an innovative concept to compensate induced voltage drop in axial flux permanent magnet wind turbine...

7/31/2019 An Innovative Concept to Compensate Induced Voltage Drop in Axial Flux Permanent Magnet Wind Turbine Gener

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AN INNOVATIVE CONCEPT TO COMPENSATE INDUCED VOLTAGE DROP IN

AXIAL FLUX PERMANENT MAGNET WIND TURBINE GENERATOR

HASHEM HASSAN ABED

COLLEGE OF GRADUATE STUDIES,

UNIVERSITI TENAGA NASIONAL

2012


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AN INNOVATIVE CONCEPT TO COMPENSATE INDUCED VOLTAGE DROP IN

AXIAL FLUX PERMANENT MAGNET WIND TURBINE GENERATOR

By

HASHEM HASSAN ABED

A Dissertation Submitted in Partial Fulfilment of

the Requirements for the Degree of Master in Electrical Engineering,

COLLEGE OF GRADUATE STUDIES,

Universiti Tenaga Nasional

MAY 2012


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i

Abstract

Wind energy is a viable option to complement other types of pollution-free generation.

A given wind turbine has a rated wind speed that is generally defined by its mechanical

and electrical characteristics. Energy extraction for the wind turbine, designed for a

rated speed and energy profile, is lower than rated value as the wind pattern continuously

varies.

This dissertation discusses the development of an innovative concept for axial

flux direct-drive permanent magnet variable speed power generator for wind power

applications. The proposed concept is able to compensate induced voltage drop during

low wind speeds by shifting the permanent magnet poles of the axial flux machine

radially. An analytical model of the concept layout is developed, using mathematical

modeling techniques in MATLAB, and the modeled equations are modified based on

the new expressions derived from the variable radius AFPM design concept.

Results obtained from the analytical model of the new axial flux permanent magnet

design concept shows that the stator coil induced voltage has less dependency on the

angular speed of the wind turbine which reflects better stability of the system in lower

angular speeds. The model also suggests an increase in the overall annual power

generation.


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ACKNOWLEDGEMENT

As humans we should be thankful to our only creator, the Almighty God, who did create

the entire creatures and from among them he bestowed knowledge, dignity and honor

for the mankind. Then first and foremost, I would like to express my sincere gratitude

to my supervisor Assoc. Prof. Engr. Dr. Vigna Kumaran for the continuous support for

my master research, patience, motivation, enthusiasm, and immense knowledge. His

guidance helped me in all the time of my study and research.

Besides my supervisor, I would like to thank my co-supervisor Assoc. Prof. Ir. Dr. Faris

Tarlochan for giving me a great boost in my research tools through his vast knowledge

in mathematical modeling and analysis.

My thanks to Mr. Syed Khaleel and Mr. Mohd Fairuz bin Hj. A. Gani for the latex

lectures and support they have provided to help me writing my dissertation. I thank my

fellow power systems lab-mates for the stimulating discussions, and for all the fun we

have had in the last six months.

Also I thank all my friends in Universiti Tenaga Nasional. Last but not the least, I would

like to thank my family and especially my parents, for supporting me throughout my life

which I owe it to them along with all my achievements.


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Contents

Page

ABSTRACT i

ACKNOWLEDGEMENT ii

DECLARATION iii

CONTENTS iv

LIST OF FIGURES vii

LIST OF TABLES ix

LIST OF SYMBOLES AND SUBSCRIPTS x

LIST OF ABBREVIATIONS xi

Chapter 1 INTRODUCTION 1

1.1 Wind Energy Background 1

1.2 History of Axial Flux Permanent Magnet 2

1.3 Problem Statement 6

1.4 Objectives 6

1.5 Scientific Contribution of the Work 7

1.6 Scope of Work and Methodology 7

1.7 Summary of Chapters 8

Chapter 2 FEATURES OF AXIAL FLUX PM MACHINES 10

2.1 Introduction 10

2.2 AFPM Classification 11

2.3 Permanent Magnet Materials 12

2.3.1 Properties of Neodymium-iron-boron Permanent Magnets 13

2.4 Construction of AFPM 15


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2.4.1 Single Sided Machines 15

2.4.2 Double-Sided Machines With Internal PM Disc Rotor 15

2.4.3 Double-Sided Machines With Internal Ring-Shaped Core Stator 16

2.4.4 Double Sided Salient Pole AFPM 17

2.4.5 Torque Production in AFPM 19

2.5 AFPM Machines Without Stator Cores 20

2.5.1 Advantages and Disadvantages of Cor-less Stators 22

2.5.2 Calculation of Core-less Winding Inductance 24

2.6 Induced Voltage Equations for Overlapping Stator Winding 24

2.6.1 Stator Element Induced Voltage 26

2.6.2 Stator Coil Induced Voltage 27

2.7 Summary 28

Chapter 3 WIND TURBINES FOR ELECTRIC POWER GENERATION 29

3.1 Introduction 29

3.2 Power in the Wind 30

3.2.1 Kinetic Energy in a Parcel of Air 31

3.2.2 Wind Power Extraction 32

3.2.2.1 Coefficient of Power of Wind Turbine System 33

3.2.2.2 Wind Turbine Tip Speed Ratio 36

3.3 Wind Turbine Electrical Generator Types 37

3.4 AFPM Machines and Wind Power Generation 41

3.5 Summary 42

Chapter 4 ANALYTICAL MODEL 43

4.1 Explaining the Concept of Variable Radius AFPM 45

4.1.1 Considering Each Coil As a Fictitious Electric Generator 46

4.2 Plotting the Torque Versus Poles Radius 484.3 Choosing Suitable AFPM Machine Type 51


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4.3.1 Advantages of AFPM Machines with Slot less Windings 52

4.4 Modeling Stator Coil Induced Voltage 53

4.4.1 Creating an Expression for Coil Side Angle with Radius 56

4.4.2 Creating an Expression for Radius Change with Shaft Speed 57

4.4.3 Slicing Active Portion of Stator Coil 58

4.5 Finalizing the Analytical Model 59

4.6 Summary 60

Chapter 5 RESULTS AND DISCUSSION 62

5.1 Induced Voltage for Range of Shaft Speeds with Fixed Radius 63

5.2 Induced Voltage for Range of Radii with Fixed Shaft Speed 64

5.3 Coil Side Angle Change with Slice Radius 65

5.4 Max Induced Voltage versus Coil Side Angle 66

5.5 Max. Induced Voltage versus Machine Outer Radius Shift 67

5.6 Coil Voltage Versus Radius Shift in Different Shaft Speeds 67

5.7 Coil Voltage versus rpm and Radius Shift 68

5.8 Coil Voltage versus rpm and Radius Shift in Different Outer Radius

Ranges 70

5.9 Summary 73

Chapter 6 CONCLUSION AND RECOMMENDATION FOR FUTURE

WORK 75

6.1 Recommendations for Future Work 76

BIBLIOGRAPHY 77

APPENDICES 85


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vii

List of Figures

Figure No. Page

1.1 Types of AFPM machine configurations 4

1.2 Research methodology 8

2.1 Basic topologies of AFPM machines 12

2.2 Historical development of rare earth magnets 13

2.3 Single sided disc type machines structure 16

2.4 Double-sided machines with one slot-less stator cross section 17

2.5 Double-sided Machines with One Slot-less Stator Internal View 18

2.6 Double-sided machine with one internal slotted stator and buried

PMs 19

2.7 Windings and PM polarities of a double-sided rotor with one

internal slot-less stator 20

2.8 Double-sided AFPM Brush Less Machine with Internal Salient-

pole Stator and Twin External Rotor 21

2.9 Double-sided AFPM brush less machine with 3-phase, 9-coil

external salient-pole stator and 8-pole internal rotor 22

2.10 Stator conductors and the interacting magnet flux density on the

stator disk 23

2.11 Cartesian Halbach array 23

2.12 Layout and dimensions of a normal three-phase overlapping air-

cored stator winding 25

2.13 Single-turn coil in sinusoidal field 26

3.1 Packet of air moving with speed u 32

3.2 Power in the wind and power extraction 33


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3.3 Wind speed versus power coefficient Cp 34

