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Degree project in

Design of a Permanent MagnetSynchronous Generator for a Vertical

Axis Wind Turbine

Nima Madani

Stockholm, Sweden 2011

XR-EE-EME 2011:013

Electrical EngineeringMaster of Science

Design of a Permanent Magnet SynchronousGenerator for a Vertical Axis Wind Turbine

NIMA MADANI

Master of Science Thesis in Electrical Machines and Power Electronicsat the School of Electrical Engineering

Royal Institute of TechnologyStockholm, Sweden, June 2011

Supervisor: Dr. Alija CosicExaminer: Professor Chandur Sadarangani

XR-EE-EME 2011:013

AbstractDifferent types of permanent magnet generators for wind power applica-tion have been subject of research during last two decades. In this the-sis different topologies of electrical generators have been investigated forsmall scale vertical axis wind turbine application. A two stage inductiongenerator is proposed as a alternative solution with respect to the cost ofsuch a system. However, a biggest emphasis in the report has been puton the design of Permanent Magnet Synchronous Generator (PMSG)suitable for a small scale Vertical Axis Wind Turbine (VAWT)The char-acteristics of PMSG makes it highly compatible for variable speed WindEnergy Conversion System (WECS) without any pitch mechanism.

Chapters 2 and 3 summarize a thorough literature survey on windenergy systems and corresponding electrical machines. The principlesof wind aerodynamics is preceded by a review on wind turbine charac-teristics and challenges with emphasis on VAWT s. Further differenttopologies of electrical machines with focus on PMSG s including Per-manent Magnet (PM) configurations, different windings and thermalbehavior is presented. In chapter 4 a brief review on an alternativesolution which includes an Induction Generator (IG) for fixed speedWECS is given.

Next, In chapters 5, 6 and 7, a PMSG is designed and the de-sign is verified by means of Finite Element Method (FEM) analysis andthermal modeling. Chapter 5 describes an analytical optimisation of alongitudinal, inner rotor, radial flux, surface mounted PMSG with con-centrated winding and natural air cooling system. Cost of active mate-rial is chosen as the optimisation criterion. Concepts like "constraints","requirements", "parameters" (including material, geometry and wind-ing) and procedure of the design are described here. In chapter 6, aFEM model of the optimised machine is developed and the results areillustrated. The iron losses, calculated in this chapter are utilised inthermal analysis in chapter 7 . Thermal model developed is based on alumped parameter circuit . It ensures the safe thermal behavior of themachine in nominal operation mode.

Keywords: vertical axis wind turbine, permanent magnet ma-chines, permanent magnet generator, Finite Element Method,fractional concentrated winding

Referat

Olika typer av permanentmagnetgeneratorer för vindkraftapplikationhar varit föremål för forskning under de senaste två decennierna. I dennarapprt har olika typer av elektriska generatorer undersökts för småskaligvertikalaxelvindkraftverkstillämpning. Utifrån kostnasdhänsyn för ettsådant system, en dubbellindad asynkrongenerator föreslås som en all-ternativ lösning. Emellertid, har den största vikten i raporten lagts påundersökningen och design av en permanentmagnetsynkrongeneratorför en småskalig vertikalaxelvindkraftverk. Egenskaper hos permanent-magnetsynkrongenerator (PMSG) lämpar sig väldig bra för variabel-hastighet vindenergysystem utan pitch mekanismen. I kapitel 2 och 3,presenteras en grundlig genomförd litteraturstudie på vindkraftsystemoch motsvarande elektriska maskiner. Principerna för vindaerodynamikföregås av en genomgång på vindturbin egenskaper och utmaningar medtonvikt på vertikalaxelvinkraftverk. Vidare, presenteras olika topologierav elektriska maskiner med fokus på permanentmagnetsynkrongenera-torer inklusive permanentmagnet(PM) konfigurationer, olika typer avlindningar och termiskt beteende. I kapitel 4 ges en kort översikt av enalternativ lösning, vilken omfattar en dubbellindanasynkmronenerator.Därefter i kapitel 5, 6 och 7, ges analytisk undersökning och design av enpermanensynkrongenerator, vilken sedan understöds och verifieras medhjälp av Finita Element Metoden (FEM) och termisk modellering. Kapi-tel 5 beskriver ett analytiskt optimiserings process av en longitudinell,inre rotor, radial flödes, permanetmagnetsynkrongenerator med ytmon-terade magneter, koncentrerad lindning och en naturlig luftkylning sys-temet. Kostnadden av aktivt material har valts som ett optimering kri-terium. Begrepp som begränsningar", "krav", parametrar"(inklusive ma-terial, geometri och lindningar) och arbetsflöde för design är beskrivnahär. I kapitel 6, ges en beskrivning av den utvecklade FEM-modell avden optimerade maskinen och resultaten presenteras tydligt. Järnförlus-ter beräknade i detta kapitel, utnyttjas vidare i den termiskanalysen ikapitel 7. Den termiska modellen baseras på punktvis fördelade param-eterkretsen. Detta garanterar en säker drift av maskinen vid nominelllast.

Nyckelord: vertikalaxelvindkraftverk, permanentmagnet maskiner,permanentmagnet generator, Finita Element Metoden, koncentrerad lind-ning

Acknowledgment

During past seven months I have had the most fascinating time working on thisthesis. So I would like to express my gratitude for the people who made this greattime.

This work has been possible by guidance of my examiner professor ChandurSadarangani throughout the entire work. His confidence in me to tackle this taskis highly appreciated. Next appreciation goes to my supervisor Dr. Alija Cosicwho provided me with assistance whenever I needed it. I am grateful of his efforttowards guiding me along the way.

I also feel thankful of my friends and officemates for their friendship. ShafighNategh and I spent a lot of time on our long discussions. Moreover, I had a nicetime with Sergio, Xiaohu, Roberto, Arif,... . EME staff are appreciated for theirhelp whenever I turned to them: including Peter Lönn, Eva Pettersson, AndreasKrings, Naveed Malik, ....

I, additionally, would like to express my gratitude towards my parents and sib-lings. Endless love of my father, who is my hero, and my mother made it possiblefor me to bear the distance. I wish the best for my little sister and my brother intheir lives in return of their support during this period. I, moreover, had a greattime in Uppsala with my aunt and my cousins that I will never forget.

Stockholm

Midsummer 2011

Nima Madani

List of Symbols and Abbreviations

List of Symbols

aP M temperature coefficient of remanence flux den-sity of PM material

K−1

A wind turbine swept area m2

Acu copper area per slot m2

bs0 stator slot opening mbts stator tooth width mBm maximum of airgap flux density TBr0 remanence flux density of PM material at 20C TBr,m remanence flux density of the magnet at working

temperatureT

Brs peak fundamental stator yoke flux density T

Bts peak fundamental stator teeth flux density T

Brr peak fundamental rotor yoke flux density T

Bδ peak fundamental airgap flux density T

ccu cost coefficient for copper Eurokg

cF E cost coefficient for steel sheet Eurokg

cP M cost coefficient for PM material Eurokg

Cb empirical bearing coefficient w.secrad.m3

Cf empirical friction coefficient wkg .( sec

rad)3

Cp power coefficient (aerodynamic efficiency) −dF E thickness of lamination mDi,min generator’s minimum shaft diameter mDi,min,failure generator’s minimum shaft diameter in failure

conditionsm

Di,min,normal generator’s minimum shaft diameter in normalconditions

m

Dm average diameter of generator’s bearing mDy generator’s outer diameter mE kinetic energy of a fluid mass in wind turbine w.sec

kg

f frequency Hzfs stator slot fill factor −

J current density Am2

hrr rotor yoke height mhrs stator yoke height mhss stator slot height mhsw stator slot wedge height mI rms value of nominal current Akcoil end winding coefficient −kexcess Excess loss coefficient w

m3 ( Tsec)1.5

kh Hysteresis loss coefficient w.secT 2m3

kj Stacking factor −kkey correction factor for strength weakening of the

shaft due to the key slot−

kfailure safety factor under failure conditions −knormal safety factor under normal conditions −lav average length of half a turn of the winding coil mlF E stator core length mlm magnet thickness mL generator’s airgap cylinder length m

m mass flow in wind turbine kgsec

Mbend bending moment acting on generator’s shaft N.mnn generator’s base speed rpmnr generator’s rated speed rpmns number of turns per slot −p number of poles −Pbearing rotor’s bearing losses wPmech mechanical extracted power from wind turbine wPn generator’s rated power wPwind available power in wind wPwindage rotor’s windage losses wPcu total copper losses wPcu−cs copper losses in coil sides wPcu−ew copper losses in end windings wPF E iron losses calculated in FEM wq number of stator slots per pole per phase −Qs number of stator slots −r wind turbine’s rotor plane radius mR generator’s airgap cylinder radius mRcu phase winding resistance ΩRth thermal resistance C/wT temperature CT0 average temperature of ambient CTn generator’s rated torque N.mα magnet angle electrical

αmech geometrical correction factor −β blade pitch angle

βmech geometrical correction factor −γ undercut angle

δ airgap length mδe effective airgap length mη efficiency %ϑ wind velocity m

secλ tip speed ratio −µr relative permeability of the magnet −ρ air mass density kg

m3

ρcu copper resistivity Ω.m

ρF E steel sheet material’s mass density kgm3

ρP M PM material’s mass density kgm3

σ classical loss coefficient (conductivity) ( 1Ω.m)

σperm permissible strength of shaft material Nm2

σyield yield strength of shaft material Nm2

τs slot pitch m

ω wind turbine’s rotor tip angular speed radsec

ωm mechanical angular speed of generator’s rotor radsec

List of Abbreviations

AC Alternative Current

BLAC Brushless Alternative Current

DC Direct Current

DFIG Double Fed Induction Generator

DOL Direct Online

EMF Electro-Motive Force

FEM Finite Element Method

HAWT Horizontal Axis Wind Turbines

IEC International Electrotechnical Commission

IG Induction Generator

IPM Interior Permanent Magnet

LCM Least Common Multiple

MMF Magneto-Motive Force

MPPT Maximum Power Point Tracking

PM Permanent Magnet

PMSG Permanent Magnet Synchronous Generator

PMSM Permanent Magnet Synchronous Machine

PWM Pulse Width Modulation

RFPM Radial Flux Permanent Magnet

rpm Rotation Per Minute

rms Root Mean Square

SCIG Squirrel Cage / Short Circuit Induction Generator

SCIM Squirrel Cage / Short Circuit Induction Machine

SG Synchronous Generator

SMPM Surface Mounted Permanent Magnet

VAWT Vertical Axis Wind Turbine

WECS Wind Energy Conversion System

WRIG Wounded Rotor Induction Generator

WRIM Wounded Rotor Induction Machine

WRSG Wounded Rotor Synchronous Generator

Contents

Contents

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Wind Energy Systems 52.1 Wind Turbine Aerodynamics . . . . . . . . . . . . . . . . . . . . . . 52.2 Wind Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 Working Principle of VAWT . . . . . . . . . . . . . . . . . . 72.3 Mechanical Drive Train . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 Fixed Speed or Variable Speed . . . . . . . . . . . . . . . . . 102.3.2 Geared or Direct Driven . . . . . . . . . . . . . . . . . . . . . 11

2.4 Operation Sequence and Control . . . . . . . . . . . . . . . . . . . . 112.4.1 Operation Sequence . . . . . . . . . . . . . . . . . . . . . . . 112.4.2 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.5 Comparison Between VAWTs and HAWTs . . . . . . . . . . . . . . . 152.5.1 Design: Yaw Mechanism . . . . . . . . . . . . . . . . . . . . . 152.5.2 Design: Axis of Direction . . . . . . . . . . . . . . . . . . . . 152.5.3 Design: Direct Drive . . . . . . . . . . . . . . . . . . . . . . . 152.5.4 Design: Wind turbine construction . . . . . . . . . . . . . . . 162.5.5 Design: Structural Mechanics . . . . . . . . . . . . . . . . . . 162.5.6 Aerodynamics: Performance . . . . . . . . . . . . . . . . . . . 162.5.7 Aerodynamics: Power Control . . . . . . . . . . . . . . . . . . 162.5.8 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.6 Vibrations in Wind Energy Systems . . . . . . . . . . . . . . . . . . 172.6.1 Torsional Vibrations of the Drive Train . . . . . . . . . . . . 17

2.7 Noise Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3 Electrical Machines for Wind Energy Systems 193.1 Different Topologies of Electrical Machines . . . . . . . . . . . . . . 19

3.1.1 DC Generators . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1.2 Induction Generators . . . . . . . . . . . . . . . . . . . . . . . 193.1.3 Synchronous Generators . . . . . . . . . . . . . . . . . . . . . 22

3.2 PM Synchronous Machines . . . . . . . . . . . . . . . . . . . . . . . 243.2.1 Radial Flux or Axial Flux . . . . . . . . . . . . . . . . . . . . 243.2.2 Longitudinal or Transversal . . . . . . . . . . . . . . . . . . . 263.2.3 Inner Rotor or Outer Rotor . . . . . . . . . . . . . . . . . . . 27

3.3 PM Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3.1 Surface Mounted Magnets . . . . . . . . . . . . . . . . . . . . 283.3.2 Inset Magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.3 Buried Magnets . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.4 Winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.4.1 Distributed Winding . . . . . . . . . . . . . . . . . . . . . . . 313.4.2 Concentrated Winding . . . . . . . . . . . . . . . . . . . . . . 313.4.3 Single Layer Concentrated Non-Overlapping Winding . . . . 34

3.5 Thermal Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.5.1 Consequences of Temperature Rise . . . . . . . . . . . . . . . 343.5.2 Cooling System . . . . . . . . . . . . . . . . . . . . . . . . . . 363.5.3 Heat Transfer Theory . . . . . . . . . . . . . . . . . . . . . . 363.5.4 Losses in PMSG . . . . . . . . . . . . . . . . . . . . . . . . . 37

4 Induction Generator 434.1 Fixed Speed Induction Generator . . . . . . . . . . . . . . . . . . . . 434.2 Selection of Induction Motor as Generator . . . . . . . . . . . . . . . 44

4.2.1 Temperature Rise . . . . . . . . . . . . . . . . . . . . . . . . 454.2.2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.2.3 Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.3 Two Step Fixed Speed Induction Generator . . . . . . . . . . . . . . 454.4 Self Excited Induction Generator . . . . . . . . . . . . . . . . . . . . 46

5 Analytical Design of PMSG 495.1 Design Requirements and Constraints . . . . . . . . . . . . . . . . . 49

5.1.1 Mechanical Calculation: Minimum Shaft Diameter . . . . . . 495.2 Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.2.1 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.2.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.2.3 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.2.4 Winding (Concentrated) . . . . . . . . . . . . . . . . . . . . . 52

5.3 Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.4 Design Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6 FEM Simulation of PMSG 596.1 Initial Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 596.2 Results of FEM Simulations . . . . . . . . . . . . . . . . . . . . . . . 606.3 Iron Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

7 Thermal Modeling of PMSG 697.1 Thermal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697.2 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 72

8 Conclusions and Further Work 738.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 738.2 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

A Datasheet of M400 50A by Surahammar Bruk AB 77

Bibliography 79

List of Tables 82

List of Figures 83

Chapter 1

Introduction

1.1 Background

Energy demands of the modern society has made the way open to invest greatamount of technological effort and capital to renewable energies. Figure 1.1 showsthe amount of annual capital investment in new renewable energies (excluding largescale hydro power, traditional biomass) between 2004 and 2009. The values includeenergy converted into electricity and heat.

Wind energy is one of the renewable energies which has attracted a lot of in-terest in recent years. By end of 2009, the capacity of wind energy power plantshas reached 158 gigga watts worldwide. The interest in producing electricity putscertain demands on the electrical machines and drives. Mechanical energy from re-

Figure 1.1. Annual capital investment in new renewable energies between 2004 and2009 in US Dollars [1].

1

CHAPTER 1. INTRODUCTION

Figure 1.2. Renewable energy share of global energy consumption by 2008 [1].

newables injected to electrical machines is not controllable. This challenge has ledto many technological advancements in induction machines and permanent magnetsynchronous generators. The author, however,would like to emphasize that there isa great room for growth in renewable energies 1. So far wind energy contributes to0.3 % of global energy consumption.

