conceptual design and performance analysis

7/25/2019 Conceptual Design and Performance Analysis

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Conceptual Design & Performance

Analysis of a 3MW HTS Synchronous

Generatorby

Rebecca Bisangwa

Report submitted in partial fulfilment of the requirements of the module Project (E) 448 for the

degree Baccalaureus in Engineering in the Department of Electrical and Electronic Engineering at

Stellenbosch University.

Study Leader: Prof R.J. Wang

November 2014


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AcknowledgmentsI would like to thank the following people for their contribution to the project:

God, for His guidance, motivation and for keeping me strong and healthy through it all.

My supervisor, Professor Rong-Jie Wang for his guidance, patience, encouragement andavailability throughout the semester.

My friends and family for their constant support. Special appreciation goes out to my parents, as

well as Angelique Roux & Nikita Zietsman for their advice and counsel on a few aspects of the

project.

The staff at the EMLab for providing the much-needed office space from where I analysed my

machine design.


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DeclarationI, the undersigned, hereby declare that the work contained in this report is my own original work, unless

indicated otherwise.

Rebecca Bisangwa Date


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AbstractHigh maintenance costs and other problems associated with geared drive-train wind generator systems

has resulted in a need for the design and construction of compact yet highly efficient direct drive wind

generators. The aim of this project was to come up with a conceptual design of such a generator - the

High Temperature Superconducting Direct Drive Wind Generator. This design was carried out using a

combination of classical electrical machine theory and finite element analysis. A performance analysis of

the design was conducted and the results were documented. Comparison between the results obtained

from the analytical design methodology employed in this project and the finite element analysis showed

a reasonable correlation between them, hence validating the methodology that was used. Further

comparison between the High Temperature Superconducting and a conventional electrically excited

direct-drive generator with the same power rating showed that the former was much more compact

than the latter.


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OpsommingHo onderhoudskoste en ander probleme wat verband hou met gedrewe wind kragopwekker stelsels

het gelei tot 'n behoefte vir die ontwerp en konstruksie van kompakte maar hoogs doeltreffende direkte

dryf wind kragopwekkers. Die doel van hierdie projek was om 'n konseptuele ontwerp van so 'n

kragopwekker formuleer - die Ho Temperatuur Supergeleier Direkte Dryf Wind Opwekker. Hierdie

ontwerp is uitgevoer met behulp van 'n kombinasie van klassieke elektriese masjien teorie en eindige

element analise. 'n Prestasieontleding van die ontwerp is uitgevoer en die resultate is gedokumenteer.

Vergelyking tussen die resultate van die analitiese ontwerp metode wat in hierdie projek en die eindige

element analise het 'n redelike korrelasie tussen wat die metode wat gebruik is ondersteun. Verdere

vergelyking tussen die Ho Temperatuur Supergeleier en 'n konvensionele elektries opgewonde Direkte

Dryf kragopwekker met dieselfde krag gradering het getoon dat die voormalige is veel meer kompak is as

die laasgenoemde.


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Table of Contents

Acknowledgments ................................................................................................................... i

Declaration ............................................................................................................................ ii

Abstract ................................................................................................................................ iii

Opsomming ........................................................................................................................... iv

List of Figures ....................................................................................................................... vii

List of Tables ....................................................................................................................... viii

List of Abbreviations .............................................................................................................. ix

CHAPTER 1: INTRODUCTION .................................................................................................. 1

Section 1.1: Background ...................................................................................................... 1

Section 1.2: The Science behind Superconductivity .............................................................. 3

Section 1.3: Types of Superconductors ................................................................................ 6

Section 1.4: LTSs vs. HTSs .................................................................................................... 7

Section 1.5: 1G HTS vs. 2G HTS ............................................................................................ 7

Section 1.6: Determination of the Operation Point of YBCO Tape ........................................ 9

1.6.1. Load Line Concept of HTS Field Windings ................................................................. 9

Section 1.7: HTS Generator Design Considerations ................................................................ 12

1.7.1. Main Topologies of HTS Machines .......................................................................... 13

CHAPTER 2: ANALYTICAL DESIGN METHODOLOGY ................................................................ 16

Section 2.1: Design Theory & Procedure ............................................................................ 16

2.1.1. Operating Temperature of HTS Field Winding ........................................................ 17

2.1.2. Electric Loading of the Machine .............................................................................. 17

2.1.3. Airgap Design ........................................................................................................... 17

2.1.4. Rotor and HTS Coils Design ..................................................................................... 18

2.1.5. Stator and Armature Winding Design ..................................................................... 19

2.1.6. Machine Axial Length Calculation ........................................................................... 20

Section 2.2: Design Case Study - 3MW Direct Drive Wind Turbine Generator ..................... 20

2.2.1. Design Variables Used ............................................................................................. 20

2.2.2. Results Obtained ..................................................................................................... 212.2.3. Cooling System ........................................................................................................ 23

CHAPTER 3: FEM MODELLING AND DESIGN ........................................................................... 25

Section 3.1: Finite Element Method ................................................................................... 26

Section 3.2: Performance Analysis ..................................................................................... 26

Section 3.3: DD Wind Generator Comparison .................................................................... 30


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3.3.1. Challenges faced during the Maxwell simulation of the HTS generator ................. 30

CHAPTER 4: CONCLUSION AND RECOMMENDATIONS ........................................................... 30

Section 4.1: Conclusion ..................................................................................................... 30

Section 4.2: Recommendations ......................................................................................... 31

4.2.1. Analytical Design Methodology Recommendations ............................................... 314.2.2. Performance Analysis Recommendations ............................................................... 31

Bibliography ......................................................................................................................... 31

Appendix A: Project Plan ..................................................................................................... 35

Appendix B: Project Specification ......................................................................................... 36

Appendix C: Outcomes Compliance ...................................................................................... 37

C.1 Problem Solving .......................................................................................................... 37

C.2 Application of Scientific and Engineering Knowledge ................................................... 37

C.3 Engineering Design ...................................................................................................... 37

C.4 Investigations, Experiments and Data Analysis............................................................. 37

C.5 Engineering Methods, Skills and Tools, including Information Technology .................... 37