3.4 Typical wind-speed probability density curve 36

3.5 Tip speed ratio versus power coefficient Cp 37

3.6 Wind turbine generating systems 39

4.1 Methodology flow chart 44

4.2 AFPM coils as a fictitious electric generators 48

4.3 Fictitious generators at short radius 49

4.4 Breaking torque versus active radius of the fictitious generator set 50

4.5 Power versus wind speed 51

4.6 Layout of normal overlapping stator winding 54

4.7 Coil side angle change with radius 55

4.8 Coil side angle tangent 56

4.9 PM poles shift radius as rpm change 57

4.10 Slicing active radius 59

5.1 Induced coil voltage versus time at fixed radius 64

5.2 Coil side angle vs. slice radius 65

5.3 Slice induced voltage factor (k) vs. slice radius 66

5.4 Max induced coil voltage vs. shaft speed 67

5.5 Induced voltage versus radius shift 68

5.6 Coil induced voltage versus outer radius shift at (200, 225, 250) rpm 69

5.7 Coil induced voltage versus shaft rpm and radius shift 70

5.8 Coil voltage versus shaft rpm in different outer radius ranges 71

5.9 Stator coil voltage versus shaft speed with average outer radius at

(0.23) meter 72

5.10 Coil voltage for fixed and variable radius setup with shaft speed 73

5.11 Typical wind-speed probability density curve 74


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List of Tables

Table No. Page

2.1 Typical properties for Nd-Fe-B magnets 15

4.1 Fictitious machine parameters 49

5.1 Machine parameters 63

5.2 Max induced voltage versus shaft speed at fixed outer radius 63

5.3 Max induced voltage versus radius in steps 64


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LIST OF SYMBOLES AND SUBSCRIPTS

Coil position

Flux linkage (in weber turns)

Electrical speed (in radians per second).

polegen Angular speed of the fictitious electric generator

rotor Angular velocity of AFPM rotor

m Coil pitch, Slot pitch angle

la The spatial period (wavelength)

nM The number of PM pieces per wavelength

rpolegen The radius of the fictitious electric generator

rrotoract Active Radius of the AFPM rotor

rrotorav The average active radius of the AFPM rotor

tw The thickness of the stator winding

vpmav Average linear velocity of the permanent magnet poles with respect to the

windings in the stator


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LIST OF ABBREVIATIONS

Sm-Co - Samarium-Cobalt Permanent Magnet

Nd-Fe-B - Neodymium-Iron-Boron Permanent Magnet

HAWT - Horizontal-Axis Wind Turbine

VAWT - Vertical-Axis Wind Turbine

PMSG - Permanent Magnet Synchronous Generator

AFPM - Axial Flux Permanent Magnet

VRAFPM - Varialbe Radius Axial Flux Permanent Magnet


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CHAPTER 1

INTRODUCTION

1.1 Wind Energy Background

Every unit (kWh) of electricity produced by the wind displaces a unit of electricity

which would otherwise have been produced by a power station burning fossil fuel.

However, this is not the only benefit of pollution free wind energy; about 1.6 billion

people or a quarter of the worlds population lack the access to electricity and many of

those people are in rural areas with no hope of connection to the electrical grid [1].

The availability of wind turbine generators can be a life saver for areas that have

average wind speeds, where electricity can be produced. The main advantages of

electricity generation from wind like any other renewable resource are the absence of

harmful emissions and the infinite availability of the prime mover that is converted into

electricity.

Variable speed operation and direct drive generators have been the recent developments

in wind turbine drive trains. Compared with constant speed operation, variable speed

operation of wind turbines provides 1015% higher energy output, lower mechanical

stress and less power fluctuation. In order to fully realize the benefits of variable

speed wind power generation systems (WPGS), it is critical to develop advanced control

methods to extract maximum power output of wind turbines at variable wind speeds [2].


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1.2 History of Axial Flux Permanent Magnet

The history of electrical machines shows that the first machine designed was realized

in a form of the axial-flux machine. The first primitive working prototype of an axial

flux machine ever recorded was M. Faradays disc (1831). The disc type construction

of electrical machines also appears in N. Teslas patents, e.g. U.S. patent No. 405 858

[P2] entitled Electromagnetic Motor and published in 1889.

Radial-flux machines were invented later and were patented firstly by Davenport in

1837 [3]. Since then, radial-flux machines have dominated the markets of the electrical

machines. The first attempts to enter the industrial motor market with radial-flux

Permanent Magnet Synchronous Machine (PMSM) in the 1980s was made by the

former BBC, which produced line-start motors with SmCo-magnets.

With wind power rapidly becoming one of the most desirable alternative energy sources

world-wide, wind turbine power system are becoming more and more a de facto element

in any sustainable energy project where a low speed Axial Flux Permanent Magnet

(AFPM) generator is usually driven by a wind turbine. AFPM generators offer the

ultimate low cost solution as compared with solar panels [4].

Permanent magnet generator is like the synchronous or AC generator except that the

rotor field is produced by permanent magnets rather than current in a coil of wire. This

means that no field supply is needed, which simplify the construction and reduces costs.

It also means that there is no I2R power losses in the excitation field, which helps to

increase the efficiency.

One disadvantage is that the reactive power flow cannot be controlled if the PM

generator is connected to the utility network. This is of little concern in an asynchronous

mode [5].


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The main idea in the early stage of the PMSMs was to increase the efficiency of the

traditional electric motors by permanent magnet excitation. However, the efficiency

increase was not enough for the customers and the attempts to enter the market failed

and there were multiple reasons for abandoning the axial flux machine which may be

summarized as follows:

Strong axial (normal) magnetic attraction force between the stator and rotor;

Fabrication difficulties, such as cutting slots in laminated cores and other methods

of making slotted stator cores;

High costs involved in manufacturing the laminated stator cores;

Difficulties in assembling the machine and keeping the uniform air gap.

Despite this setback, several manufacturers introduced permanent-magnet machines

successfully during the latest decade. Regardless of the success of radial-flux

permanent-magnet machines, axial-flux permanent magnet machines have also been

under research interest particularly due to special-application limited geometrical

considerations. A possibility to obtain a very neat axial length for the machine makes

axial-flux machines very attractive applications in which the axial length of the machine

is a limiting design parameter. Such applications are, for example, electrical vehicles

wheel motors [6] and elevator motors [7]. Axial flux machines have usually been used

in integrated high-torque applications. Possible configurations are:

Structure with one rotor and one stator, see Fig. 1.1 (a).

Structure, in which the stator is located between the rotors, Fig. 1.1 (b).

Structure, in which the rotor is located between the stators, Fig. 1.1 (c).

Multistage structure including several rotors and stators Fig. 1.1 (d).


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Figure 1.1 Types of AFPM machine configurations

The single-rotor single-stator structure, shown in Fig. 1.1 (a) is the simplest axial-flux

permanent-magnet machine configuration [8] but this structure suffers, however, from

an unbalanced axial force between the rotor and the stator.

This demands a more complex bearing arrangements and a thicker rotor disk to maintain

a constant air gap, which is easily accomplished in structures in which axial forces are

balanced like the double lateral rotors. Shown in Fig. 1.1 (b) is a TORUS type

axial-flux machine, that has its phase coils wound around the slotted stator [9, 10] or

non-slotted stator.

The first TORUS type permanent-magnet machine, with non slotted stator, was

introduced in the late 1980s [11]. The toroidally wound phase winding has short end-

windings, which improves the machine efficiency and power density.


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As a drawback, the fixing of the stator to the frame is more complex, and compared to

the opposite structure in which the rotor is located between the stators, less space is left

for the winding [12, 13].

More complex arrangements can be found by assembling several machines lined up on

the same shaft and by forming a multistage axial-flux machine according to Fig1.1 (d).