1.2 Objective

Main objective of this thesis is to design a suitable permanent magnet syn-chronous generator working with a vertical axis wind turbine. Wind energy con-version system consisting of above mentioned elements works on a variable speedprinciple. In small scale wind turbines, blade pitch mechanism usually is not applied.Instead, a power electronics converter compensate variation for the wind variationand thus it contributes to high power coefficient. The corresponding topology ofPMSG is a surface mounted machine with concentrated winding. This type ofwinding suits for low speed applications since implementing high number of polesis easy. The major benefit of high pole numbers is eradication of gearboxes. Gear-boxes result in lower availability of the entire system and they cause high amount ofnon-user friendly audible noise. Reduction of magnetic noise by the machine is tar-geted at the design stage. Additionally, the chosen topology can be easily scaled byincreasing the length of the machine. Of paramount, at the design stage, objectivefunction is to reduce manufacturing expenses and cost of active material.

1.3 Contents

This section describes the contents of each chapter.

1see Figure 1.2.

2

1.3. CONTENTS

• Chapter 2 gives an in depth knowledge of wind energy concepts and termi-nology for electrical designer. The emphasis is on VAWT.

• Chapter 3 reviews the principles of rotating electrical machines for wind speedapplication. The emphasis is on PMSG.

• Chapter 4 offers an alternative option for PMSG.

• Chapter 5 illustrates analytical design stage with optimisation.

• Chapter 6 verifies the optimised PMSG with the help of FEM analysis.

• Chapter 7 investigates thermal behavior of the optimised machine.

• Chapter 8 clinches the work, conclusions and further suggested work are givenhere.

3

Chapter 2

Wind Energy Systems

Wind energy systems have been subject of research for decades. They consistof wind turbines and electrical generators. The first section covers the basics ofVAWT . Initially in this section, aerodynamics of wind turbines are presented.Subjects like control, dynamic vibration and noise emission in VAWT are covered.Furthermore, a separate section is dedicated to a comparison between HorizontalAxis Wind Turbines (HAWT) and VAWT .

The role of a wind energy system is to capture mechanical energy in the airflowand convert it to electrical energy. Usually it consists of a wind turbine rotor, for theformer purpose, and an electrical machine working as generator for the latter. Thevariation in the wind speed is one of the factors that affects the specifications of windenergy systems. In other words design of the wind systems’ components demandsspecial consideration. The amount of accessible mechanical energy depends on thesize of the wind turbine and the wind regime of the site.

2.1 Wind Turbine AerodynamicsThe amount of the kinetic energy in the air flow can be determined based on

the size of wind turbine and the wind speed. The elementary momentum theorygives an explaination of energy conversion in ideal circumstances. The amount ofthe kinetic energy of a fluid mass m with a mass density ρ , moving at a velocity ϑthrough the area A is

E = 12

· m · ϑ2 (2.1)

and the mass flow ism = A · ρ · ϑ (2.2)

The power available in the wind is equal to the amount of energy yield passing persecond.

Pwind = E · m = 12

· ρ · A · ϑ3 (2.3)

It is obvious that a small variation in the wind speed influences the availablewind power drastically. It was first in 1922, the German engineer Betz showed that

5

CHAPTER 2. WIND ENERGY SYSTEMS

Figure 2.1. Power coefficient versus tip speed ratio [3].

the amount of extractable energy from an air stream is limited. It was shown that,in a free air stream, the maximum energy is extracted if the wind speed is reducedby three times far behind the turbine in comparison to in front of it. The maximumextractable power becomes then, 16/27 of available wind power [2].

For steady state analysis of aerodynamic conversion, a power coefficient diagramis used. As mentioned, it is not possible to capture all the power in the air flow asthis would result in air standstill immediately after the wind turbine. Aerodynamicefficiency represents a ratio of captured power and available wind power. In windpower terminology, it is more known as the power coefficient. Betz factor is themaximum value for the power coefficient.

The power coefficient Cp is a function of the tip speed ratio λ and the bladepitch angle β. Equation 2.3 above, is modified according to equation 2.4.

Pmech = Cp.Pwind = 12

· ρ · A · Cp (λ, β) · ϑ3 (2.4)

whereλ = r · ω

ϑ(2.5)

ω is the rotor tip angular speed and r is the rotor plane radius. Blade pitchingmeans that the rotor blades are rotated along their axis, in order to control theamount of the absorbed power. 1 In wind turbines which are not equipped withthe control of the blade pitch, power coefficient is merely function of the tip speedratio. Figure 2.1 shows a typical power coefficient diagram. Power coefficient ismaximum at the optimum tip speed ratio i.e. in order to capture the maximumenergy, the wind turbine rotor has to be run at this ratio. When the wind turbinerotor is run at other tip speed ratios, eddies will develop at the blade tip. Thisphenomenon reduces the captured energy and it is called stall. It explains the dropof the power coefficient at other tip speed ratios.

1see section 2.4.2

6

2.2. WIND TURBINES

It can be observed from the power coefficient diagram in Figure 2.1, that thewind turbine is not self starting. For low values of the tip speed ratio, the value ofthe power coefficient is negative. Many lift based wind turbines require a minimumtip speed ratio before they can start to absorb the power [4]. Accordingly, in orderto start up the wind turbine rotor, energy has to be supplied. There are differentways to do so, one is to utilise an auxiliary self starting turbine like for exampleSavonious wind turbine. Another is certain modification in the design of the windturbine. Furthermore, electrical starting of wind turbine is yet another possibility.The generator is, then, fed by the grid for a short duration of time and works asa motor in order to start the wind turbine. In this solution the wind power plantcannot operate as a stand alone unit.

2.2 Wind TurbinesWind turbines are categorised based on two different criteria; First due to their

aerodynamic function; second based on their design.Considering the aerodynamic performance, wind turbines are divided into drag

based and lift based. The rotors which utilise the drag force of the wind are recog-nised as low speed turbines. However, in some turbines, the possibility of employingthe lift force is also provided. The lift based turbines are recognised as high speedrotors. These are capable of capturing higher amount of the wind power comparedto their drag based counterparts and therefore they are the most common solutiontoday.

Due to the second criterion, wind turbines are classified based on their axisof rotation. It is more common to distinguish wind systems as HAWT or VAWT.HAWT s have benefited from technological advancements in the aircraft engineeringbecause of the blades’ propeller like design. For instance, to achieve more lift forces,blade shapes’ optimisation are proposed and applied. Power coefficients up to 0.5of HAWT s have been reported. Today’s VAWT s have reached power coefficientup to 0.4 at maximum. Figure 2.2 and Figure 2.3 show a H rotor VAWT and aninstalled HAWT respectively. Simplicity of the design of the VAWT s is beneficial,especially the possibility to accommodate some of the drive train components onthe ground together with absence of the yaw system 2. Some disadvantages of thesystem are the lower optimum tip speed ratio, inability to self start and inability toimplement blade pitching for power control purposes. In some of the researchers’opinion the VAWTś power coefficient can exceed that of HAWT s’ . A comparisonbetween HAWT s and VAWT s is presented in section 2.5.

2.2.1 Working Principle of VAWT

Figure 2.4 shows a horizontal plan of a VAWT . The hub is assumed to belocated at the centre of the coordinate system. The area with a positive value on

2see section 2.3 and section 2.5.1

7


Figure 2.2. An H rotor VAWT [3].

y-axis in Cartesian coordinate system is defined as upwind region and the remainingarea is defined as the downwind region. The angle of attack is the relative anglebetween the chord line of the blade cross section and the wind direction. Thisangle, seen by the blades in the upwind region, is negative. Since the angle ofattack is negative, the lift force vectors produced on the blade section will pointinwards the rotor. The force can be decomposed into two different components, atangential and a normal. The former is along the tangent of the blade and the latteris perpendicular to the blade.

Moreover, the lift force will be created in downwind region. Here the angle ofattack is positive, the consequent lift force vectors will point outwards the rotor.Tangential lift forces, originated from upwind and downwind regions, contribute tothe torque production in the rotor. The normal forces lead to thrust along the winddirection.

8

2.2. WIND TURBINES

Figure 2.3. A 450 kw HAWT with 37 m rotor diameter (Bonus) [2].

Figure 2.4. Horizontal plan of a VAWT [5].

9


2.3 Mechanical Drive Train

The term "mechanical drive train" stands for all rotating parts of the wind systemfrom the rotor hub to the rotor of the generator. In conventional power plant tech-nology, two requirements by mechanical drive are met: First equity of input powerto the generator with the amount of needed power by the load; Second matching thespeed levels of the prime mover with the speed of the generator. In wind systems,however, mechanical drive train does not meet neither of these requirements. Thepower production depends on the available wind resource which is not controllable.Furthermore, wind speed is far from rated speed of the conventional generators.

The drive trains are classified according to implementation of a wind system inorder to compare their characteristics. Each drive type possesses specific advantagesand disadvantages, such as aerodynamic and dynamic performance, controllability,reliability, maintenance , etc.

2.3.1 Fixed Speed or Variable Speed

In fixed speed wind systems, the rotor speed is determined by the grid frequencyand its variation is limited to around ±1% of the nominal speed. Usually, thefixed speed wind systems is designed in such a way that it has its optimum windspeed equal to site mean wind speed. No means for power control is applied andthe advantage is simplicity of operation. Disadvantages are low efficiency of windenergy system in other wind conditions aside from the mean wind speed, and severedynamics performance. Since no control method is implemented, any fluctuationsof power i.e. disturbances in the grid and/or turbulence in the wind, are passedthrough the system without any damping. This reduces the quality of the deliveredpower to the grid and also causes mechanical stress on the wind turbine rotor. Weakpower systems are sensitive to low power quality delivered by such wind systems.

The efficiency of electrical machines varies with varying electrical load condi-tions. Therefore most of the fixed speed wind energy systems are designed in a wayto provide the generator with high load. This can be achieved by means of twogenerators with different ratings. Another solution is to have two windings withdifferent pole numbers in the same generator.

In Variable Speed wind systems, power electronics converters keeps the rotorspeed and the grid frequency apart. Therefore it is possible to vary the rotorspeed independent of the grid frequency. Hence, the variation in the input powerwill result in the rotor speed variation. The output power from wind system willbe slightly lower than the input power which results in more stable and smoothdelivered power to the grid. The power quality of these wind energy systems ismuch better compared to their fixed speed counterparts. Furthermore, they havelower noise in low wind conditions [6]. In variable speed systems, the wind turbineis operated in a wider speed range, keeping the tip speed ratio at the optimum. Theadvantage is higher energy capture, however, the disadvantage is more complicatedcontrol method [7].

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2.4. OPERATION SEQUENCE AND CONTROL

2.3.2 Geared or Direct Driven

Wind energy systems can be distinguished based on whether or not they in-clude gearboxes. Wind turbine rotors are capable of rotating at tens of rotationsper minute. However, the conventional electrical machines runs at much higherspeeds e.g. hundreds of Rotation Per Minute (rpm) . The role of a gearbox is totransfer mechanical energy from low speed to high speed; A step up gearbox is usedthen. Implementation of a gearbox has its own disadvantages, e.g. maintenance,installation complication, cost of equipment, audible noise and losses. The gearboxis one of the reasons for audible noise in wind energy systems. The losses in thegearbox are comparable to the losses in the electric machine. Newly designed windsystems are usually adapted for gearless operation. This solution has become morereliable, more efficient and less noisy. The main disadvantage is a need for a specialdesigned generator which tends to be bulky.

Due to the possibility of employing power electronics converters, gearless, orin other words, direct driven systems can suite for variable speed applications [8].Converters offer the possibility to operate the generator at low speeds. Althoughthe converters are source of losses, controllability is a huge advantage compared tothe gearboxes.

Knowledge about construction and operation of gearboxes alleviates their after-math. Gearboxes are divided into two different configurations; Parallel shaft or spurgear which has a simpler mechanical construction and a gear ratio of up to 1 : 5in each stage; Planetary or helical gearbox which has more complicated mechanicalconstruction and a gear ratio of up to 1 : 12 in each stage. HAWT s run typicallyat 20rpm and usually requires more than one stage. Tooth flank friction and oilflow are the origins of power losses in the gearboxes. The average amount of lossesdepends on the gear ratio and the type of the gear. It is estimated as approxi-mately 2% of full power per stage for parallel shaft gears and as 1% of full powerper stage for planetary gears. In practice precise dimensioning of gearbox is ofimportance. Otherwise maintenance and operation will experience many problemsand the lifetime will be affected.

2.4 Operation Sequence and Control

2.4.1 Operation Sequence

Operation sequence of the wind turbine is determined by means of three thresh-old points.

• Cut in velocity ϑCI which is the wind speed the wind turbine starts to deliveroutput power. For instance, in VAWT s captured power for low wind speedsis negative, and the cut in velocity has to be chosen at values greater than thewind speed at which power coefficient becomes positive.

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• The rated wind velocity ϑR is the wind speed at which the captured powerreaches the generator rated power.

• The cut out velocity ϑCO is the highest wind speed at which the wind energysystem is able to operate mechanically safe. Typically this is less than 25 m/s.

As a result, operation sequence of a wind turbine is divided into, at least, fourregions.

• Region 1, at which the wind speed is less than the cut in speed. In this region,captured power does not suffice to compensate the internal consumption andlosses. Hence the turbine is parked and is not run.

• Region 2, at which the wind speed is between the cut in speed and the ratedspeed. It is sometimes called sub-rated region and the wind turbine is con-trolled using Maximum Power Point Tracking (MPPT) in order to achieve theoptimum tip speed ratio. MPPT is introduced thoroughly in subsection 2.4.2.

• Region 3, at which the wind speed is between rated speed and cut out speed.In this region, there are various control options, namely constant rotor speed,constant rotor torque and constant rotor power. The first two, comes with therisk of torque and current overload and they need additional control measuresfor overload protection. In the latter two, the speed does not reach to therated speed, therefore constant rotor power is proposed [9] .

• Region 4, at which the wind speed exceeds the cut out speed and the windturbine is shut down.

2.4.2 ControlThe purpose of the control is:

• Limiting the torque and the power experienced by the drive train in order toincrease lifetime.

• Maximising the energy yield for various conditions.

Drive train suffers from fatigue caused by aerodynamic and structural loads. Thestructural strength of the wind turbine can be maintained up to a certain windspeed. In addition, another limiting factor is the rated power of the generator. Therated power of the generator is reached at rated wind speed of the turbine.

Energy yield depends on the available wind power of the site as well as powercapture by the wind turbine. The energy available in the wind is uncontrollablesince it depends on the wind regime of the site. However, the power capture by thewind turbine can be maximised by the control method.

There are four different ways to influence the rotor captured power and theturbine loads. They are:

12

2.4. OPERATION SEQUENCE AND CONTROL

• Angle of attack (blade pitching)

• Flow velocity (variable speed rotor)

• Blade size (variable blade length)

• Blade section aerodynamicsThe first two methods are implemented in most of all modern HAWT s and thework principle behind the control of the power coefficient. They are introduced inthe following subsections.

The working principle behind the variable diameter blade is the control of theswept area that is useful for minimising the load during high wind speeds. Controlof blade section aerodynamics is implemented by means of active flow control. Thisstate of the art method is growing rapidly and has the potential to be implementedon large scale HAWT s [10] .

Generally, control can be implemented in either active or passive way, dependingon utilisation of external energy. Yaw mechanism, blade pitching and variable speedrotors are examples of contemporary active control methods.

Blade Pitching

In a conventional control method of HAWTs the pitch angle of the rotor bladeis changed mechanically. Blade pitching means that the blades are turned alongtheir longitudinal axis with the help of an active mechanical device. In this way,the angle of attack and thereby also the absorbed power varies. The angle of attackcan be changed in two different ways either by decreasing or increasing it. Bothcases reduce the captured power, provided that the angle of attack is in a conditionwhere the power coefficient is at the maximum. The former requires higher bladepitching for the same difference in the power coefficient. Hence, the output poweris controlled more precisely.

Fixed-speed-fixed-blade VAWTs suffer from high demands on the self stall reg-ulation property. Usually, small scale VAWT s are not equipped with the bladepitching control for simplicity reasons. In fixed blade VAWTs, at which the rotorspeed is kept constant, the more the wind speed increases, the larger the angle ofattack becomes. Thus the amount of stall will increase as well. In fixed speedwind systems, which are connected to the grid directly, the rotor speed is constantand accordingly the self regulatory stall is always present. From the wind systemcomponents’ point of view, there are several demand points which are listed below.

• Aerodynamic load will be large. Therefore the stiffness and mechanical strengthof the turbine has to be high.

• Overload capacity of the generator has to be high.

• Either the wind turbine rotor should have high starting torque or additionalmeasures for starting should be provided. This is because self starting bymeans of pitching the blades is not provided.