C.6 Professional and Technical Communication ................................................................. 37

C.7 Independent Learning Ability....................................................................................... 37

Appendix D: Machine Design Code ....................................................................................... 38


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List of Figures

Figure 1: The immediate disappearance of the electrical resistance of liquid mercury at T=4.2K

[6]..................................................................................................................................................... 2

Figure 2: The Order of Discovery of different superconducting materials i.e. their critical

temperature vs. the year of discovery [7] ....................................................................................... 3Figure 3: Cooper pair formation [6]............................................................................................. 4

Figure 4: The Critical Surface of Superconducting Materials [7]................................................. 5

Figure 5: Type 1 Superconductors [6] ............................................................................................. 6

Figure 6: Type 2 Superconductors [6] ............................................................................................. 6

Figure 7: Basic Structure of the BSCCO (1G HTS) and YBCO (2G HTS) conductors [8]..................... 7

Figure 8: Effect of magnetic field orientation on the critical current value in 4mm YBCO tape [10]

......................................................................................................................................................... 8

Figure 9: The load line vs. critical current per 12mm of HTS wire; on the right of the performance

curves of the wire is the cross-sectional area of the HTS wire, showing the a, b and c axes that

are used to describe the direction of the magnetic field that is incident on the field windings

[10]. ................................................................................................................................................ 10

Figure 10: Normalized Critical Current Values of YBCO tape using Bmax= 0.6T [13]..................... 11

Figure 11: Geared wind turbine system [1] ................................................................................... 12

Figure 12: Synchronous DD Wind Generator [1] ........................................................................... 12

Figure 13: Conventional Stator Teeth and Yoke and Magnetic Rotor [22]................................... 13

Figure 14: Air-gap Stator and Pole Winding with Stator Back Iron Yoke [22] ............................... 14

Figure 15: Air-gap Stator Winding with Magnetic Rotor [22]....................................................... 14

Figure 16: Air-gap Pole with Magnetic Stator Teeth [22]............................................................. 15

Figure 17: Electrical Design Steps implemented in MATLAB R2013b ........................................... 16

Figure 18: Graphical Representation of the relationship among the pole number of a machine,

the outer stator radius and machine length ................................................................................. 21

Figure 19: Graphical Representation of the relationship among the pole number, electrical

loading and HTS Tape amount required ........................................................................................ 22

Figure 20: Relationship between pole number and generator power density ............................. 22

Figure 21: Relationship among the Pole Pitch Ratio, Airgap Flux Density and Electric Loading... 23

Figure 22: DD HTS Wind Turbine Generator Setup [23] ................................................................ 24

Figure 23: Cold Rotor HTS Synchronous Generator [37], [23]..................................................... 24

Figure 24: Maxwell 2D representation of HTS Synchronous Generator Model ........................... 26

Figure 25: Armature Phase Current ............................................................................................... 27

Figure 26: Induced Voltage (EMF) at the Stator ............................................................................ 27

Figure 27: Generator Torque ......................................................................................................... 28

Figure 28: Magnetic Flux distribution in the generator ................................................................ 28

Figure 29: Flux Density Distribution at Field Coils ......................................................................... 29


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List of Tables

Table 1 Electrical & Mechanical Properties of YBCO Tape [13] ...................................................... 9

Table 2: Main Generator Specifications ........................................................................................ 25Table 3: Materials used to model the generator in Maxwell 2D .................................................. 26

Table 4: Results obtained from the analytical and FEM analyses ................................................. 29

Table 5: Generator Dimensions Comparison (dimensions got from [40]) .................................... 30


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List of Abbreviations

HTS High Temperature Superconductor

DD Direct Drive

LTS Low Temperature Superconductor

1G-HTS First-generation High Temperature Superconductor

2G-HTS Second-generation High Temperature SuperconductorBSCCO Bismuth Strontium Calcium Copper Oxide

YBCO Yttrium Barium Copper Oxide

FEM Finite Element Method

EMF Electro Motive Force


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CHAPTER 1: INTRODUCTIONIncreasing environmental concerns associated with fossil fuel combustion for generating electricity have

led to research into and exploitation of renewable resources, such as the sun and wind. Wind farm

installations are increasing at a high rate all over the world. Over time, different types of generatorsystems have been considered for these wind farms. These include the geared and direct drive

generator systems.

Geared wind generator systems have been widely used. However, the high costs of fixing and

maintenance of the gearboxes have become a serious issue. To avoid the problems associated with the

use of gearboxes, some companies have switched to direct-driven synchronous generator wind turbine

technologies, such as the generators at ENERCON in Germany. These generators are mainly designed for

large power ratings, and off-shore wind farm applications, where the system reliability is the highest

priority [1]. This results in low rotational speeds, which in turn lead to a higher machine torque. The

direct proportional relationship between torque and electrical machine size dictates that a heaviermachine results [2]. This presents installation and servicing challenges, particularly for higher power

ratings (>5MW) and off-shore wind farms.

The discovery and large-scale manufacture of superconducting materials has prompted plenty of

research work to be done on their applications in electrical machine design. HTS-DD wind turbine

generators could potentially be lighter and more compact than their conventional counterparts, since

the current density value in HTS coils can be up to 20 times or higher than that of the conventional

copper windings [3]. It has been reported that HTS generators weigh about 30-50% less than

conventional machines of the same power rating [4], [5]. In addition to this, superconductors have zero

resistance to electrical current flow and so power dissipation due to copper losses is effectively

eliminated. Consequently, higher machine efficiency could be realized with HTS generators. The

possibility of realizing a much more compact, direct drive, highly efficient direct drive wind turbine

generator is one of the core reasons behind the research and design of HTS machines.

The aim of this project is to present a conceptual design of a 3MW HTS-DD synchronous generator, and

evaluate its performance using a combination of classical electrical machine theory and finite element

analysis. The design procedure and software simulations were carried out, and it was discovered that

while the performance of the machine produced satisfactory results, the mechanical considerations

regarding the cooling system of the generator were not fully studied/taken into account and yet this is

very important.