Such machines may be considered for ship propulsion drive use [14], Adjustable-Speed

Pump Application [15] and high-speed permanent-magnet generator applications [16]

and machine research purposes like unbalanced load sharing [17].

Permanent Magnet Axial Flux machines are increasingly adopted for many reasons;

the decrease cost for low earth magnets, comprehensive research, versatile approaches

and designs following the advances in AFPM newly created applications like electric

vehicle, along with low rotation speeds generation, to name a few.

These machines propose many exceptional features. They are usually more efficient

then their radial flux sibling because their field excitation losses are eliminated resulting

in considerable rotor loss reduction. Thus, the machine efficiency is greatly improved

and higher power density is achieved. Moreover, AFPM machines have small magnetic

thickness which results in small magnetic dimensions. The wide availability and

reducing cost of high-remanence, neodymium-iron-boron (NdFeB) permanent magnets

have made axial-flux machines a cost-effective alternative for low-and medium-power

motor and generator applications.

The very short axial length required to accommodate the magnetic and electric

components can lead to designs that do not require separate bearings and the high

moment of inertia of the rotor can serve a useful flywheel function. Particular examples

of the use of axial-flux machines are for direct drive wind generators, compact engine-

generator sets, either for general applications [18] or in a hybrid electric vehicle, or as


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in-wheel electric motors [19, 20].

1.3 Problem Statement

Wind energy is clean, abundant and a continuously growing power industry in the last

two decades. A given wind-turbine has a rated wind speed that is generally defined by

its mechanical and electrical characteristics.

Energy extraction for the wind turbine, designed for a rated speed and energy profile, is

lower than rated value as the wind pattern continuously varies.

To maintain the energy extraction performance in such conditions, the electromechani-

cal power system should continuously adapt and match the variable wind energy profile.

This dissertation focuses on increasing the stability of the stator coil induced voltage

of the generator, through dynamically modifying its electro-mechanical characteristics.

This is obtained by shifting rotor poles radius, to suit the variable angular speeds

delivered from the wind turbine, thus maintaining the energy extraction performance.

1.4 Objectives

A given wind turbine power generator have a fixed mechanical and electrical

characteristics optimized to operate in a rated wind speed, and as the wind pattern

continuously varies, the actual energy extracted over a period of time will be less than

the rated.

The objective of the dissertation is to develop an analytical model of the stator coil

voltage based on a new concept AFPM design to stabilize stator coil voltage in lower


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and higher than the rated wind speed.

In the literature, several new and promising AFPM topologies are discussed. Axial flux

surface magnet PM machines including slot-less and slotted topologies with different

number of rotors and stators are also reviewed.

1.5 Scientific Contribution of the Work

The scientific contributions are:

1. A review study for the latest research in low speed high efficiency AFPM for the

purpose of wind power electrical generation have been provided.

2. This dissertation introduced an innovative concept of AFPM power generator that

withstands lower wind speeds by utilizing a variable active stator radius design

concept to maintain stable level of stator coil induced voltage at lower and higher

speeds than the generator rated speed.

1.6 Scope of Work and Methodology

The scope of this dissertation covers the literature review of the advancement in AFPM

and its increasing importance in low speed direct drive wind turbines.

The methodology used in this dissertation is summarized in the flow chart shown in Fig.

1.2.

The scope of work in this dissertation is confined to the analytical model of the stator

coil induced voltage in distributed slot less and core less winding AFPM machine in

relation with the variable shaft speed.


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Figure 1.2 Research methodology

The parameters that are affected by the radius shift and have direct effect on the stator

coil induced voltage of the machine are covered in general.

The analytical model is kept relatively simple, to provide a better understanding

for the new concept, and the possibilities for future developments. Thereby, some

simplifications are included in the computation model; e.g. air gap flux leakage is

neglected.

1.7 Summary of Chapters

The chapters of this dissertation are organized in the following manner:


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Chapter 2 gives a description about the principles of types of AFPM and their

structure topologies. The chapter also presents the latest research advancement in

AFPM, particularly for power generation purposes.

Chapter 3 focuses on the wind power generation systems and the rule of AFPM

in direct drive wind power generation.

Chapter 4 presents the new concept of variable radius AFPM and the analytical

model to represent it.

Chapter 5 contains the analytical modeling results for the variable radius AFPM

operating in a range of rotating speeds, and discusses the results obtained from

MATLAB modeling.

Chapter 6 concludes the results and findings, and gives recommendations for

further research.


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CHAPTER 2

FEATURES OF AXIAL FLUX PM MACHINES

2.1 Introduction

The history of electrical machines shows that the first machines were realized in a

form of the axial-flux machine. The first one was invented by Faraday in 1821 and

was practically a primitive permanent-magnet DC machine [21]. Radial-flux machines

were invented later and were patented firstly by Davenport in 1837 [3]. Since then

radial-flux machines have dominated excessively the markets of the electrical machines.

The main idea in the early stage of the PMSMs was to increase the efficiency of

the traditional electric motors by permanent magnet excitation. Axial-flux permanent

magnet machines have also been under research interest particularly due to special-

application limited geometrical considerations. A possibility to obtain a very neat axial

length for the machine makes axial-flux machines very attractive into applications in

which the axial length of the machine is a limiting design parameter. Such applications

are, for example, electrical vehicles wheel motors [6] and elevator motors [7]. Axial

flux machines have usually been used in integrated high-torque applications.

In this chapter, the basic principles of the AFPM machine are explained. Classification

of the AFPM is given and considerable attention is paid to the machine variant

topologies and construction, as well as presenting the role of high performance

permanent magnet materials in its development. The torque production and stator coil

induced voltage equations are also presented in this literature.


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2.2 AFPM Classification

Axial flux machines may be classified [22] as follows:

Single-sided AFPM machines

with slotted stator (Fig. 1.3a)

with slot less stator

with salient-pole stator

Double-sided AFPM machines

with internal stator (Fig. 1.3b)

* with slotted stator

* with slot less stator

with iron core stator

with core less stator (Fig. 1.3d)

without both rotor and stator cores

* with salient pole stator

with internal rotor (Fig. 1.3c)

* with slotted stator

* with slot less stator

* with salient pole stator

multistage (multi-disc) AFPM machines


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Figure 2.1 Basic topologies of AFPM machines: (a) single-sided slotted machine, (b)

double-sided slot less machines with internal stator and twin PM motor, (c)

double-sided slotted stator and internal PM rotor, (d) double-sided core less motor with

internal stator. 1-stator core, 2-stator winding, 3-rotor, 4-PM, 5-frame, 6-bearing, 7-shaft [22]

2.3 Permanent Magnet Materials

The development of rare earth permanent magnet materials started in the 1960s with the

Samarium-Cobalt alloys. The material properties of SmCo5 and Sm2Co17 make these

permanent magnet materials very suitable to be used in electric motors and generators,

but they are expensive due to the rare raw material Cobalt.

The newest, important addition to permanent magnet materials was made in 1983,

when the high performance Neodymium-Iron-Boron permanent magnet material was

introduced which is comparing to Sm-Co permanent magnets offer compatible material

properties but are much cheaper. A historical development of the rare earth permanent

magnets is illustrated in Fig 2.2.


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Figure 2.2 Historical development of rare earth magnets [23]

With the development of the high performance Nd-Fe-B permanent magnet materials,

a trend towards the use of permanent-magnet machines in large-scale industrial

applications got started and is recently proven by Waltzer. As the design of a permanent-

magnet machine is concerned, it is relevant to understand some properties of the

permanent magnet materials discussed in detail by Campbell [23].

2.3.1 Properties of Neodymium-iron-boron Permanent Magnets

Recently, Nd-Fe-B magnet material with remanence a flux density Br of 1.52 T and a

maximum energy product of 440 kJ/m3 was reported [24]. An Nd-Fe-B magnet material

of this grade has become commercially available since the year 2004 and the values

are close to the practical performance limit of sintered Nd-Fe-B magnets because the

theoretical maximum energy product for Nd1Fe14B1 crystal is 510 kJ/m3.