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As a result, application of fixed blade VAWTs with variable speed wind systemsrather than with the fixed speed systems are proposed.

The VAWTs’ power coefficient’s optimum is transferred to the lower tip speedratios compared to HAWTs’, which according to E. Hau, is their major disadvantage.As the speed of the VAWT is lower, in order to achieve the same power, VAWTsrequire higher torque rate. This might increase the stiffness requirements on VAWTs [2] .

Maximum Power Point Tracking

The maximum Power Point Tracking is a control method which controls thewind turbine rotor speed by controlling torque of the generator. The blade pitchingdrive is a mechanical equipment which has a delay in response time in rapidlychanging wind conditions. Thus in gusty and turbulent winds, it can influence theenergy yield and subsequently causes mechanical stress on the turbine. However,in order to maximise the power production, the rotor speed of the generator can becontrolled electrically. MPPT techniques, accordingly, are developed in an attemptto achieve the maximum power coefficient. This is usually done by adapting therotor speed to the optimum tip speed ratio. Rotor speed of an electrical machinecan be controlled by means of the difference in its input power and output power.The output power of the generator, in a variable speed wind system is controlledwith the help of a power electronics converter. If the speed of the rotor needs to beincreased, the output power is kept lower than captured power. On the other hand,when the rotor deceleration is required, the output electric power is maintainedhigher compared with the captured power.

There are different ways of making the wind speed reference for MPPT . Thesimplest one is to measure the wind speed by anemometers that is send it to thecontroller. However, there are several issues associated with the wind speed mea-surement. Generally, measuring the wind speed at a distant place in a large windsystem comes with a certain time delay. In small VAWT s, anemometers, which areinstalled nearby are provided. However, lack of quick response time can be influen-tial on reliability, since small VAWT s are usually installed in areas with turbulentwinds.

Sensorless MPPT method is a control method without the wind speed measure-ment. There are several different approaches for implementation of of such controlmethod such as constant output power, fixed voltage and the wind speed prediction.Usually, autoregressive statistical models are used for prediction of the wind speed,based on the historical data [11]. Captured energy from each set of data is usedfor predicting the wind speed at the next time frame. The accuracy of the windspeed prediction depends on many factors including the length of the sampling timeframe. The shorter the sampling time frame, the higher the accuracy of wind speedprediction.

One of the major considerations when selecting control method is its easy im-plementation. Short computation time and low sensitivity to parameter adjustment

14

2.5. COMPARISON BETWEEN VAWTS AND HAWTS

is a benefit.

2.5 Comparison Between VAWTs and HAWTsA comparison between VAWTs and HAWTs is presented below, both in terms

of design and performance aspects [8]. Furthermore, detailed description is givenfor some aspects mentioned earlier in the text

2.5.1 Design: Yaw Mechanism

Unlike the VAWTs , the HAWTs are in need of a yaw mechanism. The functionof yaw mechanism is to direct the rotor in the wind direction in order to maximisethe aerodynamic efficiency. It includes an electrical motor as a drive mechanism anda control system, which detects the wind direction and command the mechanismto rotate. The main disadvantages are need for maintenance and the cost of theequipment, installation and operation. Additionally, there is a delay in rotationof of the nacelle in the right direction due to the time response. VAWTs, on theother hand, do not need yaw mechanism, while they are omnidirectional and theycan rotate in both directions. This property makes VAWT s highly suitable forlocations where the wind is gusty or turbulent like mountainous areas and urbanneighborhoods.

2.5.2 Design: Axis of Direction

Some advantages and considerations for VAWT s come with vertical axis ofrotation. Usually, HAWTs’ drive train is located in nacelle on top of the tower.This increases mechanical stress on the tower, which requires strong foundation. InVAWTs, a part of the drive train i.e. the generator and the control equipment canbe located on the ground. The mechanical power is transferred via a long shaftfrom the hub to the generator, which has many advantages. The generator size andweight will have low priority as a design constraint. However, torsional vibrationsof the long shaft with high torque might become a problem. A long airgap might bea remedy. The disadvantage of this is that it might influence the machine design,which makes the machine costly. A dynamic analysis is proposed.

2.5.3 Design: Direct Drive

VAWTs are more suitable for direct drive applications compared with the HAWTs.Electric machine in direct drive wind system usually operates with low speed andhigh torque. For a constant power rating and constant torque density of a machine,weight is positively correlated with the torque rating. Consequently design withhigher torque in direct drive will have more weight. In HAWT s higher weightof the machine in direct drive puts more mechanical stress on the tower. UnlikeHAWTs, this is not an issue for a VAWT, as the machine is located on the ground.

15


2.5.4 Design: Wind turbine construction

Construction of the blades for VAWTs is easier compared with that of HAWTs[3]. One reason is that the blades of a HAWT are supported at their root byconnection to the hub and they have to be stiff and self-supportive. Furthermore,they are twisted along their length for aerodynamical purposes, i.e. to increasethe power capture. This makes the mechanical construction of blades tougher. Onthe other hand VAWT s’ blades are connected to the hub in their middle point.Additionally, the VAWT s’ blades are straight and not twisted along their length,which makes manufacturing of the blades much easier.

2.5.5 Design: Structural Mechanics

HAWT s and VAWT s are both subject to different mechanical stresses. Theblades of HAWT suffer from cyclic reversing gravity loads as well as periodical loadsdue to wind shear. Meanwhile, the blades of VAWT s are associated with bendingmoments caused by centripetal acceleration. Torque ripple is generally higher inVAWTs compared with HAWTs. This alleviates, in variable speed applications,with higher number of blades and higher size of the wind turbine rotor.

2.5.6 Aerodynamics: Performance

Aerodynamic efficiency of commercialised HAWT s is higher compared with theirVAWT counterparts. A measure for this is the power coefficient, which typically forHAWT is between 0.4 and 0.5, while for VAWT this is typically 0.4 . HAWTs havebeen subject of research for decades and the design optimisation has progressed.It seems that development of wind power plant technology, with more emphasison HAWT, has made it possible to reach higher values of the power coefficient.HAWTs can start at low wind speeds; On the other hand, VAWTs have poor startingcharacteristics and they require to be started by other means.

2.5.7 Aerodynamics: Power Control

HAWT and VAWT can use different methods to control the power flow. Powercontrol is a necessity otherwise wind turbine rotors might be damaged mechanicallyin high wind speeds e.g. 25 m/s . Unlike HAWTs which use blade pitching forpower control, the small VAWT s use electrical machine to control the absorbedpower, since implementation of blade pitching does not suit their scale. The differ-ence between the input power and the output power from the generator can eitheraccelerate or decelerate the wind turbine rotor speed.

2.5.8 Noise

VAWTs have lower noise compared with that of HAWTs [3]. There are two dif-ferent sources of noise; First is aerodynamic noise generated by the blades; Second,

16

2.6. VIBRATIONS IN WIND ENERGY SYSTEMS

the mechanical noise generated from the drive train. In general, VAWTs have loweraerodynamic noise which is strongly related to the wind turbine rotor speed. Inwind systems with power control, rotor speeds are controlled by the optimum tipspeed ratio. HAWTs’ optimum tip speed ratio value is typically between 5 and 7while it is 4 for VAWTs.

2.6 Vibrations in Wind Energy SystemsWind systems are prone to vibrations because of slender and elastic construction.

Cyclically alternating forces can be origins of excitation of vibrations and possibleresonances, which can lead to vibration of either one component or entire windsystem. Therefore, in the design stages the vibrational modes of entire wind systemand its subsystems have to be analysed in order to assure dynamic stability. Maindynamic vibrational behaviours are:

• Aeroelastic instability of the rotor blades.

• Torsional vibrations of the drive train.

• Dynamics of yaw system (limited to HAWT s).

• Vibration of the entire wind turbine.

2.6.1 Torsional Vibrations of the Drive TrainThe frequency response of the system is a major criterion to determine the

dynamics of its vibrations and it gives information about all natural frequencies.Natural frequency is called eigen frequency in the subject of dynamics. Since res-onance might occur in the natural frequencies, they are sometimes also referred asresonant frequency. Therefore, it has to be ensured that natural frequencies of thesystem or of its components are far from the applied excitation frequencies, duringthe design stage.

Dynamics of the mechanical drive train of the wind systems is influenced byforced torsional vibrations. The vibrations depend on different characteristics ofparticipating masses, namely

• Mass moment of inertia.

• Damping constant.

• Rotational stiffness.

Depending on the number of degrees of freedom, the system has one or more eigenfrequencies. In a drive train modeled with one degree of freedom, value of dampingratio is proportional to the damping constant and inversely proportional to the massmoment of inertia and the eigen frequency. The damping ratio determines amountof damping the system intrinsically has. When, in systems with low damping,

17


resonance occurs, amount of angular displacement might be dramatic that leads tofatigue or fracture.

A dynamic analysis of mechanical drive train components is proposed. Dynamicsof drive train’s components i.e. electrical machine, shaft and gearbox influencetorsional vibrations of each other and also the drive train entirely. In [12], thevibration of electromagnetic origin is presented for PMSG s, and essential vibrationmodes with shape of possible deflections are distinguished. The gearbox, in gearedsystem, affects the damping of the system severely. A complete dynamic study isout of scope of this work. However, the author emphasizes that this study is vitalto guarantee a noise free performance and an acceptable lifetime.

2.7 Noise EmissionWind system noise emission is of significance especially in populated areas. In

the field of acoustics, it is measured by sound pressure level in dB(A). The accept-able noise level is subject of technical design specifications, standards and legisla-tions. However, for small scale wind systems, its main significance is in customersatisfaction. The amount of acceptable sound pressure level is legislated, based onthe time (day/night) and surrounding type (variation from fully residential to fullyindustrial). Generally, amount of accepted sound pressure level in industrial sur-roundings is higher compared with the residential surroundings. It is also higherfor days than nights.

Aerodynamic noise of wind systems is less problematic as the wind speed in-creases. High wind speed contributes to ambient noise, when the wind collides withobstacles,but it also contributes to high aerodynamic noise of the wind system.However, on a lower scale it increases 2.5 dB(A) per 1 m/s increase in the windspeed, where on the other hand wind turbine noise increases only 1.0 dB(A) per 1m/s increase in the wind speed. In low wind speeds, wind turbine noise is highercompared with the ambient noise. As the wind speed increases, the ambient noisestarts to exceeds the wind turbine noise. When discrepancy of these noises reachesto 6 dB(A), then the wind turbine noise is no longer contributing to perceptibleincrease in sound pressure level. Generally speaking, at wind speeds higher than 10m/s, wind turbine aerodynamic noise cannot be perceived.

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Chapter 3

Electrical Machines for Wind EnergySystems

3.1 Different Topologies of Electrical MachinesThis chapter deals with different topologies of electrical machines for VAWT.

In the text, Direct Current (DC) and induction generators precede synchronousgenerators. This chapter, furthermore, discusses "Design of a Permanent MagnetSynchronous Generator for a Vertical Axis Wind Turbine". Therefore the emphasisis put on various configurations of PMSG . In sections 3.2 and 3.3, different cat-egories of PM synchronous machines are described. In section 3.4, implementablewinding techniques with their effect on performance are given. Final section focuseson thermal analysis of PM machines.

3.1.1 DC GeneratorsThe application of DC generator in wind energy systems is not widely spread,

mostly because of the high maintenance requirement of brushes and commutatorand a need of a full scale inverter in order to get connected to the AlternativeCurrent (AC) grid.

Usually, DC generators are restricted to non-grid-connected wind energy systemswith small DC loads, i.e. battery chargers [2].

3.1.2 Induction GeneratorsInduction generator consumes reactive power which leads to a poor power factor

of the machine. The power factor of smaller induction machines is lower compared tolarger ones. The consumption of reactive power is penalised by many grid operators,since it causes losses in the grid. Some solutions are offered for active or passivecompensation of reactive power. They include capacitor banks 1 or condensers 2.

1passive solutions2active solution

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CHAPTER 3. ELECTRICAL MACHINES FOR WIND ENERGY SYSTEMS

Hence these solutions are costly.

Fixed Speed

Fixed speed wind energy systems including conventional Squirrel Cage / ShortCircuit Induction Generator (SCIG) and a gearbox have been in use for decades. Abig advantage is simplicity in operation and control of the system, however, thereare also some disadvantages. In general, the wind is gusty and turbulent particularlyin urban areas, which very often varies the speed of the rotor and as a result a loweraverage efficiency is gained. Normally, dynamic disturbances are unavoidable inoperation of the wind systems. They can occur in the turbine, e.g. variation in theshaft power, and in the grid, e.g. short circuits. However, in fixed speed systemsthe damping is low. Disturbances from the turbine and the grid influence eachother harshly. Inrush current is, furthermore, an issue in wind systems with largeinduction machines. Figure 3.1 shows a block diagram of a typical fixed speed windsystem including conventional SCIG gearbox and a transformer. A fixed speed IGsolution including gearbox is suggested in chapter 4

Multi speed IG is suggested for improving the average efficiency in areas withgusty and turbulent winds. An electrical machine with usually two speed steps ischosen. First step works in partial load conditions with low wind speeds while thesecond works in full load conditions with high wind speeds. There are differentwaysof such a system implementation. One solution, which also is the simplest one,is to have one IG with two different windings and two different numbers of poles.The second and more common solution is to utilise two induction machines. Inboth implementations, it will be possible to improve the average efficiency as wellas the average power factor. The latter solution has been used in Danish windsystems during 80s and 90s [13]. Still, a complicated control system for switchingbetween the steps remains an issue. Furthermore, cost of two windings in the formersolution and cost of two IG s in the latter makes the multi speed wind systems moreexpensive.

Double Fed Induction Generator

Double Fed Induction Generator (DFIG) is a variable speed wind system in-cluding induction machine where also the rotor is connected to the grid. Part ofthe power is either provided from the grid or delivered to the grid through the ro-tor. This power is called the slip power. Frequency of the slip power is varied insuch a way that the rotor field frequency is maintained constant. Variation of thefrequency of the slip power is established by means of two power electronics backto back converters. Bidirectional flow of the power in the back to back convertersgives the opportunity to work in subsynchronous mode as well as oversynchronousmode. Back to back converter in DFIG consists of one machine-side-converter, aDC link capacitor and a grid-side-converter. Role of the machine-side-converter isto control the speed or the torque of DFIG and the machine power factor, while

20

3.1. DIFFERENT TOPOLOGIES OF ELECTRICAL MACHINES

Figure 3.1. Block diagram of a fixed speed wind energy system including a conven-tional SCIG, a gearbox and a transformer [2].

the role of the grid-side-converter is to minimise DC link capacitor’s voltage ripple.Figure 3.2 shows block diagram of a typical DFIG including a transformer.

The benefit with this solution is the possibility of utilisation of conventionalinduction generators in a wider speed range and still obtain high efficiency. Becausethe converter is connected to the rotor, it only has to carry part of the power insteadof entire rated power. Thus, the converter in DFIG is dimensioned in accordance tothe required speed range. Usually the operating speed range does not exceed ±40% of the synchronous speed. In most of the wind systems on the market today, thisis ±30 %. In [14], it has been shown that the converter rated at 30 % of generatorrated power is adequate for control of wind turbine rotor within a reasonable speedrange. In other applications which will be introduced later on, the converter isdimensioned for the full power. Thus the cost and the losses of the converters inDFIG are lower in comparison to full power converters. This might be an issue forlarge wind systems. Other advantage is that the reactive power can be controlledindependently from the active power. It means that DFIG can operate close to theunity power factor. The drawbacks with conventional DFIG s with gearbox are [2]:

• High maintenance due to the slip rings.

• Limited capability of supplying reactive power.

• High torques in the machine during faulty conditions.

• Additional measures are required to limit the start-up current.

Moreover, the most complex control, especially regarding converters in wind systemsare related to DFIG , which makes them essentially more economical for large windsystems rather than small systems.

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Figure 3.2. Block diagram of a typical DFIG including a transformer [2].

3.1.3 Synchronous Generators

The synchronous machines have many advantages over induction machines. Oneof them is a higher efficiency. It is because the magnetising current is not a partof the stator current. In induction machines reactive power for rotor excitation iscarried by stator winding as well as the active power for conversion. Accordingly,synchronous generators will have better efficiency and better power factor. In vari-able speed wind systems, usually, the synchronous generators are connected to thegrid via a power electronic converter. The amount of deliverable active power fromSynchronous Generator (SG) depends on rating of a converter in Volt-Amperes andthe power factor of SG . Thus, for the same rating of the converter, the closer thepower factor gets to unity, the more active power can be delivered.