Section 1.1: Background

Superconductivity can be defined as the almost instantaneous disappearance of resistance of a material

to the flow of electric current when it is subjected to a temperature that is below a certain value; this

value is known as the critical temperature. In light of this definition, critical temperature is the maximum

value of temperature that a superconductor can be exposed to, above which it loses its

superconductivity.


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Superconductivity was first discovered in 1911 by H.K. Onnes after mercury was cooled down to 4.2K.

He discovered that below a certain temperature (i.e. what can be called the critical temperature of

mercury - which was at around 4.2K), the resistance of mercury disappears.

Figure 1: The immediate disappearance of the electrical resistance of liquid mercury at T=4.2K [6]

Following this, everyday metals (such as aluminium, beryllium, etc.) as well as some compounds (Nb3Sn,

Nb3Ge, etc.) were tested for superconductivity, and their respective critical temperatures were

recorded.

Another important discovery, made by Bednorz & Mueller in 1986 was La2BaCuO4, a lanthanum-based

compound, with a critical temperature value of 35K. This was considered revolutionary because before

that, research had shown that the critical temperatures of superconductors could not surpass 30K [7].

The discovery of YBa2Cu3O6+xin 1987 (popularly known as YBCO) with a critical temperature of 93K

was a key milestone, and to this day it the main HTS that is employed in electrical machine applications.

A quest for room temperature superconductors (RTSs) is still underway. This will definitely revolutionize

all technology the world over, as it would eliminate the need for refrigeration of superconductors, which

to this day is a cumbersome and rather expensive and yet vital undertaking for superconductor

application. Figure 2 shows the order of discovery of the different superconducting materials.


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Figure 2: The Order of Discovery of different superconducting materials i.e. their critical temperature vs.

the year of discovery [7]

Section 1.2: The Science behind Superconductivity

As has been defined above, superconductivity presents the ability of materials to conduct electrical

current without resistive losses. A brief explanation of this mechanism is presented in this section.

It is widely known that electrical resistance in metals is due to the collision of the free electrons within

the metal with their phonons, and also (partly) the impurities within the conductor [6]. This however

does not happen with the superconducting materials, and over the years a lot of research has gone into

trying to understand why this is so. The most common theory presented to explain the

superconductivity phenomenon was presented by J.Bardeen, L.Cooper and J.R. Schrieffer in 1957 (which

came to be referred to as the BCS theory) and it put forward the existence of Cooper pairs within

the superconductors as a possible reason [7], [6]. Cooper pairs are those that result due to the attraction

of electrons that travel in opposite directions to one another and collide with the crystal lattice structure

while doing so. These Cooper pairs are said to create a current that flows through the superconducting

material without any resistance to its flow in the material [7]. Although this might seem unlikely since

electrons repel one another, due to the collision of one electron with the crystal lattice structure,

positive ions result and the other electron coming in from the opposite direction (the other Cooper

pair member) sees the resulting positive ions, resulting in forces of attraction between them. An

illustration of this process is shown in Figure 3.


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Figure 3: Cooper pair formation [6]

Some conditions however must exist for the BCS theory (of Cooper Pairs) to exist and be a valid

explanation for the superconductivity theorem [6].

1.

The Cooper Pair members (i.e. the two electrons) must be travelling in opposite directions.

2.

The two electrons must also be separated by a great distance, because if the distance between

them is small, the repulsion forces between the electrons will be stronger than the attraction to

the positive ions and the pair cannot result, and there will consequently be no superconductivity

in the material.

3.

The second electron can only be attracted to the positive ions left behind and therefore form a

Cooper Pair if and only if it gets to the positive ions created by the other electron before the

ions return to their original (equilibrium) positions.

The discovery of high-temperature superconductors (HTSs) in 1986 however led to the realization that

the BCS theory does not hold for these particular materials because condition 2 is not adhered to bythem. The repulsion forces between opposite travelling electrons within the material dominate the

attraction to the positive ions that result. To date, research into the science behind the

superconductivity in HTS materials is still on-going [7], [6].


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Critical Boundaries of Superconducting Materials

In order to use superconductors, it is essential to understand the important parameters that are

associated with them. The critical temperature, Tc, has already been mentioned. However the two other

critical parameters of superconductors include the critical current (which has already been defined), Ic,

critical current density, Jc, and critical magnetic flux density, Bc. These parameters are described/definedbelow:

1.

Critical Current Density, Jc: The maximum current density that a superconductor can carry;

beyond this value it leaves the superconducting state and its electrical resistance value returns.

2.

Critical Temperature, Tc: The maximum temperature that the superconductor can be exposed

to, above which it loses its superconductivity.

3.

Critical Magnetic Flux Density, Bc:The maximum magnetic flux density that the material can

take. The threshold for superconductors is quite high when it comes to superconductors, and

this will be discussed a bit more in the next section.

4.

Engineering Critical Current Density, Je:The current density of the superconducting materialtaking into consideration all the substrates and protective layers which are used to make the

superconducting tape, e.g. the copper layer in the YBCO tape. The main difference between Je

and Jcis thatJctakes only the superconducting layer of the tape into account, whereas the

engineering current density takes into account the entire make-up of the superconducting tape,

i.e. it is calculated by dividing the critical current by the cross-sectional area of the entire

superconducting tape [8], [9].

These critical parameters are jointly called the J-B-T characteristics of the superconductor, and when

illustrated using a co-ordinate system model (figure 4), form a critical surface of the superconductor.

Figure 4: The Critical Surface of Superconducting Materials [7]


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Section 1.3: Types of Superconductors

Superconducting materials are classified into type 1and type 2superconductors. Both types exhibit

what is known as the Meissner Effect (discovered in 1933 by W. Meissner & R.Ochsenfeld). The

Meissner Effect is a phenomenon whereby if a superconductor is placed in a magnetic field and its

surrounding temperature is reduced to a value below its critical temperature, the superconductor will

expel all the magnetic field from within it. In addition to that, if the magnetic field is suddenly removed

from the superconductor, the superconductor will remain unaffected, as opposed to the induced

currents within a normal conductor causing the fields to remain unchanged within it [6].

Type 1 superconductors:These are usually pure metals, which lose their superconductivity if the

magnetic field that it is subjected to exceeds its critical magnetic field, usually denoted as Bc.