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These high performance grades, however, suffer from a temperature dependency, as

the maximum operating temperature is limited to about 100 degrees Celsius. This is

related to the strong temperature dependence of the neodymium magnetic moment. As

the temperature increases, there appears a rapid drop in the magnetization and an even

faster decline in the intrinsic coercivity to zero at about 250 C.

The temperature tolerance of Nd-Fe-B magnets can be improved by replacing

neodymium atoms partially with dysprosium and by replacing iron partially with cobalt,

which improves the temperature behavior of the compound. However, dysprosium and

cobalt have an anti-ferromagnetic coupling, thus the magnetization and the maximum

energy product is reduced.

The best Nd-Fe-B grades, capable of tolerating temperatures up to 200 C, have

remanence flux densities of about 1.2 T and have their maximum energy product of

300 kJ/m3 at a 20 C temperature.

Nd-Fe-B materials are conductors with a resistivity of about 1.5 m at a 20C

temperature but with a rather poor thermal conductivity, about 9W/mK. For the surface-

mounted structures this may be problematic because there appear eddy currents in

the permanent magnet material due to spatial and current harmonics. Since the heat

conductivity is fairly poor, an excessive temperature rise in the magnet material is

possible. This, typically, does not concern buried magnets, since the effects caused

by the harmonics are mainly focused on the rotor iron near the air-gap surface. Typical

values for Nd-Fe-B as well as for plastic bonded Nd-Fe-B magnets are gathered in Table

2.1.


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Table 2.1 Typical properties for Nd-Fe-B magnets [24]

2.4 Construction of AFPM

Axial flux machines are formed by one or more rotor discs carrying magnets that

produce an axial flux and one or more stator discs containing the stator windings with

one or more disk shaped air gaps. Many variations in this basic design are possible.

2.4.1 Single Sided Machines

The single-sided construction of an axial flux machine is simpler than the double-sided

one, but the torque production capacity is lower. Fig. 2.3 shows typical constructions of

single-sided AFPM brush-less machines with surface PM rotors and laminated stators

wound from electromechanical steel strips. The single-sided motor according to Fig.

2.3a has a standard frame and shaft. It can be used in industrial, traction and servo

electromechanical drives. The motor for hoist applications shown in Fig. 2.3b is

integrated with a sheave and brake. It is used in gear-less elevators [22, 7].

2.4.2 Double-Sided Machines With Internal PM Disc Rotor

In the double-sided machine with internal PM disc rotor, the armature winding is located

on two stator cores. The disc with PMs rotates between two stators. An eight-pole

configuration is shown in Fig. 2.4. PMs are embedded or glued in a nonmagnetic

rotor skeleton. The nonmagnetic air gap is large, i.e. the total air gap is equal to two

mechanical clearances plus the thickness of a PM with its relative magnetic permeability


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Figure 2.3 Single sided disc type machines: (a) for industrial and traction

electromechanical drives, (b) for hoist applications. 1 laminated stator, 2 PM, 3

rotor, 4 frame, 5 shaft, 6 sheave [22].

close to unity. A double-sided machine with parallel connected stators can operate even

if one stator winding is broken. On the other hand, a series connection is preferred

because it can provide equal but opposing axial attractive forces [22, 25].

2.4.3 Double-Sided Machines With Internal Ring-Shaped Core Stator

A double-sided machine with internal ring-shaped stator core has a poly-phase slot-less

armature winding (toroidal type) wound on the surface of the stator ferromagnetic core

[26, 27]. In this machine, the ring-shaped stator core is formed either from a continuous

steel tape or sintered powders. The total air gap is equal to the thickness of the stator

winding with insulation, mechanical clearance and the thickness of the PM in the axial

direction. The double-sided rotor simply called twin rotor with PMs is located at two

sides of the stator. The configurations with internal and external rotors are shown in

Fig. 2.5. The three phase winding arrangement, magnet polarities and flux paths in the


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Figure 2.4 Double-sided machines with one slot-less stator cross section: (a) internal

rotor, (b) external rotor. 1 stator core, 2 stator winding, 3 steel rotor, 4

PMs, 5 resin, 6 frame, 7 shaft [22]

magnetic circuit are shown in Fig. 2.7. The AFPM machines designed as shown in Fig.

2.5a can be used as a propulsion motor or combustion engine synchronous generator.

The machine with external rotor, as shown in Fig. 2.5b, has been designed for hoist

applications.

A similar machine can be designed as electric car wheel propulsion motor. Additional

magnets on cylindrical parts of the rotor are sometimes added or U-shaped magnets can

be designed. Such magnets embrace the armature winding from three sides and only the

internal portion of the winding does not produce any electromagnetic torque.

2.4.4 Double Sided Salient Pole AFPM

The double-sided salient-pole AFPM brush less machine shown in Fig. 2.8 have the

stator coils with concentrated parameters wound on axially laminated poles. To obtain a

three-phase self-starting motor, the number of the stator poles should be different from

the number of the rotor poles, e.g. 12 stator poles and 8 rotor poles [26, 28]. Fig. 2.9


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Figure 2.5 Double-sided Machines with One Slot-less Stator Internal View: (a) internal

rotor, (b) external rotor. 1 stator core, 2 stator winding, 3 steel rotor, 4

PMs, 5 resin, 6 frame, 7 shaft [22]

shows a double-sided AFPM machine with external salient pole stators and internal PM

rotor. There are nine stator coils and eight rotor poles for a three-phase AFPM machine.

Depending on the application and operating environment, slot less stators may have

ferromagnetic cores or be completely core less. Core less stator configurations eliminate

any ferromagnetic material from the stator (armature) system, thus eliminating any eddy

current and hysteresis core losses in it. This type of configuration also eliminates axial

magnetic attraction forces between the stator and rotor at zero-current state. Slot less

AFPM machines can also be classified according to their winding arrangements and coil

shapes [29, 30, 31]

Toroidal.


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Figure 2.7 Three phase winding, PM polarities and magnetic flux paths of a

double-sided disc machine with one internal slot-less stator. 1 winding, 2 PM, 3 stator yoke, 4 rotor yoke [22]

where r is the radius at which the torque is produced and B is the flux density. Using

these basic formulas the sizing equation may be written in terms of the magnet flux and

the stator ampere-conductor distribution.

In Fig. 2.10 the stator conductors on a radial cross-section (in xy plane) and the

interacting magnet flux, which is in axial direction, are shown on a disk stator unit.

Since equation 2.1 and 2.2 only valid for one conductor, so in order to determine the total

amount of torque, first the sinusoidal ampere-conductor distribution must be formalized.

2.5 AFPM Machines Without Stator Cores

Core less configurations eliminate any ferromagnetic material, i.e. steel lamination or

SMC powders from the stator (armature), thus eliminating the associated eddy current

and hysteresis core losses. Because of the absence of core losses, a core less stator

AFPM machine can operate at higher efficiency than conventional machines. On the

other hand, owing to the increased nonmagnetic air gap, such a machine uses more PM

material than an equivalent machine with a ferromagnetic stator core.


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Figure 2.8 Double-sided AFPM brush less machine with internal salient-pole stator

and twin external rotor: (a) construction; (b) stator; (c) rotor. 1 PM, 2 rotor

backing steel disc, 3 stator pole, 4 stator coil [29]

Stators of AFPM machines may have solid ferromagnetic cores or be completely core

less, depending on the application and operating environment. A core less stator AFPM

machine has an internal stator and twin external PM rotor (2.1.d). PMs can be glued to

the rotor backing steel discs or nonmagnetic supporting structures. In the second case

PMs are arranged in Halbach array Fig. 2.11. The key concept of Halbach array is that

the magnetization vector of PMs should rotate as a function of distance along the array.

Halbach array has the following advantages [33]:

The fundamental field is stronger by a factor of 1.4 than in a conventional PM

array, and thus the power efficiency of the machine is doubled;

The array of PMs does not require any backing steel magnetic circuit and PMs

can be bonded directly to a non-ferromagnetic supporting structure (aluminum or

plastics).