Additionally the rotor speed does not depend on the electrical load conditions.In wind systems it is more convenient to control the rotor speed merely based on thewind speed. The other advantage is that they can have longer air gaps compared toinduction machines. In induction machines, the airgap length is kept small to limitthe magnetisation current and to improve the power factor [15] . In synchronousmachines, on the other hand, it is desirable to have a longer airgap as it helps toreduce armature reaction and the synchronous reactance which in turn improvesthe stability.

Fixed speed wind systems with SG have the same disadvantages as their IGcounterparts. The dynamics of the grid and the wind turbine are transferred toeach other without considerable damping which can lead to the loss of synchronismwith the grid. Since the rotation speed is determined by the frequency of the grid,the system becomes even more sensitive. In addition, there is also need for startingand synchronising equipment too.

The significance of a variable speed wind systems equipped with a SG lies in theircapability to meet the aerodynamic requirements in the widest speed range. To keepthe tip speed ratio at its optimum, the wind turbine rotor speed varies proportionalto the wind speed. This, unlike IGs, provides rotor speed independency from load

22

3.1. DIFFERENT TOPOLOGIES OF ELECTRICAL MACHINES

conditions. Wide operational speed range, from zero to rated speed, is beneficialfor control purposes.

Operational advantages of a SG with power electronics converters are numerous,like for example voltage regulation which is handled by the grid-side-converter.Another advantage is that dynamic disturbances of the grid and the wind turbine areisolated from each other and SG is not at risk of losing synchronism. Furthermore,starting and synchronising equipment is not needed as this is taken care of by powerelectronics converter. The only advantage of IGs over SGs is that the converter isnot dimensioned for full power. However, with recent decrease in cost of powerelectronic components, this is not of concern anymore.

Wounded Rotor Synchronous Generator

Wounded Rotor Synchronous Generator (WRSG) s have been scope of researchfor many years. The main advantage of WRSG over PMSG is that it intrinsically canproduce reactive power and subsequently regulate the voltage. Thus it is possible tocontrol the power factor according to electrical load conditions. In power productionWRSG injects the reactive power to compensate loads’ reactive power consumption.

Nonetheless the WRSG has not gained popularity among the wind turbine man-ufacturers. It is mainly because that the brushes for DC excitation in WRSG requiremaintenance. Mechanical vulnerability of rotor windings arising from rotation leadsto winding insulation damage.

Permanent Magnet Synchronous Generator

Self excitation brings about various benefits. One is the elimination of the rotorcopper losses. Hence PMSG s are more efficient compared to WRSG s. UnlikeWRSG no external power supply is needed. The maintenance is eliminated sincebrushes and slip rings as well as the rotor windings are removed.

The common issue with WRSG is the relation between the frequency inducedand the mechanical speed of the rotor. When the wind speed changes, the ro-tor speed and thereby the frequency of the induced voltage changes. However, invariable speed applications with PMSG this is usually not of concern since the gen-erator is connected to the grid through a converter that will adapt the frequency ofthe induced voltage to the grid frequency. One other consideration is that, unlikeWRSG, the field provided by magnets is not controllable. Thus, it is not possibleto regulate the voltage and the reactive power. In variable speed wind systems, thisis, usually, not an issue since the grid-side-converter regulates the output voltageand the power factor is determined by the grid. Lower maintenance requirementsand thus lower cost are the main reasons why PMSGs are proposed with variablespeed wind systems.

Yet another issue that needs to be considered is the risk of demagnetisation ofmagnets due to the temperature rise; the magnets can be partially or fully demag-netized. In partial demagnetisation the magnetic properties are weakened. In full

23


demagnetisation magnetic properties are completely lost and they require remag-netisation which is a tedious task and in some cases impossible and a new rotor isrequired. Thus a thermal study is suggested to guarantee that the magnet workingtemperature is, in any conditions, preserved low. Additionally, the partial demag-netisation is usually a case during a short circuit where some parts of the magnetsare exposed to high opposing magnetic fields.

In [16] it is shown that PMSG s are more suitable for gearless applicationscompared to WRSG s. In comparison of PMSG and WRSG and varying the numberof poles, it can be shown that once the number of poles reaches high values, the rotoryoke height of WRSG becomes thicker. Consequently, weight and size of WRSGsurpasses that of PMSG.

3.2 PM Synchronous MachinesA direct drive wind energy systems cannot employ a conventional high speed

(and low torque) electrical machines. Hartkopf et al. in [17] has shown that theweight and size of electrical machines increases when the torque rating increases forthe same active power. Therefore, it is essential task of the machine designer toconsider an electrical machine with high torque density, in order to to minimise theweight and the size. In [18] and [19], it has been shown that PM synchronous ma-chines have higher torque density compared with induction and switched reluctancemachines. Thus a PMSG is chosen for further studies in this work. However, sincethe cost effectiveness of PMSG is an important issue, low manufacturing cost hasto be considered as a design criterion in further steps. There are a number of dif-ferent PMSG topologies; some of them are very attractive from the technical pointof view. However, some of the state of the art topologies suffer from complicationin manufacturing process which results in high production costs.

PM excitation offers many different solutions. The shape, the size, the position,and the orientation of the magnetisation direction can be arranged in many differentways. Here, presented topologies include those of which are investigated for lowspeed applications or variable speed applications. This list encompasses radial oraxial flux machines, longitudinal or transversal flux machines, inner rotor or outerrotor machines and interior magnet or exterior magnet machines. Slotless machinesare not presented here.

3.2.1 Radial Flux or Axial FluxAirgap orientation can be identified in two different ways. Here a hypothetical

normal vector to the airgap is adopted along the flux direction. The axis of themachines is assumed to be along the length of the machine in the cylindrical coor-dinate system. Relation of the normal vector with the axis of the machine decidesthe radial or axial topology. If the normal vector is perpendicular to axis, machineis called radial. If the normal vector is parallel with the axis, the machine is calledaxial.

24

3.2. PM SYNCHRONOUS MACHINES

Figure 3.3. Cross sectional view in radial direction and in axial direction, respec-tively, of a typical radial flux PMSG [21].

Radial Flux Machines

Radial flux machines are conventional type of PMSG s. The manufacturingtechnology is well established which makes the production cost lower comparedwith the axial one [20]. Furthermore, they are very flexible for scaling, as thehigher power ratings of the machine are achieved by increasing the length of themachine. In other words completely new design and completely new geometry canbe avoided. They are extensively used in ship propulsion, robotics, traction andwind systems. Figure 3.3 shows cross sectional view in radial direction and in axialdirection, respectively, of a typical radial flux PMSG .

Axial Flux Machines

Various axial flux topologies have been proposed in recent years and their prosand cons are categorised. Generally, in axial flux machines length of the machineis much smaller compared with radial flux machines. Their main advantage is hightorque density, so they are recommended for applications with size constraints espe-cially in axial direction. They have found application in gearless elevator systems,and they are rarely used in traction, servo application, micro generation and propul-sion systems [22]. Figure 3.4 shows cross sectional view in radial direction and inaxial direction, respectively, of a typical axial flux PMSG .

One of the disadvantages with the axial flux machines is that they are notbalanced in single rotor single stator edition. Usually, for a better performance therotor is sandwiched between two stators or vice versa. Unlike radial flux machines,

25


Figure 3.4. Cross sectional view in radial direction and in axial direction, respec-tively, of a typical axial flux PMSG [21].

the stator windings are located in the radial direction. A circumferentially laminatedstator is required for reduction of iron losses, which complicates manufacturingprocess [23].

Scaling of axial flux machine is another drawback. Unlike radial flux machines,any increase in length is accompanied by increase in airgap diameter. Hence, toincrease the power rating a new design and a new geometry is needed [24]. Oneother way to increase the power rating is by increasing number of stators and rotors.This, however, makes the machine costly.

3.2.2 Longitudinal or Transversal

In transversal flux machines, the plane of flux path is perpendicular to thedirection of rotor motion. The use of transversal flux machines can be proposed inapplications with high torque density requirement [22]. One attractive property ofthe transversal flux machines is that the current loading and the magnetic loadingcan be adjusted independently. They are proposed for wind systems, free pistongenerators for hybrid vehicles and ship propulsion [22]. Figure 3.5 shows a fractionof a typical transversal flux PMSG. Both PMSGs in Figures 3.3 and 3.4 are oflongitudinal type.

One drawback of transverse PMSG is high leakage flux which results in poorpower factor. To achieve lower flux leakage, number of poles has to be decreasedwhich in turn reduces torque density. The task of the designer is to find a com-promise between the flux leakage and the torque density of the machine. Further-

26

3.2. PM SYNCHRONOUS MACHINES

Figure 3.5. Fraction of a typical transversal flux PMSG [22].

more the major drawback with rotational ones is relatively difficult manufacturingprocess. Yet another drawback is that, in rotating transverse PMSG, mechanicalconstruction is weak due to large number of parts.

3.2.3 Inner Rotor or Outer Rotor

The rotor surrounds the stator in outer rotor machines. In these machines, themagnets are usually located on the inner circumference of the rotor. Accordingly,for the same outer diameter of the machine, in the outer rotor machine the rotor hashigher radius compared with the stator and it can be equipped with higher numberof poles for the same pole pitch [21]. Another advantage is that the magnets are wellsupported despite the centrifugal force. Furthermore a better cooling of magnetsis provided. Outer rotor machines are common for small HAWT turbines, wheresometimes the hub carrying the blades is directly fixed to the rotor [25].

However, the inner rotor machines are a more common solution present on themarket today. In small machines, the main contributions to the losses are copperlosses and therefore the stator winding has the highest temperature rise in the activematerial of the machine.

Hence, it is more beneficial to put the stator winding, rather than the magnets,closer to the housing, where the cooling properties are good. This causes less tem-perature rise for the same amount of losses. Figure 3.6 shows an inner rotor PMSGand an outer rotor PMSG .

27


Figure 3.6. Inner rotor PMSG (left) and an outer rotor PMSG (right) [26].

Figure 3.7. A surface mounted rotor for a PMSG [15].

3.3 PM Configurations

The PMSG can be divided into different topologies depending on the magnetarrangement on the rotor. These are introduced below. However, it should bementioned that the rotor configurations are not restricted to the given examples,e.g. in interior magnets various configurations are implementable.

3.3.1 Surface Mounted Magnets

A common topology is where the magnets are mounted on the surface of the ro-tor, sometimes referred to as exterior magnet, but, more known as Surface MountedPermanent Magnet (SMPM) machine. The magnets are glued and/or bandaged tothe rotor surface in order to withstand the centrifugal force. Usually, the magnetsare oriented or magnetised in radial direction and more seldom in circumferentialdirection. The direct and quadrature reactances are almost equal. Construction ofthe rotor core in SMPM is the easiest among different PM configurations due tosimple rotor geometry. Figure 3.7 shows a surface mounted rotor for a PMSG.

28

3.3. PM CONFIGURATIONS

Figure 3.8. Two different inset magnet rotors for PMSGs [15].

3.3.2 Inset MagnetsIn inset magnet machines, rotor core of SMPM machine is modified with iron

interpoles. Iron interpoles are protrusions of rotor core wherever magnets are notpresent on the surface. Interpoles cause saliency and the inductances in directand quadrature directions are different. In these machines, part of the torque isreluctance torque and the torque density is higher compared to SMPM . Themagnets are radially magnetised. The flux leakage is higher in comparison to SMPMwhich results in lower power factor.

Therefore, in direct drive application, the inverter utilisation is lower comparedto geared applications. This topology is not common in gearless wind systems.Figure 3.8 shows two different inset magnet rotors for PMSGs.

3.3.3 Buried MagnetsIn this configuration the magnets are put inside the rotor and therefore it is

referred to as Interior Permanent Magnet (IPM) machine. There are many differentways in achieving interior magnet configuration. The magnets can be magnetisedin radial direction as well as circumferential direction. The thickness of iron bridgesbetween the magnets has to be designed carefully to avoid saturation. Again, theinductance in quadrature axes is different from that in direct axes direction. Figure3.9 shows six different buried magnet rotors for PMSGs.

The main advantage of this PM configuration is that weak PM material such asferrite can be used. Another advantage is magnetic protection against short circuitconditions [15]. It is because in faulty conditions, iron bridges between magnetsget saturated which prevents high reverse demagnetising field to reach the magnets.This topology is suggested for high speed applications due to mechanical strengthof the rotor against the centrifugal force.

Burying magnets in production stage is a complicated process. Moreover a non-ferromagnetic shaft is vital, otherwise a large part of magnets’ flux penetrates theshaft, which is located nearby, and it will not be utilised for magnetisation of the

29


Figure 3.9. Six different buried magnet rotors for PMSGs [15].

airgap. Like inset magnet machines, the flux leakage is high which reduces thepower factor, the efficiency and the inverter utilisation.

In [21] , F. Libert studies two different buried magnet topologies and concludesthat both gives rise to manufacturing problems. One is called V-shaped buriedmagnet design and the other is called tangentially magnetised buried magnet design.The author also mentions some saturation problems when the number of poles ishigh. This is a common problem for the buried magnet topologies. If the number ofpoles increases, the distance between magnets decreases (when rotor core diameteris kept constant). Therefore, the narrow iron bridges get saturated more easily.Figure 3.10 shows cross section of a pole pair of a V shaped buried magnet design(left) and a tangentially buried magnet design (right).

3.4 WindingThe windings can be divided into overlapping and non-overlapping categories.

Over lapping windings can be wound either distributed or concentrated. Non over-lapping windings can be wound solely in concentrated way. Figure 3.11.a) showsa distributed overlapping winding with Qs = 24 and q = 2 for a four pole machine.Figure 3.11.b) shows a concentrated overlapping winding with Qs = 12 and q = 1.Figure 3.11.c) shows a double layer concentrated non-overlapping winding withQs = 6 and q = 0.5, which is the traditional concentrated winding. Figure 3.11.d)

30

3.4. WINDING

Figure 3.10. Cross section of a pole pair of a V shaped buried magnet design (left)and a tangentially buried magnet design (right) [21].

shows a single layer concentrated non-overlapping winding with the same values ofQs and q as Figure 3.11.c).

The term overlapping is usually omitted. For instance "overlapping distributedwinding" is almost always referred to as distributed winding. In this text, onthe other hand, "concentrated winding" stands for "double layer concentrated non-overlapping winding".

3.4.1 Distributed Winding

Distributed winding has been used for Brushless Alternative Current (BLAC)machines for decades. One of the advantages of distributed winding is that it cangive high value of winding factor when q is high and the full pole pitch is chosen.Nonetheless, it has some drawbacks, like for instance its long end windings. Endwindings do not contribute to induction of the phase voltage. The role of endwindings is limited to carry the current from one coil to the other. Thus, endwindings are associated with copper losses and it is desired that the end windingsare as short as possible. In distributed winding, when the coil sides are far fromeach other, the copper losses will be higher and the axial length of the machine willbe longer. Thus distributed winding reduces the efficiency of the machine. If thesize of the machine is a critical design parameter, the concentrated winding shouldbe considered.

3.4.2 Concentrated Winding

In concentrated winding the coil turns are concentrated around one tooth andtherefore it will benefit from short end windings due to non-overlapping property.Another advantage is better heat conductivity between the winding and the tooth.Furthermore, segmentation of stator core teeth is possible [28]. In this way, thewindings can be pre-pressed and the coils can be made with rectangular shape,which, in turn, will give high slot fill factor and high torque density.

Concentrated winding exhibits high fault tolerance on SMPM s and is associatedwith increase in leakage inductance [29]. Implementation of concentrated winding

31


Figure 3.11. Windings in low speed PMSG a) distributed overlapping winding.b) concentrated overlapping winding. c) double layer concentrated non-overlappingwinding. d) single layer concentrated non-overlapping winding [27].

increases leakage inductance which in turn limits high currents in short circuitconditions. In fact in faulty conditions, the excitation field of WRSG is reducedto protect the machine. However, excitation of PMSG is not controllable. Hence,introduction of higher flux leakage may be an advantage. In addition, due to non-overlapping property, coils are physically and thermally seperated in a better waycompared with distributed windings. This reduces the risk of phase to phase shortcircuit in the event of damaged winding insulation. Furthermore, the torque ripple inSMPMs with high pole numbers and concentrated windings is reduced [21]. Higherflux weakening capability is another characteristics of concentrated winding.

