as Interior

Permanent Magnet Synchronous Motors (as shown in Figure 2.2) which as in the case of

an induction motor lies in slots near the air gap. The squirrel cage currents provide

starting torque while the magnet torque pulls the rotor into synchronism so that under

steady state operation there are no rotor I2R losses. Interior Permanent Magnet Motors

have come to be replacement for high efficient induction machines in small power

applications of two to 25 horsepower [18]. By enhancing this motor parameter it was

suggested that improved performance can be obtained over a wider speed range. These

claims were contested in a latter publication by Richter and Neumann [19] in which it

was shown that for some IPM machines, the cross coupling reactance is saturation

dependent and therefore disappears at low flux high speed operating conditions.

Figure 2.2: Rotor structures of interior IPM type.

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Global research on the IPM machine dates back to the late 1970s and early 1980s when

the first few papers were published; there is still very significant research interest in this

area today. The popularity of the IPM machine is due to the embedded structure of its

magnets, which lowers the risk of demagnetisation, increases the mechanical robustness

of the rotor and provides additional reluctance torque. The small airgap design in most

IPM machines makes it excellent for flux weakening, as the negative armature reaction

can effectively reduce airgap flux. The IPM machine also gives the machine designer the

freedom to vary the magnet pole geometry, thereby broadening the machine’s area of

application.

Leading studies in IPM machine technology has included patents and several papers

setting the basis for research in this area. Steen [20] filed a patent on synchronous motors

with buried permanent magnets having several geometrical configurations. He stated that

the buried magnets produced additional direct-axis (d-axis) flux in aid of the flux

generated by the inductive copper bars during no-load operation. Honsinger [21]

illustrated a detailed mathematical representation of the IPM machine which included its

magnetic fields and parameters. Rahman et al. [22] presented the equivalent circuit model

to determine the d-axis and quadrature-axis (q-axis) reactance. Consoli and Renna [23]

illustrated a detailed representation of the IPM machine in the rotor reference frame, and

demonstrated an equivalent circuit model to determine iron losses. Chalmers et al. [24]

presented a study of the IPM machine through extensive experiments with frequency

variations.

Jahns et al. [25] first addressed the IPM machine’s characteristics when used as a high-

performance variable speed drive. Jahns [26] then performed a novel study on the flux

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weakening of the IPM machine, thereby successfully extending its constant power speed

range. Since then, the use of IPM machines has soared. Honda et al. [27] did a study on

the effects of various winding types and rotor configuration on the performance of the

IPM machine. The IPM machine’s characteristics were constantly compared to those of

other AC machines. Fratta et al. [28] compared the torque density ability of the IPM

machine with the induction machine, and highlighted that the IPM would have better

electromagnetic performance if mechanical issues were resolved.

A controllability comparison between the IPM and SPM machines under various

operating requirements of the current vector control scheme was done by Morimoto et al.

[29]. Zhu et al. [30] compared the iron loss between the IPM and SPM machines. They

indicated that the iron loss of the IPM machine would be lower under open-circuit

conditions but significantly higher in the field-weakening region compared to the SPM

machine, due to the increased harmonic content in the armature field. Kyung-Tae et al.

[31] compared the effects of rotor eccentricity on the IPM and SPM rotor, in which they

concluded that the IPM is more prone to the effects of rotor eccentricity. Jung Ho et al.

[32] studied the inductance variation of a hybrid synchronous reluctance/IPM motor and

found out that the addition of buried magnets increased the saliency ratio, thus increasing

output torque and power factor.

The end of the 20th century saw drastic improvements in computational resources and

techniques. This allowed machine designers to efficiently determine parameters and

perform optimisation strategies. Yamazaki [33] illustrated a method to calculate IPM

machine parameters, including rotor and stator iron losses. Efficiency optimisation by

geometric variation was carried out by Sim et al. [34]. Ki-Chan et al. [35] studied the

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effects on machine parameters and torque performance by varying the shape of rotor link

sections. They showed that small variations of the link sections could significantly

saliency ratio. Parsa and Lei [36] studied the effects of torque ripple and performance

characteristics when key machine parameters were varied. Kioumarsi et al. [37]

attempted to reduce torque ripple and by drilling additional holes in the rotor. Han et al.

[38] attempted to reduce torque ripple by varying the number of slots and number of rotor

barriers. They showed that multi-barrier rotors with an odd number of slots per pole pair

resulted in low torque ripple. Sanada et al. [39] experimented with several designs and

proved that the use of asymmetric flux barriers was beneficial in reducing torque ripple in

multi-barrier IPM machines. Fang at al. [40] showed that torque ripple can be reduced

with a double-layer rotor. Kim at al. [41] studied the effects of geometric variations of

magnets in the IPM machine to reduce torque ripple.

Computational methods also made the calculation of losses more accurate and realisable.

Loss minimisation was also made less costly and more effective. Kawase [42] analysed

Permanent magnet eddy current losses in the IPM machine with three-dimensional finite

element (FE) analysis, and showed the effectiveness of reducing eddy current losses by

axially dividing the magnets. Zivotic-Kukolj [43] proposed geometric variations to the

multi-barrier IPM machine to reduce iron losses. Ionel et al. [44] improved the accuracy

of modeling core losses by allowing hysteresis loss to vary with both flux density and

frequency, but leaving the eddy current and excess losses to vary only with flux density.

Wang et al. [45] studied the effects of temperature on the torque performance and

machine losses in an IPM machine. Seo et al. [46] studied iron loss on machines with

integral and fractional slot DW. They showed that with fractional-slot configuration, iron

30

loss in the stator is reduced slightly, but iron loss in the rotor is increased significantly,

especially at high speeds. Yamazaki and Abe [47] further investigated the effects of

magnet segmentation in IPM motors, and concluded that the axial length of each magnet

segment should not be more than twice the skin depth of the eddy currents produced by

the dominant harmonics. Han et al. [48] attempted to minimize eddy current loss in the

stator teeth of IPM rotors and highlighted that double-layer rotor magnets resulted in

lower losses compared to single-layer rotor magnets. Tseng and Wee [49] investigated

various methods to determine core loss in the IPM machine, in which they stated the

relationship between flux and core loss as well as appropriate core loss calculation

methods to use at different stages of the machine design to save resources. Stumberger et

al. [50] studied the iron losses under different stator configuration and stated that the

rotor iron losses is substantial, despite there being a very small portion of iron is present

above the magnets. Ma et al. [51] proposed a method to increase the accuracy of

calculating iron loss using rotational fields and flux density harmonics. Barcaro et al. [52]

also studied how the design of rotor flux barriers and the amount of PM material affected

the losses in an IPM machine.

2.4 Winding Function Theory

Winding function theory has been used for years on induction and synchronous machines

[53]. Little has been done however to apply winding function theory to machines with

permanent magnets, just two examples of which are found in [54] and [55]. Its usefulness

lies in the fact that it can take into account geometrical variations of the machines and be

used to simulate transient performance.

31

The basis for applying winding function theory to interior permanent magnet motor is to

treat the magnets as coils. A permanent magnet which is magnetized in a parallel manner

can be modeled as a coil wrapped around material with the same permeability as that of

the magnet. The coils, with sufficient current, can provide the same magnetomotive force

(MMF) as the magnet itself. The MMF imposed by the magnetic layout, along with the

gap function imposed by the stator pole pieces will be used to calculate the inductance

variation. These inductances are evaluated using winding function and other equations

within the theory. The changing inductance will then be used to calculate the torque of

the rotors.

Winding function theory is based on the basic geometry and winding layout of machine

[56]. The only information required in winding function approach is the winding layout

and machine geometry. By this approach, it is possible to analyze performance of any

faulty machine with any type of winding distribution and air gap distribution around

rotor, while taking into account all spatial and time harmonics. Hence this method has

found application in the analysis of asymmetrical and fault conditions in machines, Such

as broken rotor bars [57] and fault condition in stator windings [58]. The modified

winding function approach (MWFA) for asymmetrical air-gap in an IPM machine has

been proposed in [59]. It was later more developed for non-uniform air gap machines

[60]. This theory has been applied to analyze static, dynamic and mixed eccentricity in

induction and synchronous machines [61]. Some techniques were also developed to

include rotor bar skewing, slotting, saturation effect and inter-bar currents [62].

In the previous works, based on winding function theory, the analysis of IPM machines

performance under eccentricity conditions is carried out assuming uniformity down the

32

axial length of the machine. In the other hand, the rotor axis is considered to be parallel to

that of the stator.

2.5 Why Winding Function Theory?

The d-q model of an ac machine is based on the assumption that stator windings

are sinusoidally distributed and is used to represent healthy motors and motors

under rotor faults.

The d-q model reduces the number of equations required for simulation. However

it can't give any information about rotor bars and end rings currents, and require a

modification in model structure for each fault case.

The analysis of machines as a magnetic field problem needs large resources of

digital computers to solve for complicated equations.