The magnetic field is more sinusoidal than that of a conventional PM array.

Halbach array has very low back-side fields.

The peak value of the magnetic flux density at the active surface of Halbach array is:


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Figure 2.9 Double-sided AFPM brush less machine with three-phase, 9-coil external

salient-pole stator and 8-pole internal rotor. 1 PM, 2 stator backing

ferromagnetic disc, 3 stator pole, 4 stator coil [29]

Bm0 =

Br[

1exp(h

M)]

sin(/nM)

/nM(2.3)

where Br is the remanent magnetic flux density of the magnet (= 2/la), the spatial

period (wavelength) la of the array and nM is the number of PM pieces per wavelength

[33].

2.5.1 Advantages and Disadvantages of Cor-less Stators

The electromagnetic torque developed by a core less AFPM brush-less machine is

produced by the open space current-carrying conductorPM interaction (Lorentz force

theorem). Core less configurations eliminate any ferromagnetic material, i.e. steel

lamination or SMCpowders from the stator (armature), thus eliminating the associated

eddy current and hysteresis core losses. Because of the absence of core losses, a core


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Figure 2.10 Stator conductors and the interacting magnet flux density on the stator disk

[32].

less stator AFPM machine can operate at higher efficiency than conventional machines.

On the other hand, owing to the increased nonmagnetic air gap, such a machine uses

more PM material than an equivalent machine with a ferromagnetic stator core [34].

Figure 2.11 Cartesian Halbach array [35]


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2.5.2 Calculation of Core-less Winding Inductance

The synchronous inductance Ls consists of the armature reaction (mutual) inductance

La and the leakage inductance L1. For a machine with magnetic asymmetry, i.e. with a

difference in reluctance in the d and q axes, the synchronous inductance in the d- and

q-axis, Lsd and Lsq, are written as sums of the armature reaction inductance (mutual

inductance), Lad and Laq, and leakage inductance L1, i.e.

Lsd = Lad +L1 (2.4)

It is difficult to derive an accurate analytical expression for 1s for a core less electrical

machine. The specific permeances 1s and 1e can roughly estimated from the following

semi-analytical equation [34]:

1s 1e 0.3q1 (2.5)

The specific permeance for the differential leakage flux can be found in a similar way

as for an induction machine. The thickness of the stator winding is tw and the distance

from the stator disc surface to the PM active surface is g (mechanical clearance).

2.6 Induced Voltage Equations for Overlapping Stator Winding

The layout and dimensions of a three-phase overlapping air-cored stator winding are

shown in Fig. 2.12.


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Figure 2.12 Layout and dimensions of a normal three-phase overlapping air-cored

stator winding [34]

Only one coil per pole pair per phase is used in these types of windings; there is, in this

case, no need for a distributed winding as a coil side is already distributed over one-third

of a pole pitch, and furthermore, the axial air-gap flux density in these machines is quite

sinusoidal [22, 36]. Assuming the axial flux density in the air gap is sinusoidal, Fig.

2.13 shows a coil pitch ofm = , and the coil at position with respect to the flux

density wave, the flux linkage of a turn element of radial length dr at radius r can be

determined by

=

+

+

Bp sinrd2

pdr (2.6)


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where is flux linkage (in Weber turns) and r/2 < < +r/2 . Executing the

integral of 2.6 with = t results in the following for the element flux linkage [37]:

=

4

pBprdrcos()

cos(t) (2.7)

Figure 2.13 Single-turn coil in sinusoidal field [37]

2.6.1 Stator Element Induced Voltage

The element voltage eelm =d/dt is then given by:

eelm =

4

pBprdrcos()

sin(t) (2.8)

All the element voltages in equation 2.8 at different s are in phase as their magnetic

axis are the same. From 2.8the layer voltage can be determined assuming a continuous

layer with N conductors:


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elayer =4

pBprdrNkpsin(t) (2.9)

with kp given by:

kp =1

r

+r2

r2

sin(

2)d

=2sin(r/2)

r(2.10)

2.6.2 Stator Coil Induced Voltage

The coil voltage can be determined from 2.9 in a simple way by dividing the active

length of the winding in a number of slices u each with a length drj = l/u at an average

radius rj as [37]:

ecoil =4

pBpN

u

j=1

rjl2 sin(r j/2)

ur j

sin(t) (2.11)

The analytical model in chapter 4 will use this equation in modeling the stator coil

induced voltage.


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2.7 Summary

This chapter presented the literature review of the latest research papers on AFPM,

classification, structure and machine characteristics especially for power generation

usage.

Also a detailed literature has been done on the peak induced voltage in the slot less

overlapped stator coils dual rotor AFPM for the purpose of modeling later on in Chapter

4.

The findings from literature review can be summarized in the following:

Axial flux machines can be implemented in low shaft speeds without gearbox

coupling, which leads to the simplicity of machine structure, and therefore they

are more suitable to wind power applications [38][39][40].

The latest developments in high performance permanent magnet materials have

led to an increase in its energy density, and decrease its overall production cost

but it suffers lower temperature tolerance. Plastic-bond Nd-Fe-B have higher

resistivity, thus less eddy current losses which is the main cause of temperature

raise [41, 42].


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CHAPTER 3

WIND TURBINES FOR ELECTRIC POWER GENERATION

3.1 Introduction

Wind power is an important source of environmental-friendly energy and has become

more important in recent years. The amount of installed wind power is increasing every

year and many nations have made plans to make large investments in wind power in

the near future. The wind power systems used as an alternative energy resource for

electrical power generation plays a key role in rural electrification and industrialization

programs.

There are many different types of wind turbines and they can be divided into two groups

of turbines depending on the orientation of their axis of rotation:

Horizontal-axis wind turbine (HAWT)

Vertical-axis wind turbine (VAWT)

Horizontal-axis wind turbine is the most dominant, although Vertical-axis wind turbine

has better advantages [43] as it does not require a tail or a yaw mechanism to point it

into the wind. This simplifies the construction and thereby reduces the cost. There is no

loss of performance due to misalignment of the turbine axis with the wind direction as

there is with HAWT. For VAWT, the tower is not essential as it can be installed directly

on the ground.


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In this chapter, wind energy extraction process is discussed, along with all the

parameters that affect the overall energy conversion, such as the tip speed ratio and

the coefficient factor of the wind turbine system. Furthermore, the types of electrical

generators used in wind power systems are presented. The suitability of AFPM

generators used for wind power generation is explained.

3.2 Power in the Wind

The wind has been used to power sailing ships for many centuries. Many countries owed

their prosperity to their skill in sailing. The new world was explored by wind powered

ships. Indeed, wind was almost the only source of power for ships until Watt invented

the steam engine in the 18th Century [44].

Wind turbines are aerodynamic machines where the linear motion of the wind is

harnessed by the turbine blades and converted to rotational energy that used to induce

flux density rate of change applied inside the AC generator which in turn induce voltage

used to draw current to the desired loads in the form of electrical energy [45].

Most wind turbines designed for the production of electricity consist of two or three

bladed propeller, rotating around a horizontal axis, or a simpler vertical axis wind

turbine, which have lower efficiency compared to the horizontal axis wind turbine.

Furthermore, it is cheaper and has simple design. The generator parts are also located

near the ground instead of being on top of the tower [46].

In practice, the wind turbine generator is not always generating electricity, as the wind

speed naturally fluctuates between high and low speeds. Due to structural and electrical

limitations of both the turbine rotor and the generator connected to it, only part of that

speed range is useful to produce electrical energy. For the rest of the speed range, the


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system is either forced to stop rotating to protect it from over speeding or left rotating

with no generation when the wind speed is low.

3.2.1 Kinetic Energy in a Parcel of Air

The kinetic energy in a parcel of air of mass m flowing at speed u in the x direction is

[47]:

U =1

2mu2 =

1

2(Ax)u2 (3.1)

where A is cross-sectional area in meter2, is air density in kg/meter3, and x is

thickness of the parcel in meter.