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3.4. WINDING

Fractional Slot Winding

One disadvantage with traditional concentrated winding, where q = 0.5 , is alower winding factor compared with distributed winding. The reason is that the slotpitch is 2/3 of the pole pitch and, neglecting the flux leakage due to iron saturation,only 2/3 of the magnet flux is linked to the stator. As a consequence, winding factordrops to 0.866 and torque rating of traditional concentrated winding is reduced bythe same factor.

To cope with this drawback, fractional slot concentrated winding are suggested,which utilises any feasible combination of p and Qs. Thus, it is possible to havehigher winding factors with higher torque density. In applications where weight andsize are critical design parameters, the fractional winding may be of interest.

F. Magnussen in [20] and F. Libert in [21] have studied numerous slot polenumber combinations of fractional slot winding and have categorised them regardingtheir parasitic effects. It has been reported that selection of pole and slot numbershas to be chosen very carefully because of the parasitic effects that arises with certaincombinations. These parasitic effects include, cogging torque, radial magnetic forcesand alternating magnetic fields with high frequency. The disadvantage with radialforces is vulnerability to magnetic noise, while high frequency magnetic flux leads toeddy current losses in the rotor and the magnets. Some counter active measures havebeen suggested by F. Magnussen like: magnet segmentation, rotor core laminationand high mechanical rigidity of core [20] 3.

In [21] F. Libert has studied fractional slot winding in terms of winding factor,harmonic content of Magneto-Motive Force (MMF) , torque ripple, cogging torqueand magnetic forces. The study have been carried out on the design with polenumbers between 4 and 80 and slot numbers between 6 and 90. Slot pole numbercombinations are divided in few categories and general conclusions are drawn foreach category. The categories where Least Common Multiple (LCM) is high, enjoysfrom the biggest reduction in cogging torque. The highest LCM is achieved whereslot pole numbers have values very close to each other, i.e. p = Qs±1 . However, themachines with these combinations are asymmetrical. This gives rise to radial forcesand magnetic noise. The author, ultimately, suggests that the slot-pole numbercombinations with high winding factors and with symmetrical winding layouts haveto be chosen.

IPM s with concentrated winding have lower torque density than that withdistributed winding. Concentrated winding decreases saliency ratio in IPM andaccordingly the reluctance torque reduces as well. This means that an IPM withconcentrated winding will have lower peak torque and also lower torque density.Reduction of torque density can be compensated with additional iron laminationsin axial direction as the length of the machine become shorter due to concentratedwindings; This, however, is costly [30] .

3see section 3.5.4

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3.4.3 Single Layer Concentrated Non-Overlapping Winding

An advantage of a single layer concentrated windings is simpler automatisedwinding process and better fault tolerance compared to their double layer counter-parts. They use every other tooth for winding which results in the simpler automa-tized winding. The better fault tolerance comes with better physical and electricalseparation between coil turns.

Although the benefits with this winding looks attractive, the double layer wind-ings are actually more common today. It is mostly because single layer windingsuffers from longer end windings and higher inductance.

3.5 Thermal Behaviour

There are different sources of losses in electrical machines i.e. iron losses, copperlosses, etc. The losses give rise to temperature, which has dramatic influence onperformance and lifetime of electrical machines. Hence, study of thermal behaviourof an electrical machine is vital.

The temperature rise in the machine is strongly dependent on the load. In windsystems, the speed and the torque are very often lower compared with the ratingsof the machine and varies with the wind conditions. The advantage is that theaverage temperature rise will be lower in comparison to the rated operating point.However, in order to guarantee high performance and long lifetime in any operationcondition, the thermal calculations are performed based on the rated operation.

In the following subsections, consequences of temperature rise are presented anddifferent cooling systems are discussed. A brief introduction to heat transfer theoryis given, while more detailed theory is left for the reader. The most emphasis is puton introduction of sources of losses in the last subsection.

3.5.1 Consequences of Temperature Rise

Performance

Thermal loading determines pretty much the power rating of the electrical ma-chine. Values such as current density are often limited to a certain value dependingon the cooling conditions in an electrical machine. This bounds current loadingand respectively torque rating of the electrical machine. In other words, even ifit is possible to manufacture more compact machines with higher torque densities,cooling capability restricts further reduction in the size.

Lifetime

The lifetime of an electrical machine is also affected by the so called thermalageing, which influences the insulation. One of the requirements on winding insu-lation is to transfer the heat and to tolerate thermal stresses during normal and

34

3.5. THERMAL BEHAVIOUR

Insulation Class Hot Spot Temperature in C

A 105E 120B 130F 155H 180

Table 3.1. Different classes of an insulation material due to IEC − 85.

faulty conditions. Commercially available insulation material can tolerate limitedtemperature rise. Table 3.1 summarizes standardised temperature rise categories.

Acceptable lifetime is expected, if the insulation material working temperatureconforms to above conditions. On the other hand, due to an empirical law, lifetimeof an insulation material halves with every 10 K extra temperature rise above thenominal temperature.

Temperature influences magnet characteristics and it can increase risk of de-magnetisation. Figure 3.12 shows B-H curve of a typical PM material for differenttemperatures. The coercivity and remanence flux density decrease when the tem-perature increases. The knee point also moves upwards. The working point shiftson working line of the magnetic circuit downwards when the temperature increases.Given a high enough temperature and an improperly designed magnetic circuit, theworking point will drop below the knee point, where the magnet loses its magneticproperties. If the machine is to be run again, PM has to be remagnetised, which isa complicated and tedious task.

Overload increases the risk of demagnetisation. In these conditions the tempera-ture exceeds the rated value and the remanence flux density of magnet decreases. Ifthe magnetic circuit is not properly designed, PM magnetic flux will reduce remark-ably. In order to compensate the reduction of the magnetic flux, the control unitwill tend to increase the current in the stator winding, since the load torque shouldbe kept the same. As a result, copper losses in the windings are increased and thetemperature raises more in the windings and eventually in the magnets. This leadsto even higher reduction of remanence flux density. In theory, reoccurrence of thiscycle can eventually lead to demagnetisation of the magnets. However, in orderto avoid demagnetisation during overload conditions, protection equipment againstover-temperature condition is offered.

Among PMSGs, Inset magnet machines and SMPMs are more vulnerable andare at a greater risk of demagnetisation compared to their IPM counterpart. Ironbridges around the magnets in IPMs saturates during faulty conditions and theycounteract penetration of strong reverse field into the magnets. However, the tem-perature rise can still be high, because the magnets are buried and the cooling ofmagnets is more difficult.

35


Figure 3.12. A typical magnet characteristics curve [20].

3.5.2 Cooling System

Cooling system facilitates dissipation of the heat, which will reduce temperaturerise in the machine. Usually electrical machines are forced cooled by air or water. Inair cooled machines a fan forces the air along the airgap. In water cooled machinesthe pump forces the water through tubes that are located in ducts. There aredifferent possibilities for putting the ducts inside the machine, they can be locatedaxially or spirally. Moreover, they can be located within the mantel (frame) or inthe stator core. Putting ducts in stator core provides better heat transfer, however,it influences the manufacturing process of the stator laminations.

Kylander has developed an analytical model for thermal analysis of inductionmachines based on experimental results [31]. The model introduces thermal resis-tances. Lindström has developed a thermal model for a PMSG [32].

3.5.3 Heat Transfer Theory

Heat transfer is a result of a difference in the temperature. The heat is alwaystransferred from higher temperature towards the lower temperature. It occurs inthree different forms namely conduction, convection and radiation.

36


Conduction

Heat transfer through a substance is defined as conduction. The substance canbe in any state: gas, liquid or solid. To measure conductive property of a materialthermal conductivity is introduced. Usually the value of the thermal conductivityof materials lies in the range between 0.026 W/m/K for air and 427 W/m/K forsilver [33]. Conduction is modeled by Fourier’s law which also can be applied whenheat is generated inside the body. However, when the time variation of conductionis considered, specific heat capacity of the body, which represents thermal capacity,is also introduced. In steady state analysis, however, this is neglected.

In the field of electrical machines, conduction is the most common form of heattransfer in both steady state and transient conditions.

Convection

Heat transfer from a heat source by means of fluid movement is defined asconvection. Fluid flow is caused by an external force either in natural or in forcedconditions. In the former, discrepancy in fluid density creates the force; In thelatter the force is caused by a pump or a fan. To measure convective property ofa fluid, heat transfer coefficient is introduced. Average heat transfer coefficient ofa fluid lies in a range between 6 W/m2/K for natural air convection and 120, 000W/m2/K for condensing of steam [33]. Estimation of this value is complicated, sinceit depends on many variables like geometry of the surface, temperature difference,flow mechanical characteristics and physical characteristics of fluid i.e. viscosity.Convection is explained by Newton’s law of cooling.

In the field of electrical machines, convection is the second most common formof the heat transfer in the steady state, but it does not play a remarkable role intransient conditions.

Radiation

Heat transfer by means of radiation does not need any substance. Thermalradiation is a function of couple of parameters as reflectivity, temperature difference,emissivity and geometry. It is modeled by Stefan Boltzman’s law. In electricalmachines the amount of radiation is negligible.

3.5.4 Losses in PMSG

The main function of an electrical generator is to convert energy from mechanicalinto electrical. However, a part of energy is lost during this process which is referredto as losses. In electrical machines losses are divided into two categories i.e. normallosses and stray losses. Stray losses are additional losses that arises in an electricalmachine aside from the normal losses considered in usual performance calculationsfor motor efficiency [15]. The main part of the stray losses are usually caused byeddy currents due to the leakage flux.

37


The normal losses involve copper losses in stator windings, iron losses in statorand mechanical losses such as friction. The iron and the copper losses are the biggestcontributors to the losses in PMSG . One advantage of PMSG over IG is eliminationof the copper losses in the rotor, namely slip loss [34] . Estimation of normal lossesis easy and the corresponding knowledge is well established. On the other handestimation of stray losses is complicated as they depend on many parameters. Thiscomplication might lead to inaccuracy in the calculations of the thermal behaviourof the machine. A thorough discussion of losses is presented in order to improve abetter perspective over variety of origins of losses.

Stator Core Losses

Various phenomena associated with variation of magnetic flux results in thestator core losses. Among them, the rotational and excess losses are probably lesswell known while the hysteresis and eddy current are more familiar. Here, hysteresisand eddy currents losses are introduced first together with Epstein frame test. Then,the two former are presented. Finally counteractive measures are suggested.

Eddy currents are induced in the stator iron due to variation of magnetic fieldbased on the Faraday’s Law and they create losses based on the Ohm’s Law. Theamount of losses depends on the time rate of change of magnetic flux density. As-suming sinusoidal variation of magnetic flux density, eddy currents loss will dependon electric properties of material as well as applied field, including frequency andmaximum value of magnetic flux density.

Hysteresis losses are caused by magnetic properties of ferromagnetic materialin a time varying magnetic field. The amount of these losses depends mostly onthe magnetic properties of the material but also on the applied field, including itsfrequency and maximum value of magnetic flux density.

To estimate the iron losses in the stator, the results from Epstein frame testare used in analytical calculation. Accurate prediction of iron losses is much moredifficult in comparison to copper losses. Accordingly, steel manufacturers providethe machine designer with results from the Epstein frame test. In this test the ironlosses of steel material, subjected to various magnetic flux densities (in terms ofamplitude and frequency) are measured. Simplified analytical models are developedto estimate the iron losses in electrical machines based on the results of Epsteinframe test. These analytical methods are validated by means of comparison toexperiments on similar machines or FEM simulations.

Angular direction of magnetic field is, usually, constant in the stator. But itvaries in regions of stator where the teeth and the yoke are connected to eachother. This results in rotational loss. In the region where it exists, it adds to thecore losses. Excess loss is not a well-known phenomenon. In order to include theeffect of rotational and excess losses, the value of estimated core losses is, usually,multiplied by a correction factor.

Calculated results of core losses may differ from the experimental results fora number of reasons. Applied field in the machine is assumed to be uniformly

38


sinusoidal in different physical points and the magnetic properties of the materialare assumed to be uniform. However, in real machines these conditions are notprevailing perfectly. A waveform of the magnetic flux density is non sinusoidal andnon uniform. Influence of harmonics, which results in non sinusoidal magnetic fluxdensity, on the core losses will be introduced later in the text. Furthermore, themagnetic property of material varies when it is subjected to mechanical stressesduring manufacturing e.g. punching.

There are various solutions available in order to reduce the core losses. Somemore common are laminated core with thin iron lamination, high resistivity andalloyed contents like silicon. These measures reduce eddy current losses. Anothersolution in order to reduce the iron losses is to reduce nominal frequency. However,the frequency is proportional to the rotor speed and to the number of poles. Asthe rotor speed is determined by the application, the frequency, therefore, cannotbe chosen arbitrarily. Furthermore, increasing the number of poles reduces the polepitch which in practice cannot be chosen too short.

Laminations are annealed after they are stamped or cut, in order to compensatethe manufacturing stresses. Variation of magnetic characteristics in cut edges isthen avoided.

Mechanical Losses

Mechanical losses are relatively small in comparison to other losses especially inlow speed applications. It encompasses two parts, namely windage and bearing.

Windage losses are caused by mechanical friction of air and rotor surface. Itdepends on various parameters and phenomena and it is quite complicated to cal-culate more accurately. For instance it depends on gas properties and the prevailinggas flow characteristics. In electrical machines the gas flow is mostly turbulent inhigh speed applications and it is laminar in low speed application. An experimentalequation in [35] gives a rough estimate of windage loss.

Pwindage = Cf ρπω3mR4L (3.1)

where ρ is the mass density of the gas, ωm is the mechanical angular speed ofrotor and R and L are radius and length of the airgap cylinder respectively. Cf isthe friction coefficient which is empirically determined.

Mechanical loss in the bearings depends on parameters like bearing type, lubrica-tor physical characteristics, shaft mechanical load and rotor speed, where lubricatorcharacteristics are dependent on the temperature. An experimental equation in [35]gives a rough estimate of bearing loss.

Pbearing = CbD3mωm (3.2)

Dm is the average diameter of bearing and Cb is the bearing coefficient, whichagain is an empirical factor.

39


Stray Losses

Stray losses are divided into stray no-load losses and stray load losses. Generally,the former is represented by permeance variation and the latter is represented byleakage flux. Space harmonics’ origin is due to the non-sinusoidal distribution ofwindings, saliency and slotting effect in an electrical machine. Time harmonicsare generated by power electronics converters operated with electrical machines.High frequency of parasitic effects results in induction of eddy current in metalparts. Active material of the machine like stator conductors, rotor core and rotorpermanent magnets are prone to stray losses.

In the following, stray losses are introduced based on the location of losses.First AC winding losses are discussed, second stray losses in permanent magnetsare described and finally stray losses in rotor core are mentioned.

Stator Winding

Eddy currents are induced in the stator windings in the form of skin and proxim-ity effects. If the source of varying applied field is the winding itself, the phenomenonis called skin effect. If the source of varying applied field is an external origin likerotor magnets, the phenomenon is called proximity effect. Eddy currents originat-ing from skin and proximity effects in machines will give rise to non uniform currentdensity distribution within the conductor, i.e. less concentration in the centre andmore concentration on the circumference. As a consequence, effective cross sectionarea for the current will be lower compared with the available cross section. Thisleads to higher AC resistance and higher losses.

Permanent Magnets

Eddy currents losses can be induced in permanent magnets in certain conditions.As mentioned, certain slot pole number combinations in concentrated winding de-sign will result in space harmonics. This influence is more pronounced in high speedmachines with high frequency. F. Sahin in [35] suggests an analytical estimationof eddy current losses in permanent magnets. In order to reduce these losses aproposed solution is magnet segmentation. In general no load stray losses causedby permeance variation can be reduced by increasing the airgap length or by usingmagnetic wedges.

Rotor Iron

Eddy currents losses can be induced in rotor core in certain conditions. In ab-sence of parasitic effects, the magnetic flux density in the rotor iron is constant.Harmonics, e.g. created by the slotting effect, distort magnetic flux in the rotor.However, in SMPM machines, effective airgap is large and these losses are insignifi-cant [12]. Again these losses are more pronounced in high frequency machines, but

40


it should be mentioned that a careful selection of slot pole number combination inconcentrated winding is mandatory.

41

Chapter 4

Induction Generator

A multiple step fixed speed WECS including induction generator is alreadyproposed in section 3.1.2. In order to work as fixed speed wind system, the systemhas to be operated at speeds higher than synchronous speed. Induction machineis able to start in Direct Online (DOL) mode. DOL means that an inductionmachine, which is at standstill, is able to accelerate when it is directly connectedto the grid. Another benefit in fixed speed WECS with induction generator is lessmechanical stress on the drive train compared with synchronous machine. Usually,the induction generator is operated between the synchronous speed and just abovethe synchronous speed. The dynamic disturbances in the grid and from the windturbine will be reflected in the variation of the slip i.e. the speed of the machine.