Winding function method is based on basic geometry and windings layout of ac

machine.

Winding function method with coupled magnetic circuits approach is a suitable

model for analyzing machines including faults.

The advantages of this method is that it is possible to predict transient and steady-

state performance of any machine with any type of winding distribution and air-

gap length, while taking into account the effect of all spatial and time harmonics.

This means that all faults occurring in the stator windings, rotor turns and air-gap

eccentricity can be included in the model obtained using this theory.

33

CHAPTER THREE

3.0 Analysis of Interior Permanent Magnet Motor with Winding Function Theory

3.1 Introduction

Winding function theory (WFT) has been used primarily on machines without permanent

magnets since its early development. It has seen great success when applied to induction

machines [63], switched reluctance machines [64], and synchronous reluctance machines

[65]. One of the only examples of WFT applied to a permanent magnet machine is found

in [66]. However, the radial flux density component due to the magnets is used only to

analyze the back-electromotive force (EMF) of the brushless DC (BLDC) machine. The

study undertaken here is to apply WFT theory to interior permanent magnet motor with

different stator configuration.

3.2 Winding Function Theory and its Modifications

3.2.1 Basic winding function theory

The derivation of winding function theory begins with a perfectly cylindrical and

concentric machine with conductors in the air gap. Later in the analysis, salient air gaps

will be handled. Figure 3.1 shows the machine with a two-pole winding residing within

the air gap. By Ampere’s law in (3.1), the line integral is taken around the conductor in

the path 1-2-3-4-1.

Following the path 1-2-3-4-1 around the conductor in Figure 3.1, the total MMF is calculated

in (3.2). The resultant turns function, )(n is directly proportional to the MMF in the air gap.

The MMF drop in paths 2-3 and 4-1 can be neglected however.

34

Fig. 3.1. An idealized machine with conductors in the air gap.

dsJdlH (3.1)

This is due to the assumption of the use of linear iron with high relative permeability. With a

relative permeability much greater than air, i.e. 10,000 the MMF drop through the iron is then

neglected, leaving the two terms in (3.3). The magnetic field strength around the air gap,

)(H is thus a function of the turns function, in (3.4).

in )(41342312 (3.2)

s

r

r

s

r

rrs

r

rsr

gHHrrdrrH

gHHrrdrrH

)()()(),(

)0()0()()0,(

34

12

(3.3)

)0()()( HginH (3.4)

Using Gauss’ law in (3.5), the value for the magnetic field strength around the air gap can be

found. This assumes a fictitious cylinder encompassing only the rotor of the ideal machine.

35

2

00

2

00

1

0

0)(

)(0

dHlr

dzrdHdsB

(3.5)

One of the key assumptions of normal winding function theory follows from (3.5), in that the

value of the MMF taken around the circumference of the machine must have no average

component, shown in (3.6).

0)(2

034

d (3.6)

Through the process shown in (3.7), the value of )(H is found by using the turns function.

)()()(

)(21)()0(

)(21)0(

0)()0(2

0)0()(

0)(

2

0

2

0

2

0

2

00

2

00

nngiH

dnngiH

dngiH

dngiH

dHginl

dHl

r

r

(3.7)

From the end result of (3.7), it is apparent that the magnetic field strength around the air gap

is a function of the turns function, )(n minus its average value, which is the winding

function, )(N shown in brackets. The differential flux is found in (3.8). In order to calculate

the inductances among windings in the machine, Figure 3.2 is used to make sure that

orientation is accounted for.

36

diNgrl

BrlddABd )(0 (3.8)

Figure 3.2: An idealized machine with multiple coils in the air gap. Care is taken in (3.9) to distinguish between the values of flux which can be calculated

depending upon the orientation of the winding shown in Figure 3.2. The value of (3.9) could

be positive or negative depending upon which coil side of winding A1 is encountered first.

dNigrl A

A

AAAA )('1

1

11'11

0

(3.9)

The problem with accounting for different winding orientations can be handled by including

the turns function in the calculation of the flux in (3.10). Assuming that each winding

constitutes its own phase, the mutual flux linkage is shown in (3.11).

dNingrl

dNingrl

AAAAAAAA

A

A

)()()()(2

0

00111

'1

1

111'11

(3.10)

dNingrl

AAAAA )()(2

0

011212 (3.11)

37

Now that the flux linkage has been found, the mutual inductance of the windings easily

follows in (3.12). The derivation is also valid if the windings are the same, thus giving the

magnetizing inductance in (3.13) [67] [68].

dNngrl

iL AA

A

AAAA )()(

2

0

021

21

21 (3.12)

dNngrl

iL AA

A

AAAA )()(

2

0

011

11

11 (3.13)

3.2.2 Winding function theory for machines with salient air gaps

In basic winding function theory, the inverse gap function is assumed to be composed of

only even harmonics. Figure 3.3 shows the machine with a two-pole winding residing

within the air gap. By Ampere’s law, the line integral is taken around the conductor in the

path 1-2-3-4-1 in (3.14). The MMF drops, are equivalent to the turns function of the

winding, )(n multiplied by the current, i in the winding. As with regular WFT and the

assumption of linear iron with a high relative permeability, the MMF drops through the

back iron and rotor are negligible and can thus be ignored.

Figure 3.3: An idealized machine with a salient rotor and conductors in the air gap.

38

in )(41342312 (3.14)

Winding function theory is amended as done in [67] to include a salient air gap for the

geometries studied here. An inverse gap function will be used to account for the changing

gap thickness, in the same manner that the turns function accounts for the changing MMF

throughout the machine. In (3.15), it is assumed that the average value of the MMF over the

circumference of the machine is zero, when multiplied by an inverse gap function )(1 g :

0)()( 12

0

dg (3.15)

Following the assumptions associated with (3.16), the value for the MMF can be derived as

follows:

2

0

2

0

113412 )()()()()0( digndg (3.16)

In [67], it was assumed that the salient air gap was composed solely of even harmonics,

allowing for the simplification which resulted in regular WFT. However, in the case of the

permanent magnet machine, the salient air gaps will not be limited to even harmonics. The

salient air gap could be composed of first harmonics only. In [59] and [69] which led to the

derivation and use of modified winding function theory (MWFT). However, eccentricity is

not the only factor that necessitates the use of MWFT; the simple fact of using a salient air

gap that is not built from even harmonics necessitates MWFT as well. The derivation

continues with (3.17) to find the right MMF term in (3.16), assuming that the left MMF term

is zero. Figure 3.4 to 3.9 shows Fundamental MMF Diagram for phase A and for the three

phases. The term in brackets is the modified winding function, )(M . In (3.18) and (3.19),

the modified winding function is shown as a new average value which must be subtracted

from the turns function. Figure 3.10 to 3.11 shows the Four Poles magnet flux density and airgap.

39

0 50 100 150 200 250 300 350 400-30

-20

-10

0

10

20

30

Stator Circumferential angle, [deg]

MM

F pe

r uni

t cur

rent

, Am

pere

-turn

s

Short-Pitched phase A

Figure 3.4: Fundamental MMF Diagram for Short pitched phase A

0 50 100 150 200 250 300 350 400-30

-20

-10

0

10

20

30


MM

F pe

r uni

t cur

rent

, Am

pere

-turn

s

Full-Pitched phase A

Figure 3.5: Fundamental MMF Diagram for Full-Pitched phase A

40

0 50 100 150 200 250 300 350 400-30

-20

-10

0

10

20

30


MM

F pe

r uni

t cur

rent

, Am

pere

-turn

s

Concentrated phase A

Figure 3.6: Fundamental MMF Diagram for Concentrated phase A

0 50 100 150 200 250 300 350 400-30

-20

-10

0

10

20

30


MM

F pe

r uni

t cur

rent

, Am

pere

-turn

s

Fundamenral MMF Diagram for Short-Pitched Distributed Winding

phase Aphase Bphase C

Figure 3.7: Fundamental MMF Diagram for Short pitched Distributed Winding

41

0 50 100 150 200 250 300 350 400-30

-20

-10

0

10

20

30


MM

F pe

r uni

t cur

rent

, Am

pere

-turn

s

Fundamental MMF Diagram for Full-Pitched Distributed Winding


Figure 3.8: Fundamental MMF Diagram for Full-Pitched Distributed Winding

0 50 100 150 200 250 300 350 400-30

-20

-10

0

10

20

30


MM

F pe

r uni

t cur

rent

, Am

pere

-turn

s

Fundamenral MMF Diagram for Concentrated Winding


Figure 3.9: Fundamental MMF Diagram for Concentrated Winding

42

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

rotor position [rad]

[T]

Four Poles MMF Diagram

Figure 3.10: Four Poles magnet flux density

0 1 2 3 4 5 6 7-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

rotor position [rad]

Sta

tor t

ooth

leng

th

AIRGAP

Figure 3.11: Airgap

43

2

0

1134

3412

2

0

1112

2

0

1112

)()()(2

1)()(

)()()0(

)()()(2

1)0(

)()()()0(2

dgng

ni

in

digng

digng

(3.17)

2

0

11

)()()(2

1)( dgng

M (3.18)

)()()( MnM (3.19)

Assuming two windings A and B, a radius r, and a stack length l, the new inductance values

using the modified winding function are given in (3.20) for the mutual inductance and in

(3.21) for the magnetizing or self inductance. The flux linkage AB is the flux in winding A

due to the current in winding B, while the flux linkage AA is the flux in winding A due to its

own current.