Looking at the parcel in Fig. 3.1, with side x moving by speed u and the opposite side

fixed at the origin, the kinetic energy increases uniformly with x, because the air mass

is increasing uniformly.

The power in the wind, Pw, is the time derivative of the kinetic energy:

Pw =dU

dt=

1

2Au2

dx

dt=

1

2Au3 (3.2)

Equation 3.2 shows that the wind turbine power is proportional to the wind speed to the

power of three. For example, if the wind speed decreases 1m/s from 5m/s to 4m/s this

will cause the wind power to drop to almost half its value:


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Figure 3.1 Packet of air moving with speed u [47]

Pw = 5343

53 = 48.8% (3.3)

3.2.2 Wind Power Extraction

Generally, 1 kilowatt of power requires an 8 meter diameter turbine to extract from a 5

m/s or 18 kph wind speed. This assumes that the turbine is 30% efficient.

In most locations, wind speeds tend to be low and the design of wind power systems

focuses on extracting the maximum wind energy at the prevailing wind speeds.

According to Betzs limit [48], 60% of the power can be extracted from the available

wind energy, as shown in Figure 3.2. The power available in the wind is proportional to

the third power of the wind speed, and as the square of the turbine diameter, as shown

in equation 3.2. For small changes in wind speed, there is an enormous changes in the


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Figure 3.2 Power in the wind and power extraction [47]

energy extracted.

3.2.2.1 Coefficient of Power of Wind Turbine System

The coefficient of power of a wind turbine represents the aerodynamics efficiency of the

wind turbine and it is a function of the tip speed ratio. It is also a measurement of how

efficiently the wind turbine converts the energy in the wind into electricity [50].

Figure 3.3 shows that the turbine power curve can be divided into three regions:

Region 1 when the wind speed is lower than cut-in wind speed, the turbine may

rotate but with no power production.

Region 2 when the wind speed ranges between cut-in speed and rated speed, the

system will generate power lower than the rated power.

Region 3 when wind speed ranges between rated speed and cut-off speed, the


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Figure 3.3 Wind speed versus power coefficient Cp [49]

wind turbine will generate the system rated power, and above cut-off speed there

will be no generation and protection systems will be activated until wind speed

drop below cut-off limit.

Cut-in wind speed is a characteristic design of the wind power system and it depends

on:

Airfoil design and pitch angle of the blades.

Gear box ratio.

Electrical generator design.

Cut-out wind speed is defined mainly by the airfoil design and the material of the blades

and hub, as higher speeds will cause structural fatigue, due to centrifugal forces exerted


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on the structure of the wind turbine rotor.

The amount of power, P, that can be absorbed by a wind turbine, as shown in Fig. 3.3

can be found from [47]:

P =1

2CPA

3 (3.4)

where CP is the power coefficient, is the density of air, A is the swept area of the

turbine and is the wind speed.

The power coefficient Cp is a value less than 1 and indicates the power available in the

wind, and it represents the aerodynamics efficiency of the wind turbine.

Total annual wind energy available for a specific location follows a probabilistic curve

as shown in Fig. 3.4 , which can be obtained through a comprehensive data acquisition

of wind speed for that location. The amount of electrical power produced by the wind

turbine, follows a similar curve accept the part when the wind speed is not useful as

it goes below the cut-in wind speed or above the cut-off speed for the particular wind

turbine power system.

In order to study wind power in a particular site, the long term records of wind speed

have to be statistically analyzed. The most widely used statistical distribution functions

are:

The Weibull distribution which has been used to assess the potential of wind

power in many countries [51, 52].


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The Rayleigh distribution which has been widely used to fit the measured

probability distribution functions in various locations [53].

Figure 3.4 Typical wind-speed probability density curve [54]

3.2.2.2 Wind Turbine Tip Speed Ratio

The power coefficient Cp can be represented as a function of the tip speed ratio , which

is defined as the ratio of the linear speed of the blade tip to the wind speed at hub height

[55], and represented as:

=R

(3.5)

where is the rotational frequency of the turbine, R is the turbine radius and is the

wind speed at hub height.


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Assessment of tip speed ratio is a key factor in wind turbine blade design, and it is

recommended to be between 6 and 8. For example, a grid connected wind turbine with

3 blades, the optimum ratio is suggested as 7 [55].

Figure 3.5 Tip speed ratio versus power coefficient Cp [49]

Maximum aerodynamic efficiency is achieved at the optimum tip speed ratio opt, at

which the power coefficient Cp has its maximum value Cpmax . Since the rotor speed

is then proportional to wind speed , the power increases with 3 and 3, and the

torque with 2 and 2 [56].

3.3 Wind Turbine Electrical Generator Types

Three different wind turbine generating systems are widely applied. The first is the

directly grid coupled squirrel cage induction generator used in constant speed wind


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turbines.

Wind turbine rotor is coupled to the generator through a gearbox. In most turbines using

this system, the power extracted from the wind is limited using the stall effect. This

means that the rotor is designed in such a way that its aerodynamic efficiency decreases

in high wind speeds, thus preventing extraction of too much mechanical power from

the wind. When the stall effect is used, no active control systems are necessary. Pitch

controlled constant speed wind turbines have also been built.

The second system is the doubly fed or wound rotor induction generator, which allows

variable speed operation. The rotor winding is fed using a back-to-back voltage source

converter. Like in the first system, the wind turbine rotor is coupled to the generator

through a gearbox. In high wind speeds, the power extracted from the wind is limited

by pitching the rotor blades.

The third system is a direct drive synchronous generator, also allowing variable speed

operation. The synchronous generator coil has a wound rotor or be excited using

permanent magnets. It is grid coupled through a back-to-back voltage source converter

or a diode rectifier and voltage source converter. The synchronous generator is a low

speed multi-pole generator; therefore, no gearbox is needed.

Like in the second system, the power extracted from the wind is limited by pitching the

rotor blades in high speeds. The three wind turbine generating systems are depicted in

Fig. 3.6.

The direct drive generator have a wound rotor or a rotor with permanent magnets,

while the stator windings is not coupled directly to the grid, but to a power electronics

converter in order to decouple the wind turbine system from the grid [58].


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Figure 3.6 Wind turbine generating systems [57]

The efficiency and reliability of the direct coupled permanent magnet synchronous

generator (PMSG) is improved compared to the conventional wind power generation

system [59].

Wind turbine systems with induction generator were popular [60, 61] more than any

other wind turbine generator types. This has recently changed after the advancements

in permanent magnet (PM) materials that caused greater availability and decreasing cost

of high-energy permanent-magnet (PM) materials. Neodymium-Iron-Boron (NdFeB),

in particular, has resulted in rapid permanent magnet generator development, especially


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for wind energy conversion applications.

PM machine advantages [62] include:

Lightweight

Small size

Simple mechanical construction

Easy maintenance

Good reliability

High efficiency

Absence of moving contacts

PM generators can deliver power without undergoing the process of voltage

buildup

No risk of excitation loss

Permanent magnet machines usually have higher efficiency and are more compact than

electrically excited machines. However, they are still considerably more expensive and

require more advanced rectifiers because they dont allow for reactive power or voltage

control [63].

Compared with geared-drive wind generator systems, the main advantages of direct-

drive wind generator systems are higher overall efficiency, reliability and availability.

Although, the size of direct-drive generators is usually larger, it may not be a serious

disadvantage for offshore wind energy [64].

AFPM machines fall into this type and it is the focus of this dissertation. The direct

drive term indicates that it has no gearbox to adjust the shaft speed.


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The output power is usually rectified and then inverted to match the utility grid

frequency. A method for active output voltage regulation in an AFPM automotive

alternator by means of mechanical flux weakening is proposed in [65].

3.4 AFPM Machines and Wind Power Generation

AFPM Machines are the primary generators for distributed generation systems. They

are compact, highly efficient and reliable.