Figure 5: Type 1 Superconductors [6]

Type 2 superconductors: These are usually ceramic in nature, and have a much higher magnetic field

value threshold than their type 1 counterparts.

Figure 6: Type 2 Superconductors [6]


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Figures 5 and6 illustrate the difference between types 1 and 2. While the type 1 superconductors have

just one critical magnetic field value (Bc), beyond which it loses its superconductivity, type 2

superconductors have two critical magnetic field values (Bc1and Bc2) whereby beyond the Bc2value is

where they lose their superconductivity. Between Bc1and Bc2, it is unable to completely penetrate the

superconductor and the Meissner Effect is still strong. However, beyond Bc2, the superconductivity does

vanish, and this value is much higher than that of the type 1 superconductors. This therefore makes type

2 superconductors the most applicable to electrical machine design (due to their very high magnetic

field tolerance).

Section 1.4: LTSs vs. HTSs

The main distinguishing feature between Low and High Temperature Superconductors is their operating

temperature values. The operating temperature range for LTSs is 4-18K, while that of HTSs is 20-77K.

Economically speaking, the HTS options are better to deal with as the refrigeration costs can be cut

down considerably.

HTSs can be further broken down into 1G- and 2G-HTS materials. The most recent discovery is MgB2(2001) with a Tc= 39K. Its application into electrical machines is still being fully studied [7].

Section 1.5: 1G HTS vs. 2G HTS

The most commercially used and available HTS materials for electrical machine design include:

Bi2Sr2Ca2Cu3O10(BSCCO): Discovered in the 1990s and is referred to as 1G-HTS material.

Y Ba2Cu3O6(YBCO): Discovered later than the Bi-2223 material, hence the name 2G-HTS [7].

Figure 7: Basic Structure of the BSCCO (1G HTS) and YBCO (2G HTS) conductors [8]


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Figure 7is a pictorial representation of the general structure and overall components of both 1G and 2G

HTS material that are used in industry. The superconducting element itself makes up a very small

percentage of the total conductor thickness (usually 1-3m) [8].

The major advantage of the 2G HTS conductors over the 1G HTS ones is the reduced magnetic

anisotropy of the 2G HTS tape at higher temperature and magnetic field values as compared to the 1GHTS ones. Magnetic anisotropy is defined as the effect that the perpendicular component of the

magnetic field acting on the HTS tape has on the critical current value. Research shows that the critical

current in HTS tape is significantly affected by a small increase in the perpendicular magnetic field that is

incident on it [7].

Figure 8: Effect of magnetic field orientation on the critical current value in 4mm YBCO tape [10]

Figure 8shows the effect of perpendicular magnetic field incident on YBCO tape on the critical current

value. The perpendicular component of the magnetic field to the tape sets the minimum critical current

value, while the parallel component sets the maximum value [10]. At 90 degrees to the face of the tape,

the critical current is 2-3 times larger than for the other angular positions [10], [11]. 1G HTS tape (Bi-

2223) demonstrates a much bigger spike of 10-200 under the same conditions [7], [10].This is unstable

and therefore undesirable for wind generator design, leaving YBCO as the better choice for this design.

The maximum acceptable perpendicular component of the magnetic field on 2G tapes has to be scaled

according to this spike, in order to agree with the minimum value critical current that was provided in

the YBCO tape specifications.

Other characteristics of 2G conductors that make them more desirable and attractive for use in industry

than 1G HTS conductors include better mechanical properties (e.g. bending radius of the material), the

potential to be a cheaper option over time as compared to Bi-2223, [8]. 2G HTS conductors also present

more stable J-B-T characteristics overall than 1G HTS conductors [12]. For this particular design, 2G

(YBCO) tape was used as the generator field windings. The tape specificationsboth electrical and

mechanicalare documented in the next section.


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Section 1.6: Determination of the Operation Point of YBCO Tape

The mechanical and electrical characteristics of YBCO tape are documented in table 1 [13], [14].

Table 1 Electrical & Mechanical Properties of YBCO Tape [13]

PARAMETER VALUE

Tape Width (mm) 4

Tape Thickness (mm) 0.1

Minimum double-bend diameter (mm) 11

Critical Current [77K, 0 T] (A) 100

Critical Temperature, Tc(K) 92

Critical Tensile Stress (MPa) (at 77K) >550

Maximum Rated Tensile Strain (at 77K)

(%)

0.45

The key parameter that was required for the field winding design was the field current. The procedure

to determine this value is different from the conventional copper windings, and it was discussed in detail

in this section. Before this procedure was discussed, however, the load line concept of HTS tapes had to

first be explained. This is due to the fact that the HTS material load lines play an important role in

determination of the HTS field windings operation point, and consequently the rated field current.

1.6.1.

Load Line Concept of HTS Field Windings

The main aim of the HTS load line is to take into account the self-field that is created by the

superconducting tapes when current runs through it. Research work that explains the load line analysis

only takes into consideration the perpendicular component of the self-field in their experimental

procedures and results due to the anisotropic nature of HTS materials. This approach was also adopted

in the work that is documented in this paper [15], [16].

Load Line Equations

Nah, Hwangbo & Ye presented a number of equations in their paper that are used to plot the HTS

material load lines in order to determine the critical currents in Bi-2223 wires [15].

=

=

Where: Bxmax and Bymaxare the x and y components (respectively) of the maximum magnetic field

J is the current density of the HTS tape (field winding)

is the shape factor; defined as the ratio of the winding height to its width.

Fp() andFn() are field factors, which are directly proportional to .The shape factor can easily

be determined, and with constant field a factor, the load line is simply plotted using the HTS tape

magnetic field and current density. These equations are applicable to the YBCO field windings in this


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design. Armed with this information, the procedure that must be followed in order to determine the

operating point of the tape can now be discussed.

Procedure to determine the Operation Point of the YBCO Field Windings

A.

First and foremost, the operating temperature of the generator must be determined. According

to SuperPower Inc. [13], the operating temperature for HTS generators and motors is chosen inthe range of 30-65K [17].In order to cut down on the refrigeration costs of the generator, the

field windings operating temperature was set at 65K.