One disadvantage with the induction generator is reactive power consumption.Therefore, induction generators require some form of reactive power compensation.This can be provided with introduction of capacitor banks. Some control of thecapacitor banks should be implemented due to the power variation of the load.However, this may add some extra cost. Another disadvantage with the inductiongenerator is their so called inrush current. During starting, the current in inductionmachine is high, which may cause some damage to the windings.

4.1 Fixed Speed Induction Generator

Fixed speed wind turbine is still a popular concept in the rapidly growing globalwind market. Figure 4.1 shows the market share of installed fixed speed WECSin large wind turbine market. The cost of power produced by WECS is a functionof capital cost, system reliability and the energy yield. According to the theory,energy yield of variable speed WECS is higher compared with the fixed speed one.However a lower capital cost and higher reliability makes the fixed speed WECSan attractive solution. Values between 4 % - 20 % have been reported for theincrease in energy yield by utilizing variable speed instead of fixed speed systems.The reason for variation in the reported values is the methodologies adopted bydifferent researchers. Therefore, in this chapter a more cost effective fixed speed

43

CHAPTER 4. INDUCTION GENERATOR

Figure 4.1. Time variation of market share of yearly installed power of fixed speedWECS (including induction generator, capacitor banks, soft starter and output trans-former) [37].

WECS is to be verified.One possible topology for fixed speed WECS is an induction generator connected

to the line where the load is located in between. The grid maintains the voltageand the frequency and provides the machine with magnetizing current which isassociated with reactive power consumption. As a result, the machine is capableof production of active power. The power produced by the generator may exceedthe power consumption by the load and the remaining power can be injected to thegrid. However, there should be an agreement between the grid operator and theowner of the generator how to regulate the injected power [36].

4.2 Selection of Induction Motor as Generator

Induction machines are the most prevalent motors on the market. Therefore, inorder to utilise an induction machine as generator a few considerations has to betaken into account.

44

4.3. TWO STEP FIXED SPEED INDUCTION GENERATOR

4.2.1 Temperature Rise

A higher permissible temperature rise has to be considered due to the specialrequirements by the application as well as distinction between performance in motorand in generator mode. The required lifetime of the machine is 100, 000 hours. Themain constraint on working lifetime of an induction machine is the thermal ageingof the winding’s insulation material. However, the guaranteed working lifetime ofan insulation material according to the standards, regardless of insulation class,is 20, 000 hours. Therefore a 25 C safety margin is suggested to guarantee therequired lifetime.

4.2.2 Efficiency

Efficiency of the induction motor working as generator is lower for the same slip.Therefore, it is recommended that high efficiency induction motors are chosen forgenerator applications. In order to increase the efficiency of the induction machine,thinner iron lamination together with the lower loss density material can be usedand also copper with high conductivity properties in windings.

4.2.3 Size

It is suggested that the power rating of the induction machine should be around25 % higher compared with the power rating of the wind turbine. Efficiency ofan induction machine is maximum at the rated slip. For a small scale inductionmachine this can be around 80 % . Therefore the size of the induction motor shouldbe selected in such a way that at full load, the machine works at 80 % of its rating[38]. This ensures that the temperature rise, while working either as a motor or as agenerator is the same. For instance, if a 12 kW induction generator is to be used, sizeof the induction machine is 15 kW . One should consider that in motor operationmode, the hot spot is in the stator winding, since the power losses in the statorwinding are the major fraction of the losses in the machine. In generator operationmode, the corresponding power loss has to be provided from the shaft power andlater on delivered to the stator winding via the rotor and the airgap. This causessome additional copper losses in the rotor and therefore further temperature rise inthe rotor [38]. Hence, for the same temperature rise in the machine, the inductiongenerator has to be derated.

4.3 Two Step Fixed Speed Induction GeneratorMultiple step fixed speed WECS is proposed to increase energy yield of fixed

speed wind system. Rotation speed of the wind turbine in a fixed speed WECSincluding an induction generator is determined by the induction machine’s operatingrange. Therefore in a single step fixed speed system, selection of a gear ratio is ofconcern. Since the rotation speed will be maintained independent of the wind speed,

45

CHAPTER 4. INDUCTION GENERATOR

the tip speed ratio will vary quite often. This means that the power coefficientdeviates from its optimum value. The choice of the wind speed corresponding tothe optimum tip speed ratio influences selection of gear ratio and vice versa. If alow gear ratio is selected, the rated wind speed is at a high wind speed and for lowwind speeds the power coefficient is low. On the contrary, if a high value for gearratio is chosen, the machine rotates slowly and the rated wind speed is at a lowwind speed and then power coefficient drops for high wind speeds [39] .

The concept of two step induction machine aims to have high value of powercoefficient for both low and high wind speeds. With a two step induction generator,it is possible to adapt the rotation speed of the system to the prevailing wind speedfor the same gear ratio. Therefore, the variation of the tip speed ratio is halved.Two step induction generators with two different windings have two different polenumbers. The low speed step works at low wind speeds while the high speed stepis at high wind speeds.

The list of functions that have to be provided in a multiple step WECS is:

• Measurement of wind speed and direction.

• Starting command to the machine (to start as a motor).

• Switching command (between the two steps) to the generator.

• Mechanical brake for the wind turbine.

• Overload protection.

• Command of switching in the electrical load.

However a multiple step IG working in a WECS suffers from [40]:

• Switching transients when changing poles.

• High torque peaks with machines designed for low rated slip and high losseswith machines designed for high rated slip.

• Lower energy yield in comparison to variable speed WECS.

4.4 Self Excited Induction GeneratorIt is suggested that a two step fixed speed WECS is equipped with a capacitor

bank. A simulation study has been done by S.S. Murthy et al considering inrushcurrent, reactive power and efficiency of a single step 55 kW induction generatortogether with a fixed speed wind system [39] . The results shows that during startof the electrical machine, the motor inrush current reaches to 6 p.u. and it lastsfor almost 1 second. For the steady state analysis reactive power and efficiency arestudied for different wind speeds. A consistent reactive power, around 0.7 p.u. , isrequired from the grid even though the wind speed is very low. Subsequently, the

46

4.4. SELF EXCITED INDUCTION GENERATOR

Figure 4.2. The operating zones of induction machine [41].

produced active power is very low, around 0.03 p.u. . The power factor, therefore,is very low and varies between 0.043 and 0.67. The efficiency is very poor and variesbetween 20% and 40% .

For the case study above, it is obvious that the power factor is too low at lowload conditions. Thus, the power factor correction in some way is required. Abrief discussion on this solution, which sometimes is entitled self excited inductiongenerator, is presented below. However, in order to minimise the cost of the system,the final solution with a two step induction generator proposed in this report doesnot include a capacitor bank.

Requirements on self excited induction generator for application as wind gener-ator are:

• High efficiency.

• Low voltage regulation.

• Low harmonic contents.

Figure 4.2 shows the operating zones of the induction machine optimised for work-ing either as a generator or as a motor. Induction generator works in both saturatedand unsaturated operating zone. On the other hand the motor works only in unsat-uration mode. The diagram is drawn with magnetizing reactance on the horizontalaxis and the ratio of back Electro-Motive Force (EMF) and frequency on verticalaxis.

47

Chapter 5

Analytical Design of PMSG

This chapter treats analytical design of a longitudinal, inner rotor, radial flux,surface mounted PMSG with concentrated winding. Selection of the machine topol-ogy is supported by the discussion in chapter 3. Initially, design requirements andconstraints are presented in section 5.1. The selection of design parameters is de-scribed in section 5.2 and then the design procedure is followed. In the last section,the design objectives are discussed .

5.1 Design Requirements and Constraints

Table 5.1 shows the requirements which has to be fulfilled by the generator.

5.1.1 Mechanical Calculation: Minimum Shaft Diameter

The shaft must be able to withstand the high torque in the machine. Themechanical calculations for minimum shaft diameter guarantees the safe transfer ofthe mechanical power from the machine to the turbine. Rated torque of the machine

Rated power Pn 12 kWRated speed nr 100 rpmBase speed nn 90 rpmAirgap length δ 1.5 mmCooling system - Natural air convectionCogging torque - around 1%Outer diameter Dy < 2 mLifetime - 100, 000 hoursEfficiency η around 94 %Minimum shaft diameter Di,min > 0.1269 m

Table 5.1. Design requirements and constraints.

49

CHAPTER 5. ANALYTICAL DESIGN OF PMSG

Correction factor for strength weakeningof the shaft due to the key slot

kkey 4

Geometrical correction factor αmech 1Load dependant correction factor βmech 1Safety factor under normal conditions knormal 2Yield strength of shaft material σyield 2.2 × 108 N/m/mPermissible strength of shaft material σperm 4.4 × 107 N/m/mSafety factor under failure conditions kfailure 12

Table 5.2. Mechanical parameters involved in determination of minimum shaftdiameter.

isTn = Pn

2πnn60

= 12kw2π×90rpm

60= 1273Nm (5.1)

The bending moment acting on the shaft is chosen to be 110 of the rated torque.

Therefore Mbend = 1273 Nm10 = 127.3 Nm There are two different values for mini-

mum shaft diameter which should both be met; one for normal conditions and theother for failure conditions. The minimum shaft diameter in normal conditions is

Di,min,normal = 3

√32

πσperm

αmech

√M2

bend + 0.75(βmechknormalTn)2 (5.2)

And the minimum shaft diameter in failure conditions is

Di,min,failure = 3

√√√√16kfailurekkeyTn

πσyield

αmech

(5.3)

Table 5.2 shows the parameters used in equations 5.2 and 5.3 1. Consequently,Di,min,normal = 0.1269 m and Di,min,failure = 0.1123 m

5.2 Design ParametersSelection of the design parameters is essential for this work. In the following

subsections, they are categorised and justifications are presented. The main criteriafor selections are the cost and the electromagnetic performance.

5.2.1 MaterialActive material of the machine includes permanent magnet, steel sheet for the

rotor and stator laminations and copper for windings. Suitable materials are chosento provide sufficient electromagnetic performance and average cost.

1For a better introduction of these parameters, see section 7.1.1 in [15]

50

5.2. DESIGN PARAMETERS

Remanence flux density at 20C Br0 1.2 TTemperature coefficient of remanence flux density aP M −0.0009 1/KMass density ρP M 7700 kg/m3

Table 5.3. Characteristics of VACODYM 655 AP.

Permanent Magnet

VACODYM 655 AP by Vacuumschmelze GmbH is chosen as the permanentmagnet material. The characteristics of this material are given in Table 5.3. Thevendor produces VACODYM 2 series as well as VACOMAX 3 series. The coiceof VACODYM is because of its high energy density. VACODYM is produced indifferent shapes and they are classified in three main categories:

• HR (High Remanence)

• TP (Transverse Pressed)

• AP (Axial Pressed)

VACODYM AP series was chosen since it can have arc segment shape. Figure 5.1shows magnetic characteristics of VACODYM 655 AP.

Iron

M400 50A by Surahammar Bruk AB is chosen as steel material for stator androtor laminations. Selection of this material is fulfilled as a trade off between costand electromagnetic performance. Table 5.4 shows the characteristics of M40050A. Detailed datasheet is given in appendix A . Figure 5.2 shows the magneticcharacteristics of M400 50A.

5.2.2 Geometry

Table 5.5 shows the design parameters corresponding to the geometry. Theseare called independent geometry parameters, since their values are independentlychosen from other geometry parameters. Figure 5.3 shows typical geometry of themachine. Some of the independent geometry parameters can be seen in Figure 5.3.The geometry variables determined by optimisation are the six first independentgeometry parameters. The rest of the independent geometry parameters are selectedby the designer and selection criterion of the important ones is described in thepresent chapter.

2NdFeB base3cobalt base

51


Figure 5.1. Magnetic characteristics of VACODYM 655 AP.

thickness − 0.5 mmMass density ρF E 7700 kg/m3

Table 5.4. Characteristics of M400 50A.

5.2.3 Temperature

Insulation class E is selected for the insulation material. Table 5.6 shows thenominal temperatures.

5.2.4 Winding (Concentrated)

Based on the discussions presented in section 3.4.2 fractional slot double layerconcentrated winding is chosen. Table 5.7 shows the winding parameters.

Selected pole slot combination is done in accordance to discussion presented insection 3.4.2, for instance:

• Winding factor is as high as 0.945 .

• The machine is symmetrical with 8 similar sectors.

• Least Common Multiple is as high as 576.

52

5.2. DESIGN PARAMETERS

0 2000 4000 6000 8000 10000 120000

0.5

1

1.5

2

Magnetic !eld in [A/m]

Flu

x d

en

sity

(T

)

Figure 5.2. Magnetic characteristics of M400 50A.

Stator tooth width bts

Stator yoke height hrs

Rotor yoke height hrr

Stator slot height hss

Airgap diameter DMagnet thickness lmStator slot wedge height hsw

Number of poles pNumber of stator slots Qs

Magnet angle αAirgap length δUndercut angle γStator slot opening bs0

Table 5.5. Independent parameters in machine geometry.

53


Figure 5.3. Typical geometry of an inner rotor surface mounted PMSG [21].

Maximum hot spot temperature 120CAmbient temperature 20 CPermitted average temperature 70 C

Table 5.6. Nominal temperatures in the machine.

Connection type − WyeNumber of poles p 64Number of stator slots Qs 72Stator slot fill factor fs 0.5Nominal line-line voltage − 400 V

Table 5.7. Winding parameters of the machine.

54

5.3. DESIGN PROCEDURE

Figure 5.4. Flowchart showing the optimisation procedure of PMSG.

5.3 Design Procedure

Figure 5.4 shows the flowchart followed for optimisation of PMSG. In the firststep, design requirements and constraints are introduced. In the next step, de-sign parameters like characteristics of chosen material, winding parameters, etc areintroduced. In this step, still the design variables are not assigned any value.

Magnetic design is the first step after assigning the values to the airgap diameter

55


Peak fundamental airgap flux density Bδ(T ) (0.2, 1.2)Stator yoke flux density Brs(T ) (1.1, 1.5)Stator teeth flux density Bts(T ) (1.5, 2.0)Rotor yoke flux density Brr(T ) (1.3, 1.6)Current density J(A/mm2) (3.0, 5.0)

Table 5.8. Design limitations suggested by J. Pyrhönen in [42].

and airgap flux density. The magnet thickness can be calculated by

Bm = Br,m1

1 + µrδelm

(5.4)

where Bm is the maximum airgap flux density, Br,m is the remanence flux densityof the magnet at the working temperatures of the machine. µr is the relativepermeability of the magnet, δe is the effective airgap length and lm is the magnetthickness. The stator and the rotor yoke height together with the stator tooth widthare determined, according to.

hrs = αBmD

pkjBrs(5.5)

hrr = αBmD

pkjBrr(5.6)

bts = αBmτs

kjBts(1 − 2δ

D) (5.7)

In these equations kj is the stacking factor and τs is the slot pitch. Table 5.8includes design limitations of the flux density in various localities of the machine.The slot geometry can be calculated in this step. Table 5.8 , moreover, includesthe limitations of the current density of a standard non salient pole synchronousmachine4. This is to ensure safe thermal behaviour of the machine.

5.4 Design ObjectiveElectrical machines can be designed for different purposes, thus the optimisation

criterion will be different. Some of the criteria are presented below:

• torque per unit length

• efficiency

• weight/size

• cost4see Table 6.1 and Table 6.2 in [42] for more information

56

5.4. DESIGN OBJECTIVE

D/Bδ 0.3 T 0.4 T 0.5 T 0.6 T 0.7 T 0.8 T 0.9 T 1.0 T 1.1 T 1.2 T0.245 m N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A0.440 m 3.1 3.8 4.4 4.9 5.2 5.4 N/A N/A N/A N/A0.635 m N/A N/A N/A N/A 11.6 12.0 12.1 11.9 N/A N/A0.830 m N/A N/A N/A N/A N/A N/A 21.4 21.1 20.2 18.81.025 m N/A N/A N/A N/A N/A N/A N/A N/A 31.5 29.31.220 m N/A N/A N/A N/A N/A N/A N/A N/A N/A 42.21.415 m N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A1.610 m N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A1.805 m N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A2.000 m N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

Table 5.9. Torque per unit length of considered machines in kNm.