The advantages of PM machines over electrically excited machines can be summarized

as follows [64]:

higher efficiency and energy yield,

no additional power supply for the magnet field excitation,

improvement in the thermal characteristics of the PM machine due to the absence

of the field losses,

higher reliability due to the absence of mechanical components such as slip rings,

lighter and therefore higher power to weight ratio.

However, PM machines have some disadvantages, which can be summarized as follows:

high cost of PM material,

difficulties to handle in manufacture,

demagnetization of PM at high temperature.


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3.5 Summary

Wind speed is a natural phenomenon which cannot be controlled, and the wind turbine

systems in general are limited by their capability to adapt to these natural phenomena.

The power available in the wind is proportional to the third power of the wind speed,

and to the square of the turbine diameter.

In this chapter, wind energy extraction process is discussed, along with all the

parameters that affect the overall energy conversion, such as the tip speed ratio and

the coefficient factor of the wind turbine system. Furthermore, the types of electrical

generators used in wind power systems are presented. The suitability of AFPM

generators used for wind power generation is explained.


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CHAPTER 4

ANALYTICAL MODEL

In this chapter, an explanation of variable radius machine concept is presented, and

simple fictitious generators analogy is used. The selection of AFPM layout topology,

suitable for the modeling is presented.

The modeling of stator coil induced voltage, uses a less simplified analytical method,

based on the coil induced voltage equation in section 2.11. A mathematical model is

built and converted to MATLAB script to describe the induced voltage for the variable

radius design concept, along the shaft speed curve. Different setups for the values of

outer machine radius Rout, shaft speed and the outer radius range are applied.

According to the AFPM textbooks, even in newest models (Gieras2008), the analytical

model of axial-flux PM machine is obtained by using the average radius of the machine.

This approach is sufficiently accurate to predict the machine performance if the magnet-

width-to-pole-pitch-ratio is fixed. In other terms, the relative magnet width is constant

with respect to the pole pitch, which is a function of the average stator radius. This is not

the case in this new concept, as the relative magnet width varies along the motor radius.

The waveform of the no-load air-gap flux density will change as well as the induced

back-EMF. In designing the analytical model, this effect was taken into account.

After modeling the basic machine, it is important to emphasis the advantages of the new

concept, by building an expression that inversely relates the shaft speed to the machine


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Figure 4.1 Methodology flow chart

outer radius. The computed effect of the shifted radius is presented. The methodology

used in this dissertation is shown in Fig.4.1.

Overlapped slot less stator winding type is chosen for modeling the variable radius

AFPM for many reasons. An important radius-related parameter is the coil side angle,

which decreases with the radius. This is explained in detail in this chapter.

Special MATLAB scripts are created to describe the following:


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Slicing the active radius range into small parts to calculate the effect of slice

position on the coil side angle.

Effect of the coil side angle on the coil induced voltage.

Effect of shaft speed on coil induced voltage for a fixed machine radius

Creating an expression to inversely relate the machine radius to the shaft speed.

Using the above expression to study the effect of both radius and shaft speed on

coil induced voltage.

Study the effect of different ranges for the radius shift on the stator coil induced

voltage curve with shaft speed.

4.1 Explaining the Concept of Variable Radius AFPM

The energy available in the wind is directly related to the wind speed. Thus, the power

generated will suffer the same fluctuations of the wind, and there will be times where the

power system will operate at the boundary of its nominal ratings, or even stop generating

for short or long periods of time.

Wind turbines are fixed devices when it comes to size and power ratings, so as the

generators connected to them, or this how it have been done so far. This limitation

have a negative effect on the overall power extraction process, considering a fluctuating

power source like the wind.

The idea of the new concept design is to have a generator that can adapt its parameters

to the variable power input. This adaptation is facilitated via a variable radius machine

where the rotor magnet poles shifts within a range of machine outer radii, affecting the

value of the stator coil induced voltage.


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To achieve such functionality for the generator, giving it the ability to be continuously

suitable to the variable power delivered from the wind turbine shaft to maintain higher

overall power extraction in the process.

The direct effects of shifting the poles radius for the same angular speed will affect the

following:

Ability to compensate the value of the stator coil induced voltage drop as the wind

speed drop.

A machine with radius dependent electrical torque as the position where the

electromagnetic force is exerted is variable.

4.1.1 Considering Each Coil As a Fictitious Electric Generator

Fictitious Generators (FG) analogy is used here to simplify the idea of the new concept

of the Variable Radius AFPM (VRAFPM) machine. Assuming each stator coil as a

small generator mechanically coupled to the rotor disk at the designated radius. The

FG set have the ability to shift their coupling diameter in order to adapt to the variable

speed delivered by the wind.

In AFPM machine, the permanent magnet poles are passing by the stator coils within

air gap distance at average linear velocity described by:

vpmav = rotor rrotorav (4.1)

where vpmav is the average linear velocity of the permanent magnet poles with respect

to the windings in the stator, rotor is the AFPM rotor angular velocity and rrotorav is


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Figure 4.2 AFPM coils as a fictitious electric generators

where T is the torque, F is the breaking force exerted by the fictitious electric generators

on the rotor disk and rrotoract is the active radius of the AFPM rotor disk. The load

torque is linearly proportional to the active radius.

4.2 Plotting the Torque Versus Poles Radius

The breaking torque follows a linear relationship with the poles active radius, as they

impose a breaking force on the rotor disk. Plotting the breaking torque versus the active

radius of the FG set will result in a straight positive slope line as shown in Fig. 4.4.

Consider the fictitious machine shown in Table 4.1:

Consider a continuous breaking torque along the circumference of the active radius, and


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Figure 4.3 Fictitious generators at short radius

Table 4.1 Fictitious machine parameters

using simple MATLAB script to plot the relationship between the breaking torque and

the active radius of the fictitious generator set, results in a straight line as shown in Fig.

4.4.

Comparing this plot with the plot from section 3.3 for wind power versus wind speed

shown in Fig. 4.5. The power curve follows a similar positive slope at region 2 versus

wind speed. Knowing that power and torque are related by the angular speed:


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Figure 4.4 Breaking torque versus active radius of the fictitious generator set

P = T (4.4)

where P is the power, is the angular speed and T is the torque.

To manipulate the fictitious generators mechanical torque and speed, the machine radius

is shifted inward or outward to match the desired speed/torque criteria to maintain

generation.

From the fictitious generator perspective, shifting the active radius will cause the

following:

Controlling the radius enable the control of the mechanical torque delivered to the

FG set.

Controlling the radius will have direct effect on the angular speed delivered to the

FG set.


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The angular speed of the wind turbine can be in direct or inverse relationship with active

radius depending on the control scheme, along with other wind turbine control factors

like blade pitch control and Maximum Power Point Tracking (MPPT).

In this dissertation, only the inverse relationship between the angular speed and the

active radius is studied, while the direct relationship will be out of the scope of this

study.

Figure 4.5 Power versus wind speed [49]

4.3 Choosing Suitable AFPM Machine Type

Variable radius concept is suitable for Axial Flux Machine, as the disk-shaped structure

of the air gap allows for radial shift of poles. The Radial Flux Machine (RFM) on the

other hand, does not allow for such pole shift manipulation due to the cylindrical-shaped


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air gap.

Below are the reasons for selecting the AFPM design:

1. Low speed suitability, the axial flux permanent magnet machines are well suitable

for low-speed applications, since their performance, efficiency and power factor,

does not depend on the rotation speed to the same extent as it is the case for

induction machines.

2. In integrated systems, like wind turbine power systems, an important demand

is to select the most suitable electrical machine for a particular application.

Traditionally, AFPM is chosen due to its simple structure durability, less

maintenance and simple assembly. Furthermore, its disk shaped form factor along

with the elimination of gearbox, enable its integration within the hub structure of

the wind turbine.

3. Due to the development of the permanent magnet materials, for some particular

applications, using radial-flux machines seem to be no more the most adequate

solution. If the machine axial length is limited by the application demands or if it

appears to be possible to integrate the rotor directly into the driven machinery, the

electrical machine based on the axial flux topology may be a competitive or even

a better choice in such applications.