B.

The operating point of the HTS field windings was then determined by use of the load line (has

been described in the previous section), and the Ic(B,T) curves of the field windings at different

temperatures. This load line is then plotted against the Ic(B, T) vs. B curves of the HTS material,

and the intersection point between the two indicates the operating point of the field windings

of the generator [18]. Preliminary research has shown that the range of the magnetic fields on

the field windings is 1-3T for motor and generator applications [17]. FromFigure 9,the

maximum magnetic field (at 65K) is 1.8T.

Figure 9: The load line vs. critical current per 12mm of HTS wire; on the right of the performance curves

of the wire is the cross-sectional area of the HTS wire, showing the a, b and c axes that are used to

describe the direction of the magnetic field that is incident on the field windings [10].

As was discussed in the previous section, the maximum acceptable perpendicular component of the

magnetic field must be scaled down in order to adhere to the minimum critical current that is set in the

tape specifications.

1

Where Bperp: maximum acceptable perpendicular field


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Bmax: maximum magnetic field obtained from the intersection of the load line and J-B-T curves

of the HTS field windings.

From this equation, a value of Bperp 1T was estimated.

C.

The critical current value that is obtained from the above steps is then used to find the rated

field current of the HTS field windings. A safety margin of 80% must be used to determine the

rated field current of the windings, such that they operate at a point that is slightly below the

load line and HTS field windings intersection point. This effectively eliminates any possibility of

quenching of the field winding [14], [19].

Figure 9shows the load line and Ic-B characteristics at T = 65K. Figure 10was then used at Bmax= 1T

(obtained from Figure 8) to determine the critical current of the tape.

Figure 10: Normalized Critical Current Values of YBCO tape using Bmax= 0.6T [13]

Figure 10 shows that the value of the critical current lift factor (at Bmax= 1T) can be approximated as

1.1.

1,65 1 . 1 0,77 = 1.1 100 = 110

The rated field current of the field windings, If, was then determined, taking into account the

aforementioned 80% safety margin.

=0.8 1,65 =88


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Section 1.7: HTS Generator Design ConsiderationsThe steps that were taken to design the HTS synchronous generator were outlined in this section.The

possible HTS generator types that can be designed include a homopolar, synchronous or inductiongenerator. However, the specifications dictated that a synchronous generator was most suited for this

particular application.

Two possible drive-train topologies for wind turbine generator systems are the geared and direct drive

generator systems.As can be deduced from its name, the geared drive-train system considers a gearbox

as part of the entire system. The main advantage with employing this topology is that the gearbox

enables the slower blades (wind rotor) to be connected to a high speed synchronous generator (SG).

However gearbox maintenance is quite expensive and must be continuously monitored to avoid failure

[20].

Figure 11: Geared wind turbine system [1]

The Direct Drive generator system considers a direct connection to the wind turbine rotor, i.e. a gearless

system. Such a generator rotates at a low-speed and therefore requires a higher torque to produce the

required output power. A larger torque implies that a larger generator must be built [21].However due

to the high current density that is possessed by superconducting materials, the size problem can easily

be addressed; this topology was therefore used for this design project.

Figure 12: Synchronous DD Wind Generator [1]


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1.7.1. Main Topologies of HTS Machines

There are different topologies of HTS machines; each with their own advantages and disadvantages.

Material selection, winding layout and HTS field coils placement are important design considerations.

Cooling arrangements are also important as high temperature superconductors can only maintain theirvery attractive zero resistance and higher current density properties at low (cryogenic) temperatures [6].

For this design, four possible topologies/generator designs were considered [22], [23]:

I.

Conventional Slotted Stator and Salient Pole Rotor.

II.

Slotless Stator Winding with Non-magnetic Rotor Poles.

III.

Slotless Stator Winding with Conventional Salient Pole Rotor

IV.

Non-magnetic Rotor Pole with Conventional Slotted Stator Winding.

The pros and cons of each of these topologies were investigated in order to determine the most

favourable option to use, taking all factorsphysical, mechanical and economical into account.

I. Conventional Slotted Stator and Salient Pole Rotor:

This is the conventional design, where copper windings are (used on the stator and) wound on

laminated steel stator teeth while the rotor (HTS) windings are wound on the iron rotor core. According

to Karmaker et al, this particular topology is constructed with an air gap length of 50mm, which is

significantly larger than the conventional generators that use copper field windings.

Figure 13: Conventional Stator Teeth and Yoke and Magnetic Rotor [22]

Advantage(s):

i.

The only advantage seen here is of an economical nature, i.e. much less HTS wire is needed for

this design [24]. This is due to the magnetic materials present in both the stator and rotor,

whose saturation values provide a natural constraint to the airgap flux density needed in theairgap and at the pole bodies of the machine.

Disadvantage(s):

i.

Relatively poor voltage regulation.

ii.

Saturation of the teeth results in smaller flux values.

iii.

Poor cogging torque in the machine.

iv.

High air-gap flux harmonics will result from this design.


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II.

Slotless Stator Winding with Ironless Rotor Poles:

Copper (stator) windings are wound on non-magnetic teeth with a back (iron) yoke/shield that confines

the flux within the machine, and the rotor (HTS) windings are air-gap wound as well.

Figure 14: Air-gap Stator and Pole Winding with Stator Back Iron Yoke [22]

Advantage(s):

i.

No cogging torque.

ii.

Good voltage regulation.

iii.

Low air gap flux harmonics.

Disadvantage(s):

i.

Economically speaking, this is the most expensive topology yet, due to the large amounts of HTS

wire that is needed.

III. Slotless Stator Winding with Conventional Salient Pole Rotor:

The armature (copper) windings are wound on non-magnetic teeth, while the field (HTS) windings are

wound on an iron rotor core.

Figure 15: Air-gap Stator Winding with Magnetic Rotor [22]

Advantage(s):

i.

Low cogging torque.

ii.

Good voltage regulation.

iii.

The HTS wire consumption is considerably less than that of option 2.


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Disadvantage(s):

i.

The HTS wire consumption is considerably less than that of option 2, but more than that of

option 1 so it becomes a bit more expensive than the conventional option.

IV.