2

0

10 )()()( dgMnrl

iL BA

B

ABAB (3.20)

2

0

10 )()()( dgMnrl

iL AA

A

AAAA (3.21)

3.2.3 Winding Function Theory Applied to Magnetic Devices

Now that the need for MWFT has been presented, it will be applied to interior permanent

magnet motor. The modeling must begin with the most fundamental component of the

IPM motor, the individual magnets themselves, first looked at in [70] and [71]. In Figure

3.12 a single magnet is shown with a magnetization vector which is parallel to its

thickness. A coil wrapped around a material of equal permeability to that of the magnet

44

will provide an equivalent magnetization vector, assuming sufficient current. The

magnets used in this analysis have a thickness, lm, of 2.5 mm and a remanent magnetism,

Br, of 1.21 T. The magnets on the interior are stacked doubly. Hence, the required MMF

for one stack of magnets is:

AtlB

lHr

mrmm 2288

052.1104)0025.0(21.1

70

(3.22)

Figure 3.12: Model of a permanent magnet which produces an equivalent magnetization vector.

In the simplest case, the magnets lie adjacent to each other and form the basis for a single

turns function, as visualized in Figure 3.13 the adjacent magnets are simply modeled as coils

which are wrapped in opposing directions adjacent to each other. These assumptions allow us

to treat the adjacent magnets as though they are part of a single phase. The turns function

reaches a magnitude of 2N if each magnet has N windings. This is due to the fact that

adjacent coil sides lie next to each other to create alternating magnetic flux vectors.

The turns functions for the windings in this study are built from Fourier series, given in

(3.23) and shown in Figure 3.14 which can be phase-shifted easily in simulations.

xh

xdh

hxdn

h

h

cossin)1(2)(1

(3.23)

45

Figure 3.13: IPM with alternating vectors form the basis for a single turns function over the circumference of the rotor.

Figure 3.14: The turns function modeled with the Fourier series.

3.2.4. Verification of a single phase per rotor

The first assumption must be verified that the magnets can be assumed to be a single phase,

rather than as multiple phases. It will be done by looking at a simple case, shown in Figure

3.15, in which an ideal four-pole machine is shown. The inductances will be calculated for

the case in which the two coils, A and B, are treated as distinct coils, and ones which are

connected in series. The stator winding arrangements in 36 slots along with the turns

function of winding A and the winding functions of windings A, B and C are shown in Figure

3.16a. The turns function shows the number of turns as a function of , and the winding

function is the turns function minus its average. The phases are assumed to have Nx windings.

The average value is used to turn the turns function into the winding function. The average

number is found in (3.24).

46

Figure 3.15: An ideal four pole machine.

4)(

21)(

2

0

Ndnn

(3.24)

The self or magnetizing inductance is found in (3.25) for phase A.

8

344

3)( 202

0

2

2

220

2

0

20 Ngrl

dNdNgrl

dNgrl

L AAA

(3.25)

Likewise, the mutual inductance is calculated in (3.26) between phases A and B.

8

14

)( 202

3

02

0

0 Ng

rlNdN

grl

dnNgrl

L BAAB

(3.26)

The total flux treating A and B as separate phases is given by (3.27). This assumes that the

currents in the phases are equal, and that the mutual inductances are equivalent as well. Then

the total inductance is computed in (3.28).

AABAAABBAAABBBBAAAs iLiLiLiLiLiL 22 (3.27)

21

81

81

83

83 2020 N

grl

Ngrl

iL

s

ss

(3.28)

Now the inductance is calculated by treating the stator phases as set of series connected coils,

47

done in (3.29). It is apparent that the inductance is the same as that found in (3.28).

2

14

4 202

0

20 N

grl

dNg

rlLAB

(3.29)

The flux linkages are calculated for each of the h magnets in the four models, and a full

rotation. The inductance is then calculated from the flux linkage for each magnet, k

produced from (3.30). The self and mutual inductances calculated for each of the different

stator configurations is shown in Figure 3.17 to Figure 3.22.

ii

Lh

kk

tot /1

(3.30)

Figure 3.16a WF, from top figure to bottom: winding arrangements in the slots turns function of winding

A, WF of windings A, B and C.

48

3.2.5 Matlab Program for Solving Machine Equations

The winding function method discussed above for calculation of the machine inductances

along with the machine equations are used to develop a Matlab program for simulating

the IPM motor. The flowchart for using MWFT to calculate the inductance is shown in

Figure 3. 23a and the flowchart showing the iterative process of solving the machine

equations is presented in Figure 3.23b. In this program, all winding functions

corresponding to the stator windings are defined as a function of stator angle according

to their winding layouts. The magnetizing and mutual inductances are calculated over one

complete revolution of the rotor.

3.2.6 MMF rise across slots

As can be seen, mmf rises linearly across slots and not in form of steps. This is for every

slots, the WF is defined as in Figure 3.16b

Figure 3.16b A slot filled with conductors and WF diagram

49

0 2000 4000 6000 8000 10000 120000.012

0.014

0.016

0.018

0.02

0.022

0.024

0.026

0.028

0.03

0.032

2 [rad]

[H]

Stator self inductance

Short-Pitched (Laa)

Figure 3.17: Self inductance of the stator winding for Short pitched

0 2000 4000 6000 8000 10000 120000.01

0.015

0.02

0.025

0.03

0.035

2 [rad]

[H]


Full-Pitched (Laa)

Figure 3.18: Self inductance of the stator winding for Full-Pitched

0 2000 4000 6000 8000 10000 120000.012

0.014

0.016

0.018

0.02

0.022

0.024

0.026

0.028

0.03

2 [rad]

[H]


Concentrated (Laa)

Figure 3.19: Self inductance of the stator winding for Concentrated

50

0 2000 4000 6000 8000 10000 12000-16

-14

-12

-10

-8

-6

-4

-2

0

2x 10

-3

2 [rad]

[H]

Stator mutual inductance

Short-Pitched (Lab)

Figure 3.20: Mutual inductance between stator winding for Short pitched

0 2000 4000 6000 8000 10000 12000-20

-15

-10

-5

0

5x 10

-3

2 [rad]

[H]


Full-Pitched (Lab)

Figure 3.21: Mutual inductance between stator winding for Full-pitched

0 2000 4000 6000 8000 10000 12000-16

-14

-12

-10

-8

-6

-4

-2

0

2x 10-3

2 [rad]

[H]


Concentrated (Lab)

Figure 3.22: Mutual inductance between stator winding for Concentrated

51

Each inductance as a function of the angular rotor position is saved in a matrix to be used

when solving the machine equations. The inductance calculations and machine equations are

run in Matlab/Simulink using a fixed time step solver. While the turns functions are built

from Fourier series, the inverse gap functions are built from piecewise-linear functions in

their exact form since they do not have to be shifted. The inverse gap function is shown in

Figure 3.24. While Figure 3.25 shows the Harmonic Order for phase A. These equations are

solved iteratively and in each iteration the rotor position is found by taking the derivative of

the rotor speed ω. Based on the new rotor position, the inductance matrices are updated to be

used in the next iteration.

Figure 3.23a Flowchart for calculated inductances using MWFT in Matlab/Simulink.

52

Figure 3.23b: Flowchart of the iterative procedure for solving machine equations.

53

Figure 3.24: Inverse gap function used for ideal machines in inductance calculations

0 5 10 15 20 250

5

10

15

20

25

30

Short-PitchedFull-PitchedConcentrated

Figure 3.25: Harmonic Order for phase A

54

3.2.7. Torque calculated from inductance

In finding the torque for IPM motor, will once again be used as a basis for comparison. In

this section, the operating point for conventional interior permanent magnet machines is

below the remanent magnetization. This is due to the demagnetization from the stator

field, as well as the excitation requirement of the air gap [72]. This reduction however

comes only due to the excitation requirement for the air gap in the IPM motor. Adjusting

for the operating point, the MMF for the magnets used in the inductance calculations is

2151 ampere-turns. The principal cause of developed torque in IPM machines is the

interaction of the fields from the permanent magnet and rotating stator electromagnetic

field. Therefore the quality of torque produced is largely dependent on the winding

design and the configuration of the magnet. This changing reluctance, is represented

in (3.31) and (3.32) as either unaligned, u, or aligned, a.

u

uu A

l

0 (3.31)

a

aa A

l

0 (3.32)

The changing reluctance translates into a change in inductance, and thus a change in energy,

as shown by the distinct energy values in (3.33) and (3.34). This is also known as the

coenergy, Wco, shown in matrix form in (3.35) as a function of the four inductances for the

IPM motor.