The criterion torque per unit length has been used in the design of PMSG for thispurpose5. Here it is assumed that other specifications like weight, size and cost willbe minimised. Various machines are investigated with respect to the fundamentalairgap flux density and the airgap diameter. Due to the violation of the restrictionsmentioned in Table 5.8 some combinations in the design are, therefore, excluded.

On the other hand, cost of active material, including permanent magnet, ironand copper, is also one of the criteria in the current application. Considering costcoefficient of active material 6 as

• cF E = 1 Euro/kg

• ccu = 8 Euro/kg

• cP M = 220 Euro/kg

The cost of active material for the machines shown in Table 5.9 is calculated andgiven in Table 5.10.

The optimised machine for the highest torque per unit length is the one withairgap diameter of 1.22 m and airgap flux density of 1.2 T . However this machineis 12 times as expensive as the optimised machine for the lowest cost of activematerial which has airgap diameter of 0.635 m and airgap flux density of 0.7 T . Inthe following chapter results of simulation in a FEM software for the latter machineare presented. 7

5see Table 5.96The given values are typical.7Usually a second run of optimisation is suggested. In the second run the optimised machine is

found for airgap diameters between 0.4400 m and 0.8300 m and airgap flux densities between 0.6T and 0.8 T . The second run of optimisation led into a machine with total cost of active materialof 1.04 kEuro which is only 20 Euro cheaper than the chosen machine. This disregarded machinehad airgap diameters of 0.635 m and airgap flux density of 0.66 T .

57


D/Bδ 0.3 T 0.4 T 0.5 T 0.6 T 0.7 T 0.8 T 0.9 T 1.0 T 1.1 T 1.2 T0.245 m N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A0.440 m 1.46 1.23 1.14 1.15 1.26 1.50 N/A N/A N/A N/A0.635 m N/A N/A N/A N/A 1.06 1.18 1.46 2.11 N/A N/A0.830 m N/A N/A N/A N/A N/A N/A 1.29 1.74 3.14 18.451.025 m N/A N/A N/A N/A N/A N/A N/A N/A 2.69 15.161.220 m N/A N/A N/A N/A N/A N/A N/A N/A N/A 12.981.415 m N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A1.610 m N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A1.805 m N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A2.000 m N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

Table 5.10. Total cost of active material of considered machines in kEuro.

58

Chapter 6

FEM Simulation of PMSG

This chapter presents the FEM model of the optimised machine in Chapter 5.The software used in the current work is Flux2D 10.4.1. In the first section, someassumptions in the process of developing the FEM model are described. Furtherelectromagnetic characteristics of the optimised machine are given in section 6.2.Last section shows the iron losses of the optimised machine. These iron losses areused in thermal analysis in Chapter 7 .

6.1 Initial ConsiderationsThis section treats some considered assumptions for the development of the

model in the software platform. It includes both technical and software aspects.

Geometry – Due to the symmetry, 18 of the machine is modeled.

– Independent geometrical parameters as Table 5.5 are introduced to themodel. Figure 6.1 shows geometry of the optimised machine.

Mesh – Mesh points are assigned as meshing tools. A parametric value is assignedto the points in order to have 5/10 points in each line element. Figure6.2 shows meshed geometry of the model.

Physics – Stator and rotor iron are of laminated steel sheet with stacking factor of0.96 .

– Magnetic characteristics of the magnet are modeled by the relative per-meability and the remanence flux density. In other words it differs fromFigure 5.1 .

– A three-layer airgap is considered: One belonging to rotor mechanical set,one belonging to stator mechanical set and the last one of compressibleair quality.

– An electrical circuit is made in Electriflux . 1 2

1Electriflux is a trademark by Cedrat.2see Figure 6.3.

59

CHAPTER 6. FEM SIMULATION OF PMSG

Figure 6.1. Representation of the machine geometry in Flux2D.

Solver – Flux2D, which is a two dimensional solver, is chosen for simulations. 3

– Study time limit is assigned to one electrical cycle with 50 points.– Initial rotor position is set to 7mech. . (see Figure 6.9 regarding finding

the value of initial rotor position.)

In Figure 6.3 Y-connection for the machine windings and the current sources ispresumed. The current sources, with sinusoidal currents, model the electrical systemconnected to the machine. 4

6.2 Results of FEM SimulationsThis section covers the simulation results in Flux2D model. Figure 6.4 illustrates

distribution of the iso value lines of the flux and the color shade of the flux densityat t = 1.25 × 10−3 sec at no load operation mode.

Figure 6.5a) shows induced voltage of the optimised machine in one electricalcycle and Figure 6.5b) shows its harmonics spectrum. As seen from Figure 6.5b)the back EMF spectrum shows very low harmonic contents. The peak fundamentalphase EMF is 251 V .

3Due to the short length of the machine compared to its radius, three dimensional simulationsare suggested for future work.

4Simulation with current sources containing Pulse Width Modulation (PWM) currents is sug-gested for future work.

60

6.2. RESULTS OF FEM SIMULATIONS

Figure 6.2. Representation of the machine geometry in Flux2D with the meshelements.

Figure 6.3. The electric equivalent circuit applied to the FEM model.

61


Figure 6.4. Iso value lines of the flux and color shade of the flux density at t =1.25 × 10−3 sec at no load operation mode.

62


0 0.005 0.01 0.015 0.02

−200

−100

0

100

200

time (sec)

Voltage (V)

Induced voltage

0 5 10 150

50

100

150

200

250

300

Harmonic ordersVoltage (V)

Harmonic spectrum of induced voltage

Figure 6.5. Induced phase voltage (phase A) a) Time variation of induced voltage(left) b)Harmonic spectrum of induced voltage (right).

Figure 6.6 illustrates distribution of the iso value lines of flux and the color shadeof flux density at t = 1.25 × 10−3 sec at full load.

Figure 6.7a) shows no load airgap flux density at t = 1.25 × 10−3 sec andFigure 6.8 shows its harmonics spectrum. As can be seen from the figure, theno load airgap flux density spectrum shows very low harmonic contents. This isstrongly dependent on the pole and slot number combination5. The peak value ofthe fundamental no load airgap flux density is 0.74 T which is 4 % lower comparedto the expected value (0.77 T )6. The sags in the waveform that can be observedfrom Figure 6.7a) represents the permeance variation caused by the slot openings.Their presence reduces the fundamental value. The order of harmonics with highestpeak value are the 5th and the 7th. Figure 6.7b) shows the airgap flux density atnominal load. The peak fundamental value of the airgap flux density at nominalload is 0.72 T . It can be noted from Figure 6.7b) , that there are some spikes,these indicate a presence of the armature reaction caused by the currents in thewindings.

Figure 6.9 shows the torque of the optimised machine at DC current. Thetorque is maximum at θ = 7 mech. .

Figure 6.10 shows the cogging torque. 7 The peak to peak value of the torquein Figure 6.10 is the absolute value of the cogging torque for the total machinewhich is 17.5 Nm . Figure 6.11 shows the torque at nominal load. The peak topeak value of the torque in the bottom of Figure 6.11 is the absolute value of thetorque ripple for the total machine which is 56 Nm . The mean value of the torqueis 1193 Nm and it is 6 % lower compared with expected value (1273 Nm ). The

5see section 3.4.2.6After optimisation, the magnet thickness was increased a bit in order to ensure the mechanical

rigidity. Therefore, analytical value of the airgap flux density increased.7250 points is used in simulation of Figures 6.10 and 6.11 .

63


Figure 6.6. Iso value lines of the flux and color shade of the flux density at t =1.25 × 10−3 sec at full load operation mode.

64


0 10 20 30 40

−1

−0.5

0

0.5

1

Position (mechanical degree)

Airgap "ux density (T)

No load airgap "ux density

0 10 20 30 40

−1

−0.5

0

0.5

1

Position (mechanical degree)Airgap "ux density (T)

Full load airgap "ux density

Figure 6.7. Airgap flux density a) At no load (left) b) At full load (right).

0 5 10 15 20 25 30−0.2

0

0.2

0.4

0.6

0.8

Harmonic orders

Airgap "ux density (T)

Harmonic spectrum of no load airgap "ux density

Figure 6.8. Harmonic spectrum of the no load airgap flux density.

2 4 6 8 10−1500

−1000

−500

0

500

1000

1500


Torque (Nm)

DC current torque of the machine

Figure 6.9. DC-current torque.

65


0 2 4 6 8 10 12−10

−5

0

5

10


Torque (Nm)

Cogging Torque of the machine

Figure 6.10. The total cogging torque in the machine.

0 2 4 6 8 10 12 14 16 180

500

1000


To

rqu

e (

Nm

)

Torque of the machine (full scale)

0 2 4 6 8 10 12 14 16 181160

1180

1200

1220


To

rqu

e (

Nm

)

Torque of the machine (partial scale)

Figure 6.11. The total torque of the machine at nominal load (Full scale at the topand partial scale at the bottom).

amount of the cogging torque is 1.5 % and the amount of torque ripple is 4.7 % .

6.3 Iron LossesThis section describes calculation of iron losses in stator and rotor lamination

in Flux2D. The Bertotti model is chosen in order to describe the iron losses in steelsheets. Equation 6.1 shows the relation between different components of the ironlosses as a function of frequency and flux density. The electrical frequency is thesame in all locations in the iron, however the flux density is different8. Iron lossesare given by equation

PF E = khfB2 + σ

6(πdF E fB)2 + 8.67 × kexcess(fB)

32 (6.1)

8For introduction of different components of iron losses, see section 3.5.4.

66

6.3. IRON LOSSES

Hysteresis loss coefficient ( W secT 2m3 ) kh 59.23

Classical loss coefficient (conductivity) ( 1Ωm) σ 723

Excess loss coefficient ( Wm3 ( T

sec)1.5) kexcess 4.05Thickness of lamination (m) dF E 0.0005Stacking factor kj 0.96Frequency (Hz) f 48

Table 6.1. Losses coefficients applied in FEM simulations.

0 0.5 1 1.50

1

2

3

4

x 104

Applied Flux Density (T)

Po

we

r L

oss

De

nsi

ty (

w/m

/m/m

)

Iron Loss Density

Fitted Curve

Figure 6.12. Fitted curve for iron loss density of M400 50A.

Iron losses in rotor in no load 3 WIron losses in stator in no load 117 WIron losses in rotor in nominal load 9 WIron losses in stator in nominal load 182 W

Table 6.2. Iron losses in rotor and stator of the optimised machine calculated inFEM simulations.

where kh and kexcess are hysteresis and excess loss coefficients, dF E is the steel sheetthickness and σ is the steel sheet conductivity. Table 6.1 shows the loss coefficientsconsidered in FEM simulations.

The first three parameters are calculated based on the curve fitting for giveniron loss density in the iron material datasheet 9. Figure 6.12 shows the fitted curvefor iron loss density of M400 50A.

By introducing the loss coefficients to FEM models, the iron losses in stator androtor are calculated at no load and at nominal load conditions. These values, whichare later used in thermal analysis, are shown in Table 6.2 .

9see appendix A

67

Chapter 7

Thermal Modeling of PMSG

Loss of energy cannot be avoided in electrical machines. It is created in differ-ent parts of the machine in the form of copper, iron and mechanical losses. Theselosses have to be cooled away through dissipation of the heat: thus the thermalconstraints influence the rating of the machine. The problem that arises with tem-perature increase for example demagnetisation of the magnets in a PMSM. Theinsulation material is very sensitive to temperature. Its lifetime reduces with highertemperatures. Because of this the study on thermal behaviour of the machine isperformed. The iron losses calculated in section 6.3 are used here. This chapterinvestigates the temperature rise in different parts of the machine by means of asimplified lumped parameter model based on the model developed in [32].

7.1 Thermal ModelA lumped parameter model is employed to model the thermal behavior of the

machine. Similar to electrical circuit model, an equivalent thermal model includingthermal resistances is adopted. The nodes are chosen at interface between differentmaterial or at loss generation points. Figure 7.1 shows chosen lumped parametermodel for thermal analysis. The nodes are chosen as

• Node 0: coolant.

• Node 1: frame.

• Node 2: stator iron.

• Node 3: coil sides of winding.

• Node 4: end windings.

Consequently, the model used in this chapter differs from the model in [32] inthese regards:

• The stator iron losses in yoke and teeth are aggregated.

69

CHAPTER 7. THERMAL MODELING OF PMSG

Figure 7.1. Lumped parameter thermal model consisting of an electric equivalentcircuit.

Loss type value in W

Iron losses in stator 182Copper losses in coil sides 342Copper losses in end windings 272

Table 7.1. Losses in lumped parameter thermal model in Figure 7.1 .

• The rotor losses (iron losses and windage losses) and relevant thermal resis-tivities are neglected.

• The losses and thermal resistivity of magnets and bearings are neglected.

• Thermal capacitances of different materials are neglected. In other words asteady state analysis is performed.

The ambient temperature is assumed to be 20C .Considered losses of the machine in the thermal analysis are given in Table 7.1.

The value of iron losses in the stator is calculated in section 6.3 by means ofsimulation in Flux2D. Total copper losses at nominal load is

Pcu = 3RcuI2 (7.1)

I = 31.14/√

2 = 22.02 A (7.2)

70

7.1. THERMAL MODEL

Thermal resistance value in C/W

Rth1 2.4041 × 10−4

Rth2 0.0058Rth3 0.0078Rth4 0.0150Rth5 0.0030

Table 7.2. Thermal resistances in Figure 7.1 .

whereRcu = ρcu((pL + (D + hss)πkcoil)n2

sq)Acu

(7.3)

1 The resistivity of copper varies with temperature.

ρcu = (2 × 10−8)(1 + 0.004 × (T − 20)) (7.4)

Since the temperature of winding is not known, the expected value could be used.Considering class E , the hot spot temperature is expected to be lower than 70C .Then ρcu = 2.4 × 10−8 Ωm

The coil side copper losses and the end winding copper losses are distinguishedby

Pcu−cs = lF E

lavPcu (7.5)

Pcu−ew = (1 − lF E

lav)Pcu (7.6)

The resistances in Figure 7.1 represents thermal resistivities according to:

• Rth1: Thermal resistance between the frame and the coolant.

• Rth2: Thermal resistance between the frame and the stator yoke.

• Rth3: Thermal resistance between the stator yoke and the stator teeth.

• Rth4: Thermal resistance between the stator teeth and the coil sides.

• Rth5: Thermal resistance between the coil sides and the end winding.

They are calculated based on equivalent conductive and convective thermal resis-tances. They are in turn calculated based on geometry and thermal characteristicsof the machine. A Matlab code is developed in this regard and the results fromthis code are presented here. Table 7.2 shows the values of thermal resistances inFigure 7.1.

1For introduction of symbols see "list of symbols and abbreviations".

71

CHAPTER 7. THERMAL MODELING OF PMSG

Parts of the machine Value in C

Frame 20Stator 31Coil sides 40End winding 41

Table 7.3. Temperature in different parts of the machine.

7.2 Steady State AnalysisConsidering average coolant temperature as a reference, the temperature in each

node was computed. Table 7.3 shows the results. The hottest node in the machineis the end winding. In reality the temperature can be few degrees more or lessin different locations in the end winding. The average temperature is much lowercompared with the permissible temperature (70C). The major reason is very lowcurrent density of 2.54 A/mm2 which results in low copper losses. If the currentdensity doubles, the copper losses increase by four times and the temperature risein the end winding increases drastically. Moreover, time harmonic losses of powerelectronics converters are neglected in this analysis. Additionally, this model is asimplification of 13 node model introduced by Lindström and for more accurateresults, it is suggested that a more advanced model is used. 2

2For suggestions on future work, see chapter 8

72

Chapter 8

Conclusions and Further Work

8.1 ConclusionsIn this work, a surface mounted, radial flux, inner rotor, longitudinal PMSG

with concentrated winding and natural air cooling is optimised with respect to thecost of active material. Active material includes iron, copper and PM material.Selection of topology is based on easy manufacturing process. For instance, to scaleup the machine for three times higher torque rating, the length of the machine canbe increased by three times and a new design can be avoided. The optimisationobjective function is set to minimise the cost of active material. Total active weightof the machine is limited to approximately 110 kg. From the requirements, thesize limit on outer diameter of the machine is met by far. The shaft diameter ishigher than the minimum permitted value 1 which represents mechanical continuousoperation despite the high torque density. A FEM model is developed in Flux2Dand the performance is verified. Results from FEM analysis show low harmoniccontents in the induced voltage and the airgap flux density. Also by employinga concentrated winding a high winding factor of 0.945 is achieved. The torqueripple and the cogging torque are very low (respectively 4.7 % and 1.5 %) and thecogging torque agrees very closely with corresponding constraint (around 1 %). Theefficiency is 93.4 % at nominal load (magneto-static analysis) and it agrees with thevalue required by the application(94 %). The machine enjoys from low temperaturerise which serves the purpose of very long lifetime well.