Ironless Rotor Pole with Conventional Slotted Stator Winding:

In this topology, the rotor (HTS) windings are air-gap wound while the stator (copper) windings arewound on magnetic teeth. It can be seen as the inverse of option 3.

Figure 16: Air-gap Pole with Magnetic Stator Teeth [22]

Disadvantage(s)

i.

Additional losses on the shield.

ii.

High cogging torque is produced in this topology.

Based on the comparison among the above different topologies, option 3 seemed to be the best option.


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CHAPTER 2: ANALYTICAL DESIGN METHODOLOGY

Section 2.1: Design Theory & Procedure

The basic generator design equations that were used to determine the main dimensions of the HTS

synchronous generator were adapted from the existing work in literature [24] , [25], [26], [27].These

design equations were used to generate code that determined the dimensions of the generator in

Matlab (see Appendix D). Figure 17 shows the sequence of the steps that were followed to write the

aforementioned code.

START

INITIAL VALUES

Electrical Loading

Airgap Flux Density

Rotor Inner Diameter

Airgap Design

Rotor & HTS Field Coils Design

END

Rotor Inner Radius Optimization

Stator & Armature Winding Design

Machine Axial Length Calculation

Electrical Loading

Iteration Process

Airgap Flux Density

Iteration Process

Figure 17: Electrical Design Steps that were implemented in MATLAB R2013b


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2.1.1.

Operating Temperature of HTS Field Winding

As has been discussed in the previous chapter, in order to make use of the zero resistance property of

HTS materials in a generator, the field coils must be kept within temperature ranges of about 30-65K

[17]. J-B-T characteristics of HTS materials show that the lower the operating temperature, the higher

the critical current density in the HTS tapes. This results in a higher power density of the machine, which

is desirable. Operation at very low temperatures, however, leads to increased refrigeration costs (and

consequently the cost of the entire machine) [7]. In addition to this, bigger mechanical design

challenges are encountered in the mechanical design of the entire cooling and isolation systems of the

machine. Therefore a working temperature, tw, of 65K was chosen as a trade-off between power density

of the generator and refrigeration costs [25], [10].

2.1.2.

Electric Loading of the Machine

Coupled with the air gap flux density, Bag, the electrical loading, ac, is the basic parameter that

determines the size of an electrical machine. The equation that is used to determine the electrical

loading of a machine is documented below [25]:

=

Where ac: Electrical Loading of the machine

Z: Total number of conductors of the Stator Winding

Icon: Current of each conductor

Dis: Inner Diameter of the Stator

2.1.3.

Airgap Design

i.

Damper Layer, ddamper

The damper layer is usually made of copper or aluminum, and its role is to shield the HTS field coils from

the transverse flux that is produced by the armature windings [27], [28].

=0.8

Where ddamper: damper layer thickness

f: generator frequency (Hz)

, : magnetic permeability and electrical conductivity of the damper material

Kt: thermal correction factor; Kt= (234 + 293/234 + tw) [25]


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ii.

The Layer Depth of the Stator Winding, dsw

It is important to know the depth of the stator winding in order to be able to determine the total airgap

length. A slotless stator winding was used in this particular design, and therefore it formed part of the

airgap design.

=

where dsw: Stator winding layer depth

J: current density of the stator winding

kfull: filling factor of winding

kiso, ksupport: isolation and support factors of the winding respectively.

iii.

Vacuum Layer Radial Length, dvv

The vacuum layerwhich is placed between the cryogenic rotor (which is kept at a very low

temperature of 65K) and room temperature stator in order to isolate the twois assumed to have a

radial thickness of dvv4mm [25].

The total airgap length can finally be calculated.

= + + +

A mechanical clearance is necessary in order to allow for rotation of the moving parts of the generator.

A similar sized synchronous machine is usually of a radial mechanical clearance of about 2.6mm [29]. A3mm mechanical correction was used in this design.

2.1.4. Rotor and HTS Coils Design

i. Rotor Body Arc length and Yoke Thickness

The equations for these two parameters are closely related, and by substitution and prior determination

of the inner rotor diameter, can be calculated using the equations below:

= +

= 0 . 3

Where Larc: Rotor Body Arc Length

tyoke: Rotor Yoke Thickness

Rir: Rotor Inner Radius

tp: pole body angle


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ii.

Pole Body Average Flux Density

=2

1

Where Bpole: pole body average flux density

Bag: airgap flux density

kleak: leakage flux factor 0.03

Ris: stator inner radius

= + + +

Where hpoleis the pole height

iii. Required MMF per Pole

= = 1 0. 5 ( + )

Where 0 = 4 10-7H.m-1

The rated field current, If, is determined using the procedure that was described in the previous chapter.

The number of turns per pole, Nf, can then be found with the Ifand MMF calculations.

iv.

Cross-sectional Area Occupied by HTS Field Coils per Pole

This formula was obtained from the work of Shafaie & Kalantar [10]. The height and width of the

windings were assumed to be equal (i.e. a square-shaped cross-section).

=

2.1.5.

Stator and Armature Winding Design

i.

Number of Winding Turns in Series per Phase of the Stator

= 2

Where Nph: number of winding turns in series per phase of the stator

Dis: inner stator diameter (= 2Ris)

m: number of phases

Iph: rated phase current


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ii.

Number of Conductors per Slot[12], [30]

=2

2 1

where Eph: stator phase voltage

ns: rotational speed in rps (revolutions per second)

ra: average radius of the armature windings

q: Slot number per pole per phase (= 4)

a: Number of parallel current paths

2.1.6.

Machine Axial Length Calculation

The axial length of the machine is determined after determining the flux per pole and average flux

density per pole into account [25].

= 1

Where L: machine effective length and p: flux per pole

=

4.44

Where Ef= armature voltage = 1.027 Vt(Terminal Voltage)

kw= winding factor (= 0.95) and f = frequency.

Section 2.2: Design Case Study - 3MW Direct Drive Wind Turbine Generator

2.2.1.

Design Variables Used

In this project, the following design variables were optimized (using the design code in appendix D) to

produce the desired power output at reasonable cost:

Pole Number

Pole Pitch Ratio, Kp.