2

21 iLE uu (3.33)

2

21 iLE aa (3.34)

o

i

oo

io

oi

iioico i

iLL

LL

iiW21 (3.35)

55

The expression for the electromagnetic torque developed by the machine can be obtained

from the component of the input power that is transferred across the air gap. The total

input power into the machine is given by:

cscsbsbsasasin iViViVP (3.36)

And the relationship between the electromechanical torque and the load torque is given as

lr

mr

mrmlr

mem Tdt

dB

dtd

JBTdt

dJT

2

2 (3.37)

where mB is the friction coefficient, lT is the load torque and mJ is the moment of inertia.

For simulation of the dynamic characteristics of the drive, we can rewrite equation in two

first order equations as:

mrmlemr JBTTP /)( (3.38)

rrP (3.39)

The mechanical dynamic equation, ignoring friction, is:

dtJTT

p lerr 2

(3.40)

where lT is the load torque, rp is the number of pairs of rotor poles and J is the total

inertia of the rotating mass. For simulation the input power is given as:

abcsabcscscsbsbsasasin iViViViVP 3 (3.41)

lossesPP inout (3.42)

where,

sabcs rilosses 23 (3.43)

And efficiency is given by:

%100Input

OutputEfficiency (3.44)

56

3.3 Clock diagram of IPM motor

The clock diagram of the machines stator winding as shown in Figure 3.26 to 3.28

indicates that,

A+ is the coil carrying current into the paper from phase A,

A- is the coil carrying current out of the paper from phase A,

B+ is the coil carrying current into the paper from phase B,

B- is the coil carrying current out of the paper from phase B,

C+ is the coil carrying current into the paper from phase C,

C- is the coil carrying current out of the paper from phase C,

3.4 Total Harmonic Distortion (THD)

The total harmonic distortion (THD) can be represented by several different methods. In

one of the most common, the THD is defined as the root mean square (RMS) value of the

total harmonics of the signal, divided by the RMS value of its fundamental signal. For

example, for signal X, the THD or harmonic factor is defined as [73]:

(3.45)

Where 22

322 ... nH XXXX

nX RMS value of the harmonic n

FX =RMS value of the fundamental signal

F

H

XX

THD

57

Figure 3.26: Clock Diagram for Short pitched (7/9) Distributed Stator Winding

3.5 The winding factor (kw)

The winding factor ( wk ) affects the shape and magnitude of flux linkage across the air

gap, and affects how harmonics of individual coil back EMF phasor are summed together

to form the overall phase EMF. A low winding factor means that the harmonic

components of the EMF are relatively high as compared to the fundamental component

resulting in lower magnitude of useful EMF. A lower winding factor can be treated as a

58

reduction in the effective number of turns per phase in stator windings [73]. The EMF in

turn affects the efficiency and torque density of the machine. It is therefore important to

obtain a high winding factor in the initial design stages with an appropriate choice of

Slots per pole per phase (Spp). This is the main contributor to the useful torque produced

by the machine. Te is related to the variation of mutual inductances between the stator

and rotor. In particular, it is the interaction between the back EMF and stator current.

Generally, the winding factor is made up of three parts [20]:

Figure 3.27: Clock Diagram for Full-pitched Distributed Stator Winding

59

Figure 3.28: Clock Diagram for Concentrated Stator Winding

sdpw kkkk (3.46)

where,

pk = Pitch factor,

dk = Distribution factor

sk = Skew factor

60

Concentrated windings are usually not skewed, as it will significantly increase the

complexity and cost of constructing the machine. Therefore the third term can be omitted.

Although the pitch factor can be easily calculated, calculating the distribution factor can

be quite complex. An alternative method that can be used to determine both the pitch and

distribution factor together is the EMF phasor method. [20]

3.6 Slot-fill Factor

The slot-fill factor otherwise known as the packing factor is inversely proportional to the

copper loss in the machine. Therefore, having the highest possible slot-fill factor is

essential for achieving optimal efficiency in the machine. The advantage that

Concentrated Winding has over Distributed Winding is that coils are wound around

individual stator teeth. This allows the use of more advanced winding methods such as

the joint lapped core method and pre-pressed windings in separable tooth pieces. Typical

slot-fill factors of up to 35% can be achieved for Distributed Winding and up to 45% can

be achieved for Concentrated Winding [74].

3.7 The Voltage Equations

The stator of a 220 V, 36-slot, 4-pole, 3 phase chorded and non-chorded distributed

winding and 220 V, 12 slot 4-pole 3 phase concentrated winding interior permanent

magnet motor was used for this study. The main dimensions of the machine are as given

in Table 4.1

In the stator reference frame, the first-order differential equations describing the electrical

circuit of a three-phase IPM motor using conventional notations are given below.

61

dtd

irV asasasas

(3.47)

dtd

irV bsbsbsbs

(3.48)

dtd

irV cscscscs

(3.49)

dtd

irV qrqrqrqr

(3.50)

dtd

irV drdrdrdr

(3.51)

Equations (3.47-3.51) can be written in matrix form as

dr

qr

cs

bs

as

drdrdrqrdrcsdrbsdras

qrdrqrqrqrcsqrbsqras

csdrcsqrscsbscsas

bsdrbsqrbscsbsbsbsas

asdrasqrascsasbsasas

dr

qr

cs

bs

as

dr

qr

cs

bs

as

dr

qr

cs

bs

as

i

iiii

LLLLL

LLLLL

LLLLL

LLLLL

LLLLL

dtd

i

iiii

r

rr

rr

V

VVVV

csc

0000

0000000000000000

(3.52)

Where,

rBAlsasas LLLL 2cos (3.53)

32cos

21

rBAasbs LLL (3.54)

32cos

21 rBAascs LLL (3.55)

32cos

21 rBAbsas LLL (3.56)

322cos rBAlsbsbs LLLL (3.57)

rBAbscs LLL 2cos21 (3.58)

32cos

21 rBAcsas LLL (3.59)

62

rBAcsbs LLL 2cos21 (3.60)

322coscsc rBAlss LLLL (3.61)

10

2

2 rl

NL r

sA

(3.62)

20

2

221

rlN

L rs

B

(3.63)

rmqasqr LL cos (3.64)

)sin( rmdasdr LL (3.65)

32cos

rmqbsqr LL (3.66)

32sin

rmdbsdr LL (3.67)

32cos

rmqcsqr LL (3.68)

32sin

rmdcsdr LL (3.69)

BAmq LLL 23 (3.70)

BAmd LLL 23 (3.71)

rmcsascsbsasbsasasasas iLiLiL sin (3.72)

32sin

rmcsbscsbsbsbsasbsasbs iLiLiL (3.73)

32sincsc

rmcssbscsbsascsascs iLiLiL (3.74)

63

3.8 Solution of Equation (3.52)

We attempt to solve the first order differential equation (3.52) to illustrate its complexity.

Now we may rewrite (3.52) as:

LIdtdIRV (3.75)

L is a function of rotor position r which is also a function of time and I, is only a time

varying function so we may write:

dtdIL

dtdL

IIRV rr )()(

(3.76)

This now implies a differential equation with time-varying coefficient. But equation

(3.95) can be rewritten as:

dtdIL

dtd

ddL

IIRV rr

r

r )()(

(3.77)

But we know that dt

d r is the derivative of position which means “speed”, or r so

(3.96) now becomes:

dtdIL

ddL

IIRV rr

rr )(

)(

(3.78)

Equation (3.89) may finally be written as:

1))(()(

r

r

rr L

ddLRIV

dtdI

(3.79)

Where dt

d rr

(3.80)

and L( r ) is the 5 5 inductance matrix appearing in (3.52).

64

Equation (3.79) shows that the solution of current at every time step involves the

computation of the derivative of the inductance matrix, r

r

ddL

)( for the particular rotor

position and the computation of the inverse of the inductance matrix 1))(( rL [75].

3.9 Torque Ripple Pulsating torque is harmonic torque which is caused by the interaction between induced

EMF harmonic and the stator current harmonic. In order to reduce the ripple torque, the

harmonic are minimum as much as possible, while induced EMF harmonic is related with

the spatial distribution and winding design of excitation magnetic field produced by

magnets. The ripple torque calculation is defined as [20]:

AvegRipp TTTT /)( minmax (3.81)

3.10 Losses in IPM Motor

A key aim in almost all high performance PM machine design is to minimise losses. In

machines used for field weakening applications, frequency related losses in particular

have to be carefully considered. Losses in PM machines are separated into two main

areas – electrical losses and mechanical losses.