8.2 Further WorkVarious tasks can be conducted based on the present design. The list below

encloses the most interesting ones.

• 3D FEM analysis: The simulation software in this task has been Flux2D. Intwo dimension simulations, effect of end windings on electromagnetic analysis

1see Table 5.1

73

CHAPTER 8. CONCLUSIONS AND FURTHER WORK

is presumed to be negligible. However, length of the optimised machine ismuch shorter than its radius. Therefore, presence of end windings on quanti-ties like inductances can be pronounced. Hence, it is suggested that a threedimension FEM analysis is taken to ensure a good performance.

• Time harmonics: In the electrical modeling of FEM analysis, the load con-nected to the machine terminals are modeled by sinusoidal current sources.However, the machine is connected to the load/grid via converters. Thismeans that time harmonics will be injected into the machine. Therefore, itis suggested that in the electrical modeling of FEM analysis, current sourcesincluding harmonics are introduced.

• Control method: Control method of the optimised machine is left out of thescope of the present work. However, it will be tremendous to investigatean appropriate control method. The decision, first, can be made betweenthe methods which either include or exclude wind speed measurement2. Thechosen control method can, moreover, influence time harmonics introduced inthe previous item.

• Wind analysis: Optimised machine’s performance is modeled only at full loadoperation mode. One of the reasons is that this ensures that the machine willalways work in safe thermal behavior. However, the wind speed and directionis consistently varying, which makes the machine to work at loads lower thannominal load, and changes its direction of rotation frequently. It will beinteresting to model the machine performance in realistic wind conditions.For instance, depending on site mean wind speed3, it might be possible toincrease the amount of copper in the machine.

• Advanced thermal analysis: The thermal model developed in this work is asimplification of the model introduced in [32] by Lindström. The assump-tions applied in this model are mentioned in section 7.1. It is recommendedthat an advanced thermal modeling is conducted to observe a more accuratetemperature pattern.

• Flux weakening capability: In the present work, base speed of the machine isassumed to be very close to the maximum permitted speed. Thus, a "constantpower speed range" is not aimed at this work. However, it would be interestingto consider the field weakening capability at the design stage. This requires amore accurate model of wind turbine torque speed diagram. When it comesto control of the machine, it is suggested that the torque trajectory of thewind turbine and the generator intersect each other in generator’s base speed.In other words, the wind turbine and the generator should have the same size.

2For a brief introduction of control methods, see section 2.4.23which is supposedly less than nominal speed

74

8.2. FURTHER WORK

• Building a prototype: This work has focused on optimisation of a PMSG andverifying its electromagnetic and thermal performance via FEM and lumpedparameter modeling, respectively. The models have authenticated that themachine works according to the expectations. The next step in this regard isbuilding a prototype based on the proposed machine in this work. The ad-vantages of validation of prototype performance are of practical and scientifictype:

1. Investigation for cost reduction: The present model of the machine ad-dresses efficiency as high as 94 % and very low temperature rise. Ifthese outstanding qualities are confirmed by measurements results, theyopen the way for making some more compromise between cost and per-formance. For instance, one possibility can be to replace copper withaluminum in the same design. This results in lighter weight and lowercost of the machine. On the other hand, it will decrease the efficiencyand will increase temperature rise. The tradeoff can be fulfilled, if theadvantages outweigh the disadvantages.

2. Control method implementation: The feasibility of a control method canbe verified by means of testing the prototype together with a controller.

75

Appendix A

Datasheet of M400 50A bySurahammar Bruk AB

77

APPENDIX A. DATASHEET OF M400 50A BY SURAHAMMAR BRUK AB

Figure A.1. Datasheet of M400 50A by Surahammar Bruk AB.78

Bibliography

[1] J. L. Sawin and E. Martinot. Renewable 2010: Global status report. Technicalreport, Renewable Energy Policy Network for 21st Century, September 201.

[2] E. Hau. Wind turbines: fundamentals, technologies, application, economics.Springer Verlag Berlin Heidelberg, 2000.

[3] S. Eriksson. Direct driven generators for vertical axis wind turbines. PhDthesis, Uppsala Univ., Sweden, 2008.

[4] J. Kjellin. Experimental vertical axis wind turbine system. PhD thesis, UppsalaUniv., Sweden, 2010.

[5] P. Deglair. Analytical aerodynamic simulation tools for vertical axis wind tur-bines. PhD thesis, Uppsala Univ., Sweden, 2010.

[6] K. Thorborg O. Carlson, J. Hylander. Survey of variable speed operations ofwind turbines. In Europ. Wind Energy Conf, pages 406–409, 1996.

[7] E. Muljadi D.S. Zinger. Annulaized wind energy improvement using variablespeeds. In IEEE trans. Industry applications, volume 33, pages 1444–1447,1997.

[8] M. Leijon S. Eriksson, H. Bernhoff. Evaluation of different turbine conceptsfor wind power. In renewable and sustainable energy reviews, volume 12, pages1419–1434, 2008.

[9] M. Andriollo et al. Control strategies for a vawt driven pm synchronous gen-erator. In SPEEDAM, pages 804 – 809, 2008.

[10] D. E. Berg S. Johnson, C.P. van Dam. Active load control techniques for windturbines. In Sandia National Laboratories tech. report, 2008.

[11] S. Islam K. Tan. Optimum control strategies in energy conversion of pmsgwind turbine system without mechanical sensors. In IEEE trans. On energyconversion, volume 19, 2004.

[12] M. Wing J. F. Gieras. Permanent magnet motor technology: design and appli-cations. Marcel Dekker Inc, Basel, Switzerland, 2 edition, 2002.

79

BIBLIOGRAPHY

[13] A. Petersson. Analysis, modeling and control of doubly-fed induction generatorsfor wind turbines. PhD thesis, Chalmers Univ. of Tech., Sweden, 2005.

[14] K.A. Nigim G.A. Smith. Wind energy recovery by a static schrebius inductiongenerator. In IEE proc.-C Generation, transmission and Distribution, volume128, 1981.

[15] C. Sadarangani. Electrical machines: design and analysis of induction andpermanent magnet motors. Royal Inst. of Tech., Stockholm, Sweden, 2006.

[16] M.R.J. Dubois. Optimised permanent magnet generator topologies for directdriven wind turbines. PhD thesis, Delft Univ. of Tech., The Netherlands, 2004.

[17] M. Hofmann T. Hartkopf and S. Jöckel. Direct-drive generators for megawattwind turbines. In Europ. Wind Energy Conf., pages 668–671, 1997.

[18] J.R. Hadji-Minaglou and G. Henneberger. Comparison of different motortypes for electric vehicle application. In EPE Journal, volume 8, pages 46–55, September 1999.

[19] P. Lampola. Directly driven, low-speed permanent-magnet generators for windpower applications. PhD thesis, Helsinki Univ. Tech., Finland, 2000.

[20] F. Magnussen. On design and analysis of synchronous permanent magnet ma-chines for field weakening operation in hybrid electric vehicles. PhD thesis,Royal Inst. of Tech., Sweden, 2004.

[21] F. Libert. Design, optimisation and comparison of permanent magnet motorsfor a low speed direct driven mixer. Lic. thesis, Royal Inst. of Tech., Sweden,2004.

[22] D. Svechkarenko. On design and analysis of a novel transverse flux generatorfor direct driven wind application. PhD thesis, Royal Inst. of Tech., Sweden,2010.

[23] D. Hanselman. Brushless permanent magnet motor design. US: The Writer’sCollective, 2 edition, 2003.

[24] A. Grauers. Design of direct driven permanent magnet generators for windturbines. PhD thesis, Chalmers Univ. of Tech., Sweden, 1996.

[25] L. H. Hansen et al. Conceptual survey of generators and power electronicsfor wind turbines. Technical report, Riso national lab, Roskilde, Denmark,December 2001.

[26] Emetor: a pmsm design tool. URL:http://www.eme.ee.kth.se/emetor/emetor.php, June 2011.

80

[27] A. M. El-Refaie. Fractional slot concentrated windings synchronous permanentmagnet machines: opportunities and challenges. In IEEE trans. on Industrialelectronics, volume 57, 2010.

[28] C. Sadarangani F. Magnussen, P. Thelin. Performance evaluation of permanentmagnet synchronous machines with concentrated and distributed windings in-cluding the effect of field weakening. In PEMD, volume 2, pages 679 – 685,2004.

[29] N. Bainchi et al. Design considerations on fractional slot fault tolerant syn-chronous motors. In IEMDC, pages 902–909, 2005.

[30] M. Degner A. Munoz, F. Liang. Evaluation of interior pm and surface pmsynchronous machines with distributed and concentrated windings. In IECON,pages 1189–1193, 2008.

[31] G. Kylander. Thermal modelling of small cage induction motors. PhD thesis,Chalmers Univ. Technol., Gothenburg, Sweden, 1995.

[32] J. Lindström. Development of an experimental permanent magnet motor drive.Lic. thesis, Chalmers Univ. Technol., Gothenburg, Sweden, 1999.

[33] D. Svechkarenko. Thermal modeling and measurements of permanent magnetmachines. Master’s thesis, Royal Inst. of Tech., Sweden, 2004.

[34] R. Bonert C. Mi, G. R. Slemon. Modeling of iron losses of permanent magnetsynchronous motors. In IEEE trans. on Inductrial Applications, volume 39,2003.

[35] F. Sahin. Design and development of a high speed axial flux permanent magnetmachine. PhD thesis, Eindhoven Univ. of Tech., The Netherlands, 2001.

[36] G. McPherson and R. D. Laramore. An Introduction to Electrical Machinesand Transformers. Canada: John Wiley and Sons Inc, 2 edition, 1990.

[37] L. H. Hansen A. D. Hansen. Market penetration of wind turbine concepts overthe years. Technical report, Riso National Lab. Roskilde, Denmark, 2008.

[38] N. Smith. Motors as Generators For Micro-Hydro Power. UK: Russel PressLtd, 2 edition, 1997.

[39] P. K. Goel S. S. Murthy, B. Singh and S. K. Tiwari. A comparative studyof fixed speed and variable speed wind energy conversion systems feeding thegrid. In Int. Conf. on PEDS, pages 736–743, 2007.

[40] L. L. Freris. Wind Energy Conversion Systems. Cambridge, UK: Prentice Hall,1 edition, 1990.

81

[41] V. Kinnares B. Sawetsakulanond. Design, analysis, and construction of a smallscale self-excited induction generator for a wind energy application. In The3rd Int. Conf. on Sustainable Energy and Environmental Protection: SEEP,volume 35 of 12, pages 4975–4985, 2009.

[42] V. Hrabovcova J. Pyrhönen, T. Jokinen. Design of Rotating Electrical Ma-chines. John Wiley and Sons Ltd., 1 edition, 2010.

List of Tables

3.1 Different classes of an insulation material due to IEC − 85. . . . . . . . 35

5.1 Design requirements and constraints. . . . . . . . . . . . . . . . . . . . . 495.2 Mechanical parameters involved in determination of minimum shaft di-

ameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.3 Characteristics of VACODYM 655 AP. . . . . . . . . . . . . . . . . . . . 515.4 Characteristics of M400 50A. . . . . . . . . . . . . . . . . . . . . . . . . 525.5 Independent parameters in machine geometry. . . . . . . . . . . . . . . . 535.6 Nominal temperatures in the machine. . . . . . . . . . . . . . . . . . . . 545.7 Winding parameters of the machine. . . . . . . . . . . . . . . . . . . . . 545.8 Design limitations suggested by J. Pyrhönen in [42]. . . . . . . . . . . . 565.9 Torque per unit length of considered machines in kNm. . . . . . . . . . 575.10 Total cost of active material of considered machines in kEuro. . . . . . . 58

6.1 Losses coefficients applied in FEM simulations. . . . . . . . . . . . . . . 676.2 Iron losses in rotor and stator of the optimised machine calculated in

FEM simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

7.1 Losses in lumped parameter thermal model in Figure 7.1 . . . . . . . . 707.2 Thermal resistances in Figure 7.1 . . . . . . . . . . . . . . . . . . . . . . 717.3 Temperature in different parts of the machine. . . . . . . . . . . . . . . 72

82

List of Figures

List of Figures

1.1 Annual capital investment in new renewable energies between 2004 and2009 in US Dollars [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Renewable energy share of global energy consumption by 2008 [1]. . . . 2

2.1 Power coefficient versus tip speed ratio [3]. . . . . . . . . . . . . . . . . 62.2 An H rotor VAWT [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 A 450 kw HAWT with 37 m rotor diameter (Bonus) [2]. . . . . . . . . . 92.4 Horizontal plan of a VAWT [5]. . . . . . . . . . . . . . . . . . . . . . . . 9

3.1 Block diagram of a fixed speed wind energy system including a conven-tional SCIG, a gearbox and a transformer [2]. . . . . . . . . . . . . . . . 21

3.2 Block diagram of a typical DFIG including a transformer [2]. . . . . . . 223.3 Cross sectional view in radial direction and in axial direction, respec-

tively, of a typical radial flux PMSG [21]. . . . . . . . . . . . . . . . . . 253.4 Cross sectional view in radial direction and in axial direction, respec-

tively, of a typical axial flux PMSG [21]. . . . . . . . . . . . . . . . . . . 263.5 Fraction of a typical transversal flux PMSG [22]. . . . . . . . . . . . . . 273.6 Inner rotor PMSG (left) and an outer rotor PMSG (right) [26]. . . . . . 283.7 A surface mounted rotor for a PMSG [15]. . . . . . . . . . . . . . . . . . 283.8 Two different inset magnet rotors for PMSGs [15]. . . . . . . . . . . . . 293.9 Six different buried magnet rotors for PMSGs [15]. . . . . . . . . . . . . 303.10 Cross section of a pole pair of a V shaped buried magnet design (left)

and a tangentially buried magnet design (right) [21]. . . . . . . . . . . . 313.11 Windings in low speed PMSG a) distributed overlapping winding. b)

concentrated overlapping winding. c) double layer concentrated non-overlapping winding. d) single layer concentrated non-overlapping wind-ing [27]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.12 A typical magnet characteristics curve [20]. . . . . . . . . . . . . . . . . 36

4.1 Time variation of market share of yearly installed power of fixed speedWECS (including induction generator, capacitor banks, soft starter andoutput transformer) [37]. . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.2 The operating zones of induction machine [41]. . . . . . . . . . . . . . . 47

83

List of Figures

5.1 Magnetic characteristics of VACODYM 655 AP. . . . . . . . . . . . . . 525.2 Magnetic characteristics of M400 50A. . . . . . . . . . . . . . . . . . . . 535.3 Typical geometry of an inner rotor surface mounted PMSG [21]. . . . . 545.4 Flowchart showing the optimisation procedure of PMSG. . . . . . . . . 55

6.1 Representation of the machine geometry in Flux2D. . . . . . . . . . . . 606.2 Representation of the machine geometry in Flux2D with the mesh elements. 616.3 The electric equivalent circuit applied to the FEM model. . . . . . . . . 616.4 Iso value lines of the flux and color shade of the flux density at t =

1.25 × 10−3 sec at no load operation mode. . . . . . . . . . . . . . . . . 626.5 Induced phase voltage (phase A) a) Time variation of induced voltage

(left) b)Harmonic spectrum of induced voltage (right). . . . . . . . . . 636.6 Iso value lines of the flux and color shade of the flux density at t =

1.25 × 10−3 sec at full load operation mode. . . . . . . . . . . . . . . . . 646.7 Airgap flux density a) At no load (left) b) At full load (right). . . . . . 656.8 Harmonic spectrum of the no load airgap flux density. . . . . . . . . . . 656.9 DC-current torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.10 The total cogging torque in the machine. . . . . . . . . . . . . . . . . . 666.11 The total torque of the machine at nominal load (Full scale at the top

and partial scale at the bottom). . . . . . . . . . . . . . . . . . . . . . . 666.12 Fitted curve for iron loss density of M400 50A. . . . . . . . . . . . . . . 67

7.1 Lumped parameter thermal model consisting of an electric equivalentcircuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

A.1 Datasheet of M400 50A by Surahammar Bruk AB. . . . . . . . . . . . . 78

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