It is important to note that the aforementioned design variables were varied such that the magnetic andelectric loading of the generator did not exceed rotating electrical machine design limits i.e. 20,000 A/m

ac 50,000 A/m for a 3 MW machine [31],[50] and 1T Bag(airgap flux density) 3T for an HTS

synchronous wind generator [12], [32], [33], [34].


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2.2.2.

Results Obtained

Pole Number

The pole number for this design was chosen based on certain criteria:

1.

The size and axial length of the HTS generator.

2.

Cost of the HTS generator.

3.

Power density of the HTS generator.

1.

Size and Axial Length of the HTS generator

The pole numbers were varied from 2 - 100, and the machine outer radius and axial lengths were

recorded for each pole number. These results were then plotted using curve fitting techniques as shown

in figure 18.

Figure 18: Graphical Representation of the relationship among the pole number of a machine, the outer

stator radius and machine length

2. Cost of the HTS generator

Since HTS coils are the most expensive components, the cost of the generator was represented in this

report as the total length of the HTS field winding length required (per pole number) for the generator.

Shorter lengths required implied lower costs incurred in the design and purchase of the generator, and

vice versa. Figure 19 reveals the results that were obtained.

y = -0.0002x2+ 0.0539x + 2.3689

y = 3.0218x-0.66800.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0

1

2

3

4

5

6

0 25 50 75 100 125

MachineLength(m)

StatorOuterRadius(m)

Pole Number

Stator Outer Radius (m) Machine Length (m)

Poly. (Stator Outer Radius (m)) Power (Machine Length (m))


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Figure 19: Graphical Representation of the relationship among the pole number, electrical loading and

HTS Tape amount required

3.

Power density of the HTS generator

The power density of a generator is closely linked to its size and length (

). Even so

the results were plotted (figure 20) in order to make the best possible choice for the pole number with

which to design the generator.

Figure 20: Relationship between pole number and generator power density

0

10

20

30

40

50

60

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

0 20 40 60 80 100 120

HTSTapeLength

ElectricLoading(A/m)

Pole Number

Electric Loading (A/m)

HTS Tape Length (km)

0

0.05

0.1

0.15

0.2

0.25

0 10 20 30 40 50 60

Powe

rDensity(MW/cubicmetres)

Pole Number


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Interpretation of Results

From figures 18 and 19, it was discovered that whereas higher pole numbers present a large stator

radius and shorter machine length, their design would result in a more expensive machine due to the

higher length of HTS tape required to build the machine. Figure 20 showed that lower pole numbers

produced lower power densities but the curve flattened at a certain point which implied negligiblechange in power density beyond a certain number of poles. An optimum value of 20 poles was chosen

from the results that were obtained.

Pole Pitch Ratio, Kp

In a similar fashion to the pole number optimization procedure, the pole pitch ratio (also known as the

pole embracein some research papers [35]),Kp (= ) was varied within a range of 0.4-0.7 (as dictatedby the electrical and magnetic loading constraints), and figure 19 was used to determine the optimum

pole pitch ratio value for the generator design.

Figure 21: Relationship among the Pole Pitch Ratio, Airgap Flux Density and Electric Loading

Kp= 0.6 was selected for this design because its corresponding electrical loading value was within the set

constraints.

2.2.3.

Cooling System

As mentioned in the previous section of this chapter, the operating temperature of the field coils was

set at 65K. This decision was made using the trade-off between maximum current density at lower

temperatures (20-40K), and the very high refrigeration costs that would result due to operation at

these lower temperatures.

1.4

1.6

1.8

2

2.2

2.4

2.6

45000

45500

46000

46500

47000

47500

48000

48500

49000

49500

50000

0.35 0.45 0.55 0.65 0.75

AirgapFluxDensity(T)

ElectricalLoading(A/m)

Pole Pitch Ratio

Electrical Loading (A/m)

Airgap Flux Density (T)


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Figure 22: DD HTS Wind Turbine Generator Setup [23]

Figure 21is a basic diagram of the direct drive HTS wind generator with an excitation power supply and

a cooling system (refrigerator). Different types of refrigerators are used in industry for HTS ElectricalMachines, some of which include [36], [10]:

1.

GM Refrigerators

2.

Stirling Machines

3.

L He Liquefiers

4.

Lockheed Martin cryocooler [10].

The GM Refrigerator is the most widely used due to its reliability [36].The arrangement of the HTS

Generator in this particular design was therefore of the cold rotor type, i.e. the entire rotor was kept

at 65K while being isolated from the stator which operated at room temperature. A detailed illustration

is shown in figure 22.

Figure 23: Cold Rotor HTS Synchronous Generator [37], [23]


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CHAPTER 3: FEM MODELLING AND DESIGNThe main design specifications of the generator were determined using the design method that was

explained in the previous section. These results are tabulated below:

Table 2: Main Generator Specifications

PARAMETER VALUE

Airgap Flux Density (T) 2.21

Electrical Loading (A/mm) 47.5

Damper Shield Thickness (mm) 25

Vacuum Layer Thickness (mm) 4

Stator Winding Layer Depth (mm) 19.4

Total Airgap Length (mm) 51.4

Pole Number 20

Rotor Inner Diameter (mm) 3500

Rotor Outer Diameter (mm) 3743.8

Arc Length of Rotor Body (mm) 349.6Pole Pitch Ratio 0.6

Rotor Yoke Thickness (mm) 104.9

Pole Shoe Height (mm) 5

Pole Height (mm) 12

Average Flux Density of Pole Body (T) 2.4952

Required MMF per Pole (A.turns) 72544.598

Current Density of HTS Field Windings (A/mm2) 250

Number of HTS Field Winding Turns per Pole 824.3704

Stator Inner Diameter (mm) 3846.6

Stator Outer Diameter (mm) 4056.4

Slot per Pole per Phase 4Total Slot Number 240

Number of Conductors per Stator Slot 19

Number of Stator Winding Turns in Series 375.2844

Machine Axial Length (mm) 1168.6

Terminal Phase Voltage (V) 5388.8774

Induced Phase Voltage (V) 5534.3771

Phase Current (A) 371.1348

HTS Tape Length required (km) 53.9057

Power Density (MW/m3) 0.1987


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Section 3.1: Finite Element Method

The dimensions in table 3 were transferred to the FEM Software in order to analyze the performance of

the designed model. ANSOFT RMXprt [38] was used in conjunction with Maxwell 2D machine design

software [39] to model the synchronous generator, as shown in figure 24.