Electrical Losses:

Core losses – Eddy current and hysteresis losses

Permanent magnet losses

Copper loss

Mechanical losses:

Bearing losses and Windage losses

65

3.10.1 Core Loss

In IPM motor frequency-related losses have to be carefully considered and minimised

due to constant operation at high frequencies. Furthermore the increase in leakage

harmonic terms as a result of applying CW makes the machine more susceptible to

increased core and rotor losses. One method of separating the hysteresis and eddy current

losses is derived from the relationship mentioned by Yeadon [76];

Thus, this approximation is valid for the breakdown of hysteresis and eddy current loss at

60Hz and the total core loss can be expressed below and this estimation gives us an eddy

current loss and hysteresis loss.

hyseddycore PPP (3.82)

Where

coreeddy PP31

(3.83)

corehys PP32

(3.84)

3.10.2 Magnet Loss

With the core loss substantially reduced by the choice of thin silicon steel laminations,

the time varying fields may still create substantial losses in the magnets, especially in

SPM machines. A great deal of research interest is focused on the study and minimisation

of magnet losses in Concentrated Winding PM machines [77]. Commonly used strategies

to reduce magnet losses are by the use of bonded instead of sintered magnets at the

expense of lower magnet strength, or the use of sintered-segmented magnets [78].

66

3.10.3 Stator Winding Loss

Stator winding loss – also known as I2R, copper or joule loss – occurs when the armature

windings are excited by an external source. Of the total loss in PM machines, the largest

portion is usually due to I2R loss [79]. I2R is not frequency dependent and is constant

throughout the speed range, so the CPSR is not affected by this loss. This is due to the

copper conductors being thin enough to have 100% skin-depth throughout the operating

region. I2R loss is described in the following formula:

(3.85)

where,

coilN = Number of turns per coil

= Conductor resistivity (1.68X10-8 for copper)

wA = Cross-sectional area of wire

3.10.4 Mechanical Losses

Mechanical losses consist of mainly bearing and windage losses [80]. Bearing loss is

dependent on factors such as the bearing type, bearing diameter, rotor speed, load and

lubricant used. Windage loss occurs when friction is created with the rotating parts of the

machine and the surrounding air. Bearing losses can be calculated with the following

formula [81]:

bbmbearing FDkP 5.0 (3.86)

where,

m = Mechanical speed of the rotor, F = Force acting on the bearing

bD = Bearing inner diameter, bk = Bearing loss constant

w

effcoil A

lINRI 22 2

67

CHAPTER FOUR

4.0 Dynamic Simulation in MATLAB/SIMULINK®

4.1 Simulation Tools

Computer-based analysis of electrical machines requires that appropriate measures are

made towards the proper selection of a simulation tool. The complex models of some

electrical machines need computing tools capable of performing dynamic simulations

with greater efficiency and accuracy. [82]. SIMULINK® has the advantages of being

capable of complex dynamic simulations, graphical environment with visual real time

programming and broad selection of toolboxes [83].

4.2 Simulation of IPM motor with Short pitched, Full-pitched Distributed Winding

and Concentrated winding using Embedded MATLAB Function Blocks

The interior permanent motor models constructed in this research work were achieved

using the Embedded MATLAB Function blocks of the MATLAB/SIMULINK® toolbox.

The machine is simulated using the actual abc phase variables model as developed.

4.3 Simulation Results

The system built in SIMULINK for the test interior permanent magnet motor is operated

with a load torque to enable notice the maximum load it can carry as shown in Figure 4.1

to 4.30 below.

68

Table 4.1: IPM motor with Short pitched, Full-pitched and concentrated winding

Voltage: 220V Rating: 110 kW Frequency: 50Hz

Rotor inertia: 0.22 kg.m2

Poles: 4 & Speed: 2400 rpm Rated Current (RMS): 208.33A

Magnetic Steel: N28UH & Remanent flux density: 1.21T Magnet coating: Ni-Cu-Ni, Core material: Non-oriented silicon steel & Magnet thickness:2.5mm

Parameter Value

Configuration Short pitched Full-pitched Concentrated Stator winding resistance, sr 0.62 0.62 0.62

d-axis leakage inductance, ldrL 0.0055 0.0055 0.0055

q-axis leakage inductance, lqrL 0.0062 0.0062 0.0062

Resistance, Rm 0.03 0.03 0.03

Stator winding leakage inductance, lsL 0.0083 0.0083 0.0083

Rotor d-axis winding resistance, drr 0.12 0.12 0.12

Rotor q-axis winding resistance, qrr 0.25 0.25 0.25

Inductance, Lm 0.09 0.09 0.09

1g 0.0003 0.0003 0.0003

2g 0.012 0.012 0.012

Amplitude of the 1st order harmonics 27.53 29.30 26.45

Stator outer diameter 130mm 130mm 130mm

Rotor outer diameter 80mm 80mm 80mm

Airgap length 1.2mm 1.2mm 1.2mm

Stator inner diameter 82.4mm 82.4mm 82.4mm

Shaft outer diameter 24mm 24mm 24mm

Stack length (Stator) 80mm 80mm 80mm

Stack length (rotor) 79mm 79mm 79mm

Area per half slot 86.3mm2 86.3mm2 86.3mm2

Stator and Rotor lamination thickness 0.35mm 0.35mm 0.35mm

Slot-opening width 1.2mm 1.2mm 1.2mm

Number of turns per coil (around each tooth) 115turns 115turns 115turns

Slot-fill factors (%) 35 35 45

69

Table 4.2: Summary of the Performance comparison of the each IPM Motor

Variables Configuration

Short pitched Full-pitched Concentrated Fundamental winding factor 0.933 0.933 0.866

Amplitude of the fundamental winding 27.53 29.30 26.45

Copper loss (kw) Low speed High speed

0.35 3.6

0.35 3.6

0.30 3.7

Pull out power (kw) 57 56 58

Quantity of copper (kg) 20 20 10

THD of mmf (%) 3.07 3.07 3.51

Torque ripple (Nm) 71 71 96

Average torque (Nm) 185 185 142

Peak torque develop (Nm) 116 116 133

Controllability Better Best Worsened

Demagnetization tolerance (%) 78 78 60

Efficiency 87 88 89

70

0 1 2 3 4 5 6 7 8-200

0

200

Ia, A

0 1 2 3 4 5 6 7 8-200

0

200

Ia, A

0 1 2 3 4 5 6 7 8-200

0

200

Time, sec

Ia, A

Chorded

Non-Chorded

Concentrated

Figure 4.1: Stator phase A’s currents

0 1 2 3 4 5 6 7 8-200

0

200

Idr,

A

0 1 2 3 4 5 6 7 8-200

0

200

Idr,

A

0 1 2 3 4 5 6 7 8-200

0

200

Time, sec

Idr,

A

Chorded

Non-Chorded

Concentrated

Figure 4.2: d-axis rotor currents

--------Short-Pitched

---------- Full-Pitched


--------Full-Pitched

71

0 1 2 3 4 5 6 7 8-200

0

200

Iqr,

A

0 1 2 3 4 5 6 7 8-200

0

200

Iqr,

A

0 1 2 3 4 5 6 7 8-200

0

200

Time, sec

Iqr,

A

Chorded

Non-Chorded

Concentrated

Figure 4.3: q-axis currents

0 1 2 3 4 5 6 7 8-200

0

200

0 1 2 3 4 5 6 7 8-100

0

100

200

Ele

ctro

mag

netic

Tor

que,

Te,

N-m

0 1 2 3 4 5 6 7 8-100

0

100

200

Time, sec

Chorded

Non-Chorded

Concentrated

Figure 4.4: Electromagnetic torques


-------- Full-Pitched


------- Full-Pitched

72

1 1.5 2 2.5 3-200

-100

0

100

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

-500

50100150

Ele

ctro

mag

netic

Tor

que,

Te

N-m

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

0

50

100

Time, sec

Non-Chorded

Chorded

Concentrated

Figure 4.5: Electromagnetic torques at synchronization

3.8 4 4.2 4.4 4.6 4.8 5-150

-100-50

0

50

4 4.2 4.4 4.6 4.8 5 5.2

-50

0

50

Ele

ctro

mag

netic

Tor

que,

Te

N-m

4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

-200

2040

Time, sec

Non-Chorded

Chorded

Concentrated

Figure 4.6: Electromagnetic torques when the load was applied

-------Short-Pitched


------- Short-Pitched


73

0 1 2 3 4 5 6 7 8-200

0

200

400

600

800

1000

1200

1400

1600

1800

Time, sec

Roto

r Spe

ed, r

.p.m

Chorded

Figure 4.7: Rotor Speeds during starting and its response to a load torque for Short pitched

0 1 2 3 4 5 6 7 8-200

0

200

400

600

800

1000

1200

1400

1600

Time, sec

Rotor S

peed

, r.p.m

Non-Chorded

Figure 4.8: Rotor Speeds during starting and its response to a load torque for Full-pitched

0 1 2 3 4 5 6 7 8-200

0

200

400

600

800

1000

1200

1400

1600

Time, sec

Rotor

Spe

ed, r

.p.m

Concentrated

Figure 4.9: Rotor Speeds during starting and its response to a load torque for Concentrated