4. The simple disk shaped structure, eases the adaptation of the shifted poles along

the radius is mechanically feasible.

4.3.1 Advantages of AFPM Machines with Slot less Windings

For AFPM machines with slot less windings, the air gap is much larger and equal to

the mechanical clearance plus the thickness of all non-magnetic materials (winding,

insulation, potting and supporting structure) that is passed by the main magnetic flux.


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Since there are no slots, the air gap will always be constant during rotation. Compared

to a conventional slotted winding, the slot-less armature winding has the following

advantages [66]:

Simple stator assembly.

Elimination of cogging torque, which is a pulsating torque due to the interaction

between the permanent magnets of the rotor and the stator slots of a PM machine.

Reduction of rotor surface losses, magnetic saturation and acoustic noise.

The disadvantages include:

More PM materials required for the bigger air gap.

Lower winding inductance sometimes causing problems for inverter-fed motors

and significant eddy current losses in slot less conductors [22].

The stator with slot less overlapping windings layout of AFPM machines shown in Fig.

4.6, is chosen for the design of the variable radius AFPM.

4.4 Modeling Stator Coil Induced Voltage

Equation 4.5 describes the stator coil induced voltage:

ecoil =4

pBpN

u

j=1

rjl2 sin (r j/2)

ur j

sin (t) (4.5)

In this equation, the only parameters that are affected by the radius change are stator

coil induced voltage and the coil side angle, where:


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Figure 4.7 Coil side angle change with radius

where Rout is the poles outer radius, Rin is the inner radius and l is the permanent magnet

radial width.

As the value of coil side angle is changing along the active radius, the value of stator

coil induced voltage for a specified small slice of the active coil radial length will be a

function of the radial position of that slice.

The active radial length of the stator coil is the part that is covered by the magnetic pole,

this length is fixed in value but subject to radial position change as the poles shifted

radially, as explained later in Fig. 4.9.

To calculate the coil induced voltage, a slicing procedure is adopted in MATLAB scripts

to calculate the summation of induced voltages of coil slices along the active radius.


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4.4.2 Creating an Expression for Radius Change with Shaft Speed

To emphasize the advantages of the concept design, it is important to build an expression

that relates the shaft speed to the machine radius. The goal of shifting radius Rout(n)

with respect to rotational speed n is to compensate induced voltage drop as the angular

speed decreases in effect to low wind speeds. Fig. 4.9 is showing that for same shaft

angular speed, a larger radius configuration of the generator will produce higher induced

voltage, compared to shorter radius configuration.

Figure 4.9 PM poles shift radius as rpm change

Thus, an expression that relates the angular speed to the active radius is formulated and

will be included in most MATLAB scripts.

The expression that relates the value of outer radius Rout to the angular speed of the

shaft n is shown in 4.9:

Rout(n) +Routmin

nmaxn

=

RoutmaxRoutmin

nmaxnmin

(4.8)


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Rout(n) = Routmin +

(nmaxn)

RoutmaxRoutmin

nmaxnmin

(4.9)

when n = nmax, the shifted outer radius Rout(n) = Routmax

when n = nmin, the shifted outer radius Rout(n) = Routmin

Where Routmin is the minimum outer radius

Routmax is the maximum outer radius

nmax is the maximum angular speed

nmin is the minimum angular speed

4.4.3 Slicing Active Portion of Stator Coil

Fig. 4.10 is showing the slicing method used to compute the stator coil induced voltage,

where the active length of the stator coil l is sliced to a number of thin slices u, as shown

in :

l = RoutRin (4.10)

The number of slices u is chosen based on the desired quality of the results, as more

slices means more processing time and more accurate results for the total coil induced

voltage .

Each slice have a radial length drj equals:


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Figure 4.10 Slicing active radius

drj = l/u (4.11)

where l is the length of active portion of the stator coil side which equals the radial length

of the permanent magnet, u is number of slices chosen for the computation process.

4.5 Finalizing the Analytical Model

To compute the coil induced voltage in a range of machine radii, a method of slicing the

active radius length is applied on equation 4.12:

ecoil =4

pBpN

u

j=1

rjl2 sin(r j/2)

ur j

sin(t) (4.12)

This formula is modeled in MATLAB script in three parts, the first is to compute the

coil side angle:

r j = atan(w/rj) (4.13)

where rj is changing along the radial length of the permanent magnet pole.


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The second part is to compute the summation of the expression inside the square

brackets (sk) in equation 4.12:

sk=

u

j=1

rjl2 sin(r j/2)

ur j

(4.14)

The third part is to find the induced voltage for a particular machine with outer radius

Rout, which will be repeated for a range of outer radius.

4.6 Summary

In this chapter, the research methodology was presented, and the concept of the variable

radius machine is explained by considering each stator as a fictitious electric generator.

Choosing the suitable AFPM type to model the variable radius concept has been done.

Furthermore, an expression for the stator coil side angle with machine outer radius was

derived and converted to MATLAB script.

In order to compensate the induced voltage drop in lower wind speeds, a relationship

between shaft speed and active machine radius was derived.

MATLAB scripts are used to calculate the effect of the variable radius on all the

parameters affecting the stator coil induced voltage.

To obtain the curves that present the effect of variable radius on AFPM machine stator

coil voltage, by sweeping the following parameters in their respective ranges:

shaft speed

outer radius


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CHAPTER 5

RESULTS AND DISCUSSION

In this chapter, results from the analytical model of the variable radius AFPM machine

is presented and analyzed. Stator coil voltage is plotted and analyzed in different

modeling setups of radius and shaft speeds. The values computed both before and after

implementing the variable radius concept design is presented.

All the parameters in equation 4.12, that was found to have effect on the stator coil

induced voltage, were included in the analytical model.

Calculations were made at different operating conditions of rpm, radius and both rpm

and radius, linked together by the expression 4.9, made specifically for this model in

Chapter 4.

The calculations are performed on the analytical model of one stator coil of a 6-pole,

slot less, over-lapped windings and surface-mounted PM poles on double lateral rotors,

shown in Table. 5.1.


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Table 5.1 Machine parameters

5.1 Induced Voltage for Range of Shaft Speeds with Fixed Radius

Equation 4.5 describes the stator coil induced voltage for a fixed radius machine as

shown in Fig. 5.1. The induced voltage curve is computed by summation of voltages

in all slices ranging from the inner radius Rin to the outer radius Rout of the machine,

as described in Chapter 4. This approach is implemented in MATLAB script, listed in

appendix A.

Each slice in the range has slightly different parameters compared to its two adjacent

slices as their radius differs.

The voltage plot shown in Fig. 5.1 is obtained at shaft speed of 150 rpm, and the coil

induced voltage values for different shaft speeds and fixed outer radius is tabulated in

Table 5.2. The induced voltage is linearly related to the shaft speed.

Table 5.2 Max induced voltage versus shaft speed at fixed outer radius


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Figure 5.1 Induced coil voltage versus time at fixed radius

5.2 Induced Voltage for Range of Radii with Fixed Shaft Speed

Table 5.3 shows the coil induced voltage versus rotor outer radius at fixed shaft speed

of 200 rpm. The active radius is shifted by steps from 0.13 to 0.17 meter to obtain

preliminary results of its effect on the coil induced voltage.

Table 5.3 Max induced voltage versus radius in steps


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5.3 Coil Side Angle Change with Slice Radius

The coil side angle is affected by the radial position of the slice. It is computed using

equation 5.1, mentioned earlier in the methodology:

Coil Side Angle (r j) = tan1

coil side width (w)

sliceradius (rj)

(5.1)

The MATLAB script listed in appendix B is used for this plot as shown in Fig. 5.2.

The coil side angle shows an inverse relation with slice radius, causing the slice induced

voltage factor k to change as shown in Fig. 5.3. The MATLAB script for this plot is

listed in appendix C.

Figure 5.2 Coil side angle vs. slice radius

an innovative concept to compensate induced voltage drop in axial flux permanent magnet wind turbine...

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