---------Full-Pitched

74

0.8 1 1.2 1.4 1.6 1.8 2 2.2

1200

1250

1300

1350

1400

1450

1500

1550

1600

1650

Time, sec

Rotor S

peed

, r.p.m

Chorded

Figure 4.10: Rotor Speeds during synchronization for Short pitched

0.8 1 1.2 1.4 1.6 1.8 2 2.2

1300

1350

1400

1450

1500

1550

1600

Time, sec

Rotor S

peed

, r.p.m

Non-Chorded

Figure 4.11: Rotor Speeds during synchronization for Full-pitched

0.8 1 1.2 1.4 1.6 1.8 2 2.2

1300

1350

1400

1450

1500

Time, sec

Rotor S

peed

, r.p.m

Concentrated

Figure 4.12: Rotor Speeds during synchronization for Concentrated



75

3.9 3.95 4 4.05 4.1 4.15 4.2

1465

1470

1475

1480

1485

1490

1495

1500

1505

1510

1515

Time, sec

Rotor S

peed

, r.p.m

Chorded

Figure 4.13: Rotor Speeds response to a load torque for Short pitched

4 4.05 4.1 4.15 4.2 4.25 4.3 4.35 4.4 4.45 4.51440

1460

1480

1500

1520

1540

Time, sec

Rotor S

peed

, r.p.m

Non-Chorded

Figure 4.14: Rotor Speeds response to a load torque for Full-pitched

3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

1460

1470

1480

1490

1500

1510

1520

1530

Time, sec

Rot

or S

peed

, r.p

.m

Concentrated

Figure 4.15: Rotor Speeds response to a load torque for Concentrated



76

0 0.5 1 1.5 2 2.5 3 3.5 4-200

0

200

400

600

800

1000

1200

1400

1600

Time, sec

Rot

or S

peed

, r.p

.m

Chorded

Figure 4.16: Rotor Speeds with the application of ramp for Short pitched

0 0.5 1 1.5 2 2.5 3 3.5 4-200

0

200

400

600

800

1000

1200

1400

1600

Time, sec

Rot

or S

peed

, r.p

.m

Non-Chorded

Figure 4.17: Rotor Speeds with the application of ramp for Full-pitched

0 0.5 1 1.5 2 2.5 3 3.5 4-200

0

200

400

600

800

1000

1200

1400

1600

Time, sec

Rot

or S

peed

, r.p

.m

Concentrated

Figure 4.18: Rotor Speeds with the application of ramp for Concentrated



77

-200 0 200 400 600 800 1000 1200 1400 1600 1800-200

-150

-100

-50

0

50

100

150

200

Rotor Speed, r.p.m

Elect

rom

agne

tic T

orqu

e, T

e, N

-m

Chorded

Figure 4.19: Torque-Speed characteristic for Short pitched

-200 0 200 400 600 800 1000 1200 1400 1600-100

-50

0

50

100

150

Elect

rom

agne

tic T

orqu

e, T

e, N

-m

Rotor Speed, r.p.m

Non-Chorded

Figure 4.20: Torque-Speed characteristic for Full-pitched

-200 0 200 400 600 800 1000 1200 1400 1600-100

-50

0

50

100

150

Elect

rom

agne

tic T

orqu

e, T

e, N

-m

Rotor Speed, r.p.m

Concentrated

Figure 4.21: Torque-Speed characteristic for Concentrated



78

20 40 60 80 100 120 140 1602

2.5

3

3.5

4

4.5

5

5.5

6x 104

Stator current, A

Outpu

t pow

er, w

atts

Chorded

Figure 4.22: Output power against stator current for Short pitched

20 40 60 80 100 120 1402

2.5

3

3.5

4

4.5

5

5.5

6x 104

Stator current, A

Outpu

t pow

er, w

atts

Non-Chorded

Figure 4.23: Output power against stator current for Full-pitched

40 50 60 70 80 90 100 110 120 130 1402

2.5

3

3.5

4

4.5

5

5.5

6x 10

4

Stator current, A

Out

put p

ower

, wat

ts

Concentrated

Figure 4.24: Output power against stator current for Concentrated


-------- Full-Pitched

79

20 40 60 80 100 120 140 1600

0.5

1

1.5

2

2.5

3

3.5

4x 104

Stator current, A

Sta

tor l

osse

s, w

atts

Chorded

Figure 4.25: Stator losses against stator current for Short pitched

20 40 60 80 100 120 1400

0.5

1

1.5

2

2.5

3

3.5

4x 104

Stator current, A

Sta

tor l

osse

s, w

atts

Non-Chorded

Figure 4.26: Stator losses against stator current for Full-pitched

40 50 60 70 80 90 100 110 120 130 1400

0.5

1

1.5

2

2.5

3

3.5

4x 10

4

Stator current, A

Sta

tor l

osse

s, w

atts

Concentrated

Figure 4.27: Stator losses against stator current for Concentrated



80

20 40 60 80 100 120 140 16060

65

70

75

80

85

90

Stator current, A

Efficien

cy, 1

00%

Chorded

Figure 4.28: Efficiency against stator current for Short pitched

20 40 60 80 100 120 14060

65

70

75

80

85

90

Stator current, A

Effi

cien

cy, 1

00%

Non-Chorded

Figure 4.29: Efficiency against stator current for Full-pitched

40 50 60 70 80 90 100 110 120 130 14060

65

70

75

80

85

90

Stator current, A

Efficien

cy, 1

00%

Concentrated

Figure 4.30: Efficiency against stator current for Concentrated



81

4.4 Discussions

In this work, various performance characteristics of both concentrated winding IPM

motor short pitched and full-pitched distributed winding IPM motor are investigated and

compared in detail. All time-stepping simulations were carried out at a constant supply

voltage of 220 V, 50 Hz using Matlab Simulink. All the results are shown for

comparison. A load torque of 40 Nm (60% of rated torque) at t = 4.0s followed by a ramp

at the same time were introduced into the simulations this leads to small speed departures

from interior permanent magnet motor. The harmonics originating from the slots and the

winding are responsible for the distortions in the waveforms of different variables shown.

Table 4.1 show different stator configuration since the Embedded MATLAB function

block was employed; the abc phase variables were written and coded inside the block

(see Appendix 1 and 2).

As it is well known, the distributed winding motor has lower torque ripple because of the

distributed magnetic flux through the teeth. Analysis results show that it has lower torque

ripple of 71 Nm compared with the 96 Nm of concentrated winding motor. And the

average torque of the distributed winding motor at the maximum speed is higher than that

of the concentrated winding motor. Hence, it results in that the distributed winding motor

is better for the torque performance.

Losses and efficiency as the concentrated winding IPM motor has shorter end coil as

mentioned, it has lower phase resistance and lower copper loss at lower speed than the

distributed winding IPM motor. In addition, the distributed winding IPM motor has more

magnetic saturation parts at the stator teeth and core loss is bigger than that of the

concentrated winding IPM motor. However, the concentrated winding IPM motor causes

82

huge amount of magnet eddy current loss by the slot harmonics at high speed operation

because permanent magnet has conductivity inherently.

Harmonics and controllability are also considered. The 3rd and 15th harmonics of the

concentrated winding IPM motor are removed inherently, but the magnitudes of

harmonics are bigger than those of the distributed winding IPM motor. As the

concentrated winding IPM motor has more harmonics than the distributed winding IPM

motor, torque ripple would be bigger and the controllability would be worsened. It can be

said that the distributed winding is superior to the concentrated winding IPM motor.

However, this torque ripple can be ignored in case the moment of inertia of the rotor and

load is enough big.

Demagnetization is generally occurred by high temperature, airgap variation and locked-

rotor high current. For both concentrated winding and distributed winding IPM motors,

demagnetization from high temperature and airgap variation would be similar and

because permanent magnets of the IPM motor are inserted in the rotor. For the

concentrated winding IPM motor, the intensive flux from the stator core affects directly

to the permanent magnet and the minimum magnetic flux density of the permanent

magnet is 0.2515 T. On the other hand, the minimum magnetic flux density of the

permanent magnet in case of the distributed winding IPM motor is 0.6422 T. This

analysis result elicits that the distributed winding IPM motor has much higher

demagnetization tolerance than the concentrated winding IPM motor.

In general, IPM motor with concentrated winding is superior to that with distributed

winding in the power density point of view because of less end coils. The approximate

weight of the IPM motor with concentrated winding is 162.6 kg and power density of that

83

is 0.670 kW/kg. On the other hand, the approximate weight of the IPM motor with

distributed winding is 182.9 kg and power density of that is 0.596 kW/kg. Major source

of the difference is the weight of stator and coil. From the calculation, it is confirmed that

the concentrated winding IPM motor is better in the power density point of view.

Table 4.2 shows the summary of the performance comparison of the each IPM motor.

Also observed that there is a slightly faster damping of oscillations in the full-pitched

distributed winding and concentrated winding than the short pitched distributed winding

and current drawn is also less for the full-pitched distributed winding and concentrated

winding. These are due to the increased impedances from the additional harmonic terms.

Another observation is that the current plots of dri and qri appears to oscillate before

arriving at steady-state when a load torque was applied for full-pitched distributed

winding and concentrated winding. This is not unconnected to the fact that there is

significant deviation from synchronous speed mode for these configurations. The farther

the speed deviates from synchronous, the longer it takes the system to attain steady-state.

84

CHAPTER FIVE

5.0 Conclusion and Recommendation

An Interior Permanent Magnet motor has been successfully simulated using the

Embedded MATLAB function. Various performance characteristics of concentrated

winding IPM, short pitched DW IPM and full-pitched DW IPM are investigated and

compared in detail using the winding function theory, harmonic contents analysis and

inductance calculations. The DW motor has lower torque ripple and high average torque

at maximum speed. Hence, DW motor is better for the torque performance. The CW IPM

motor has shorter end coil, lower phase resistance and lower copper loss at lower speed.

In addition, the DW IPM motor has more magnetic saturation parts at the stator teeth and

core loss is bigger. However, the CW IPM motor causes huge amount of magnet eddy

current loss by the slot harmonics at high speed operation and has more harmonics,

torque ripple would be bigger and the controllability would be worsened. It can be said

that the DW is superior. Demagnetization from high temperature and airgap variation

would be similar for both windings and because permanent magnets of the IPM motor are

inserted in the rotor, the DW IPM motor has much higher demagnetization tolerance than

the CW IPM motor. In general, IPM motor with CW is superior to that with short pitched

and full-pitched DW in the power density point of view because of less end coils. Major

source of the difference is the weight of stator and coil. The continued interest in IPM

motor is very promising. The number of institutions performing research into IPM motor is

increasing and continued research should yield industrial products down the road.

85

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92

Appendices APPENDIX 1: Simulink Model of the IPM with Ramp for Short pitched, Full-pitched and Concentrated Winding

wr

f(u)

Vcs

Vbs

Vas

To Workspace9

IAAcon

To Workspace8

Laacon

To Workspace7

Ic

To Workspace6

Ib

To Workspace5

Iacon

To Workspace4

Idrcon

To Workspace3

Iqrcon

To Workspace2

Time

To Workspace13

Labcon

To Workspace12

Effcon

To Workspace11

Losscon

To Workspace10

Poutcon

To Workspace 1

TorqueconTo Workspace

Speedcon

Te

Speed

Ramp

Pout

Loss

Lab

Laa

Iqdr

Int 6

1s

Int 5

1s

Int 4

1s

Int 3

1s

Int 2

1s

Int 1

1s

Int

1s

Ic

Ib

Ia

IAA

EmbeddedMATLAB Function

Ia

Ib

Ic

wr

tr

Vas

Vbs

Vcs

TL

Iqr

Idr

pIa

pIb

pIc

pwr

Te

IAA

Pout

Laa

Lab

Loss

Eff

LA

LB

pIqr

pIdr

fcn

Eff

Display 1

Display

Clock

93

APPENDIX 2: Embedded MATLAB code of IPM Motor for Short pitched, Full-pitched and concentrated winding in per unit. function [pIa, pIb, pIc, pwr, Te, LA, LB, pIqr, pIdr]... = fcn(Ia, Ib, Ic, wr, tr, Vas, Vbs, Vcs, TL, Iqr, Idr) P=4; J=0.22; Lls = 8.3e-3; Llqr = 6.2e-3; Lldr = 5.5e-3; rs = 0.62; rqr = 0.25; rdr = 0.12; Rm=30/1000; Lm=90/1000; mu=4*pi*10^-7; g1=0.3/1000; g2=g0*40; Na=27.53; Nb=29.30; Nc=26.45; LA = 1/2*mu*Rm*Lm*Na^2*pi*(g0+g1)/g0/g1; LB = 3183/10000*mu*Rm*Lm*Na^2*pi*(g0+g1)/g0/g1; al=2*pi/3; Lmq=3/2*(LA-LB); Lmd=3/2*(LA+LB); Laa=Lls+LA-LB*cos(2*tr); Lab=-.5*LA-LB*cos(2*(tr-pi/3)); Lac=-.5*LA-LB*cos(2*(tr+pi/3)); Lba=-.5*LA-LB*cos(2*(tr-pi/3)); Lbb=Lls+LA-LB*cos(2*(tr-2*pi/3)); Lbc=-.5*LA-LB*cos(2*(tr+pi)); Lca=-.5*LA-LB*cos(2*(tr+pi/3)); Lcb=-.5*LA-LB*cos(2*(tr+pi)); Lcc=Lls+LA-LB*cos(2*(tr+2*pi/3)); LSS=[Laa Lab Lac; Lba Lbb Lbc; Lca Lcb Lcc]; LS2= -0*LB*[cos(2*2*tr) cos(2*2*(tr-pi/3)) cos(2*2*(tr+pi/3));... cos(2*2*(tr-pi/3)) cos(2*2*(tr-2*pi/3)) cos(2*2*(tr+pi));... cos(2*2*(tr+pi/3)) cos(2*2*(tr+pi)) cos(2*(tr+2*pi/3))]; dLS2= 0*LB*4*[sin(2*2*tr) sin(2*2*(tr-pi/3)) sin(2*2*(tr+pi/3));... sin(2*2*(tr-pi/3)) sin(2*2*(tr-2*pi/3)) sin(2*2*(tr+pi));... sin(2*2*(tr+pi/3)) sin(2*2*(tr+pi)) sin(2*(tr+2*pi/3))]; LS=LSS+LS2; LSRa=[Lmq*cos(tr) Lmd*sin(tr);... Lmq*cos(tr-al) Lmd*sin(tr-al);... Lmq*cos(tr+al) Lmd*sin(tr+al)]; LSR1=.0*[Lmq*cos(3*tr) Lmd*sin(3*tr);... Lmq*cos(3*(tr-al)) Lmd*sin(3*(tr-al));... Lmq*cos(3*(tr+al)) Lmd*sin(3*(tr+al))]; dLSR1=.0*3*[-Lmq*sin(3*tr) Lmd*cos(3*tr);... -Lmq*sin(3*(tr-al)) Lmd*cos(3*(tr-al));... -Lmq*sin(3*(tr+al)) Lmd*cos(3*(tr+al))]; dLSS=[2*LB*sin(2*tr) -2*LB*sin(2*tr+1/3*pi) 2*LB*cos(2*tr+1/6*pi);... -2*LB*sin(2*tr+1/3*pi) 2*LB*cos(2*tr+1/6*pi) 2*LB*sin(2*tr);... 2*LB*cos(2*tr+1/6*pi) 2*LB*sin(2*tr) -2*LB*sin(2*tr+1/3*pi)];

94

dLS=dLSS+dLS2; dLSRa=[-Lmq*sin(tr) Lmd*cos(tr);... -Lmq*sin(tr-al) Lmd*cos(tr-al);... -Lmq*sin(tr+al) Lmd*cos(tr+al)]; LSR=LSRa+LSR1; dLSR=dLSRa+dLSR1; LRR=[Llqr+Lmq 0;... 0 Lldr+Lmd]; L = [LS LSR; 2/3*(LSR)' LRR]; dL = [dLS dLSR; 2/3*(dLSR)' zeros(2,2)]; V=[Vas; Vbs; Vcs; 0; 0]; R=diag([rs rs rs rqr rdr]); II=[Ia; Ib; Ic; Iqr; Idr]; pII=inv(L)*(V-(R+wr*dL)*II); pIa=pII(1); pIb=pII(2); pIc=pII(3); pIqr=pII(4); pIdr=pII(5); Ias=[Ia; Ib; Ic]; Iqdr=[Iqr; Idr]; Te = (P/2)*(.5*Ias'*dLSS*Ias + Ias'*dLSR*Iqdr); pwr=(Te-TL)*P/(2*J); TT = 2/3*[cos(tr) cos(tr-al) cos(tr+al); sin(tr) sin(tr-al) sin(tr+al); 1/2 1/2 1/2]; IQD = TT*Ias; Iq = IQD(1); Id = IQD(2); IAA = (Iq.^2+Id.^2).^.5; Loss = 3*IAA.^2*rs; Pout = 3*220*IAA - Loss; Eff=(Pout/(3*220*IAA))*100;

95

APPENDIX 3: M-file code of IPM Motor for Short pitched, Full-pitched and concentrated winding for Fundamental MMF Diagram for phase A’s and the Harmonic Order clear;clc; s1=[zeros(1,25) linspace(0,2,50) 2*ones(1,25)]; s2=[2*ones(1,25) linspace(2,3,50) 3*ones(1,25)]; s3=[3*ones(1,25) linspace(3,4,50) 4*ones(1,25)]; s4=4*ones(1,400); s5=[4*ones(1,25) linspace(4,3,50) 3*ones(1,25)]; s6=[3*ones(1,25) linspace(3,2,50) 2*ones(1,25)]; s7=[2*ones(1,25) linspace(2,0,50) 0*ones(1,25)]; s8=[0*ones(1,25) linspace(0,-1,50) -1*ones(1,25)]; s9=[-1*ones(1,25) linspace(-1,-2,50) -2*ones(1,25)]; s10=-2*ones(1,400); s11=[-2*ones(1,25) linspace(-2,-1,50) -1*ones(1,25)]; s12=[-1*ones(1,25) linspace(-1,0,50) 0*ones(1,25)]; s13=[zeros(1,25) linspace(0,2,50) 2*ones(1,25)]; s14=[2*ones(1,25) linspace(2,3,50) 3*ones(1,25)]; s15=[3*ones(1,25) linspace(3,4,50) 4*ones(1,25)]; s16=4*ones(1,400); s17=[4*ones(1,25) linspace(4,3,50) 3*ones(1,25)]; s18=[3*ones(1,25) linspace(3,2,50) 2*ones(1,25)]; s19=[2*ones(1,25) linspace(2,0,50) 0*ones(1,25)]; s20=[0*ones(1,25) linspace(0,-1,50) -1*ones(1,25)]; s21=[-1*ones(1,25) linspace(-1,-2,50) -2*ones(1,25)]; s22=-2*ones(1,400); s23=[-2*ones(1,25) linspace(-2,-1,50) -1*ones(1,25)]; s24=[-1*ones(1,25) linspace(-1,0,50) 0*ones(1,25)]; s25=[zeros(1,25) linspace(0,2,50) 2*ones(1,25)]; s26=[2*ones(1,25) linspace(2,4,50) 4*ones(1,25)]; s27=[4*ones(1,25) linspace(4,6,50) 6*ones(1,25)]; s28=6*ones(1,600); s29=[6*ones(1,25) linspace(6,4,50) 4*ones(1,25)]; s30=[4*ones(1,25) linspace(4,2,50) 2*ones(1,25)]; s31=[2*ones(1,25) linspace(2,0,50) 0*ones(1,25)]; s32=0*ones(1,600); s33=[zeros(1,25) linspace(0,2,50) 2*ones(1,25)]; s34=[2*ones(1,25) linspace(2,4,50) 4*ones(1,25)]; s35=[4*ones(1,25) linspace(4,6,50) 6*ones(1,25)]; s36=6*ones(1,600); s37=[6*ones(1,25) linspace(6,4,50) 4*ones(1,25)]; s38=[4*ones(1,25) linspace(4,2,50) 2*ones(1,25)]; s39=[2*ones(1,25) linspace(2,0,50) 0*ones(1,25)]; s40=0*ones(1,600); s41=[zeros(1,25) linspace(0,2,50) 2*ones(1,25)]; s42=2*ones(1,200); s43=[2*ones(1,25) linspace(2,0,50) 0*ones(1,25)]; s44=0*ones(1,200); s45=[zeros(1,25) linspace(0,2,50) 2*ones(1,25)]; s46=2*ones(1,200); s47=[2*ones(1,25) linspace(2,0,50) 0*ones(1,25)]; s48=0*ones(1,200);

96

NCS=16; NPS=42; A1=NCS/2*[s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 s14 s15 s16 s17 s18 s19 s20 s21 s22 s23 s24]; A2=NCS/2*[s25 s26 s27 s28 s29 s30 s31 s32 s33 s34 s35 s36 s37 s38 s39 s40]; A3=NPS/2*[s41 s42 s43 s44 s45 s46 s47 s48]; NN=3600; NQ=1200; Aw=A1-(sum(A1)/NN); Ax=A2-(sum(A2)/NN); Az=A3-(sum(A3)/NQ); tt=linspace(0,2*pi,NN); tt1=linspace(0,2*pi,NQ); td=tt*180/pi; td1=tt1*180/pi; AA=fft(Aw);AB=fft(Ax);AC=fft(Az); MA=2/NN*abs(AA); MB=2/NN*abs(AB); MC=2/NQ*abs(AC); ta=tan(atan2(real(AA), imag(AA)));tb=tan(atan2(real(AB), imag(AB)));tc=tan(atan2(real(AC), imag(AC))); figure(3); %%subplot(311); bar(MA(3:80)); subplot(312); bar(MB(3:80)); subplot(313); bar(MC(3:80)); MM=[MA(3:80);MB(3:80);MC(3:80)]; MMM=MM'; bar(MMM,1.0,'group'); legend('Chorded','Non-Chorded','Concentrated'); figure(2); subplot(311); plot(td,Aw,'k-',td, MA(3)*sin(2*tt-ta(3)),'k--','linewidth',2);grid minor; legend('Chorded phase A'); subplot(312); plot(td,Ax,'k-',td,MB(3)*sin(2*tt-tb(3)),'k--','linewidth',2);grid minor; ylabel('MMF per unit current, Ampere-turns'); legend('Non-Chorded phase A'); subplot(313); plot(td1,Az,'k-',td1,MC(3)*sin(2*tt1-tc(3)),'k--','linewidth',2); grid minor; xlabel(' Stator Circumferential angle, \phi [deg]'); legend('Concentrated phase A');

97

APPENDIX 4: M-file code of IPM Motor for Short pitched, Full-pitched and concentrated winding for Inductance calculation. clear;clc; syms ph Na Nb Nc tt g1 g0 mu R L wbb=Na*cos(2*ph); waa=Na*cos(2*ph-2*pi/3); wcc=Na*cos(2*ph-4*pi/3); k=mu*R*L; giv=1/2*(1/g0+1/g1)-2/pi*(1/g0-1/g1)*cos(4*(ph-tt)); Laa=k*int(waa*waa*giv,ph,0,2*pi); Laa=simple(Laa) Lab=k*int(waa*wbb*giv,ph,0,2*pi); Lab=simple(Lab) Lac=k*int(waa*wcc*giv,ph,0,2*pi); Lac=simple(Lac) Lba=k*int(wbb*waa*giv,ph,0,2*pi); Lba=simple(Lba) Lbb=k*int(wbb*wbb*giv,ph,0,2*pi); Lbb=simple(Lbb) Lbc=k*int(wbb*wcc*giv,ph,0,2*pi); Lbc=simple(Lbc) Lca=k*int(wcc*waa*giv,ph,0,2*pi); Lca=simple(Lca) Lcb=k*int(wcc*wbb*giv,ph,0,2*pi); Lcb=simple(Lcb) Lcc=k*int(wcc*wcc*giv,ph,0,2*pi); Lcc=simple(Lcc) R=30/1000; L=90/1000; mu=4*pi*10^-7; g1=0.3/1000; g2=g1*40; Na=27.53; Nb=29.30; Nc=26.45; tt=linspace(0,2*pi,3600); Lasas=eval(Laa); Lbsbs=eval(Lbb); Lcscs=eval(Lcc); figure(1);plot(tt,Lasas,'k',tt,Lbsbs,'r',tt,Lcscs,'b','linewidth',4);

98

APPENDIX 5: M-file code of IPM Motor for Short pitched, Full-pitched and concentrated winding for four

poles MMF diagram

clear; clc; B=0.8; C=0.6; D=pi*(1-C)/2; E=pi*C; s1=[zeros(1,180) ones(0,0.8)]; s2=[0.8*ones(1,540) ones(0.8,0)]; s3=[zeros(1,180)]; s4=[zeros(1,180) ones(0,-0.8)]; s5=[-0.8*ones(1,540) ones(-0.8,0)]; s6=[zeros(1,180)]; s7=[zeros(1,180) ones(0,0.8)]; s8=[0.8*ones(1,540) ones(0.8,0)]; s9=[zeros(1,180)]; s10=[zeros(1,180) ones(0,-0.8)]; s11=[-0.8*ones(1,540) ones(-0.8,0)]; s12=[zeros(1,180)]; A=[s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12]; tt1=linspace(0,2*pi,3600); plot(tt1,A,'k-','linewidth',2); grid minor; xlabel('4\pi [rad]'); ylabel('[B]'); title('Four Poles MMF Diagram'); ylim([-1 1]);

99

APPENDIX 6: M-file code of IPM Motor for Short pitched, Full-pitched and concentrated winding for

Airgap

clear; clc; g1=0.3; g2=50; s1=[ones(1,25)*(1/g1) ones(1,50)*(1/g2)]; s2=[ones(1,50)*(1/g1) ones(1,50)*(1/g2)]; s3=[ones(1,50)*(1/g1) ones(1,50)*(1/g2)]; s4=[ones(1,50)*(1/g1) ones(1,50)*(1/g2)]; s5=[ones(1,25)*(1/g1)]; A=[s1 s2 s3 s4 s5]; tt1=linspace(0,2*pi,400); plot(tt1,A,'k-','linewidth',2);grid minor; xlabel('\pi [rad]'); ylabel('Stator tooth length'); title('AIRGAP'); ylim([-1 4]);

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