Figure 24: Maxwell 2D representation of HTS Synchronous Generator Model

Materials Used in the model:

Table 3: Materials used to model the generator in Maxwell 2D

COMPONENT MATERIAL

Stator & Rotor Core Steel_1008_2DSDF0.950

Stator Teeth G10 Fibre Reinforced Plastic (modelled as air [14])

Armature Windings CopperField Windings YBCO Tape

Section 3.2: Performance Analysis

A transient analysis of the machine was done in ANSOFT Maxwell 2D in the software in order to analyze

the machine performance. The flux density magnitude(s) and profile(s) at each generator component

were studied and documented in this section, as well as the armature current, induced voltage and

resulting torque of the machine.


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Figure 25: Armature Phase Current

Figure 26: Induced Voltage (EMF) at the Stator


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Figure 27: Generator Torque

The magnetic flux density distribution in the FEM model were analyzed and shown in figure 28.

Figure 28: Magnetic Flux distribution in the generator


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The magnetic flux density distribution at the HTS field coils was calculated in section 1.6 to have a

maximum perpendicular field of 1T. The magnetic flux density around the field coil was analyzed in

Maxwell as shown in figure 29.

Figure 29: Flux Density Distribution at Field Coils

The results obtained from both the analytical and the FEM Model was tabulated in order to compare the

two methodologies.

Table 4: Results obtained from the analytical and FEM analyses

ANALYTICAL METHOD FEM ANALYSIS

Airgap Flux Density (T) 2.21 2.25

Rotor Pole Flux Density (T) 2.4952 2.47

Flux Density at HTS Field Coil

(T)

1 0.90

Armature Phase Current (A) 371.1 370

Induced Voltage (EMF) (V) 5534.3771 6600

Interpretation of FEM Results

Figure 26 and table 4 show that the EMF value in the FEM model was significantly higher than that of

the analytical model. This could simply be due to a slight difference in the scaling factor of the terminal

voltage between the analytical (it was approximated as 1.027 in the design code) and FE methodologies.


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From figures 28, 29 and table 4, it was seen that the results obtained from the analytical and finite

element methods were similar. The flux density at the HTS field coil was well within the limit which had

been previously set in section 1.6 for safe operation of the field coil.

Section 3.3: DD Wind Generator Comparison

The motivation behind this section was to provide a comparison between the conventional electricallyexcited DD wind generators that are commonly used in industry and the relatively new HTS technology.

The overall size and axial length, as well as the active weight of the two generators were compared in

order to highlight the main advantage of the HTS DD generator over the conventional one.

Table 5: Generator Dimensions Comparison (dimensions got from [40])

GENERATOR MACHINE AXIAL

LENGTH (mm)

STATOR OUTER

DIAMETER

(mm)

POLE NUMBER AIRGAP

LENGTH

(mm)

ACTIVE

WEIGHT

(metric tons)

Conventional

ElectricallyExcited DD

Wind

Generator

1200 5000 40 5 45.1

HTS DD Wind

Generator

1168.6 4056.4 20 51.4 29.97

From the results shown in table 5, it was concluded that while the airgap length for the HTS DD

generator was much bigger, it is much lighter than its conventional counterpart. These results therefore

validated the motivation behind this project.

3.3.1.

Challenges faced during the Maxwell simulation of the HTS generator

This comparison that was done in the previous section should also have included the efficiencies of both

types of the machines. However Maxwell 2D transient analysis with voltage source excitation seemed to

give unrealistic results. It was also difficult to account for the refrigeration power. This was the major

challenge that was faced in the performance analysis of the generator in the Maxwell simulation.

CHAPTER 4: CONCLUSION AND RECOMMENDATIONS

Section 4.1: Conclusion

The aim of the project was to come up with a conceptual design of a 3MW HTS synchronous windgenerator. The performance of the conceptual design also had to be analyzed.

In order to do this, a detailed literature study was carried out in order to, first and foremost, understand

the concept, advantages and application of superconductivity in electrical machines and secondly to

obtain some guidelines on the analytical method to obtain the dimensions of the generator. Standard

electrical machine design constraints (such as the electrical loading and airgap flux density constraints)


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31

were also required in order to create an acceptable generator design. From this study, an analytical

approach was then decided upon and used to calculate the generator dimensions. These dimensions

were then implemented in ANSOFT RMXprt and Maxwell 2D software in order to conduct a

performance analysis on the design.

The performance analysis of the designed generator was carried out. The results obtained from the FEMwere closely matched to those obtained from the analytical methodology that was followed in this

report. Due to this, the analytical design methodology was validated.

Upon comparison of the HTS DD generator with the conventional electrically excited direct drive

generator, it was discovered that the weight of the HTS generator was 33.5% lighter than the

conventional direct drive generator. This validated the weight reduction range that was mentioned in

the introduction of this report.

Section 4.2: Recommendations

Through the design and performance analysis of the generator, it became apparent that certain

improvements and/or further research can be done on this project.

4.2.1.

Analytical Design Methodology Recommendations

Further optimization of the analytical design methodology can be done in order to achieve even more

accurate results.

Further work can be done on the cooling system that is required by the field coils of the HTS generator

and the corresponding overall cost of the generator and power consumed due to the refrigeration

process.

4.2.2.

Performance Analysis Recommendations

While the software package that was used in this report (ANSOFT Maxwell version 14) provided accurate

results for most of the machine performance analysis, there was no applicable data available about the

core loss versus frequency of the material that was used to model the rotor and stator. As a result, the

core loss in the machine was calculated inaccurately, and this culminated in the inability to assess the

efficiency of the designed generator. Further work can be done on finding the low frequency core loss

properties of the materials that were used in the design in order to calculate the generator efficiency.

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[43] L. S. I. O. P. R. I. S. M. E. R. &. K. L. Arsalan Zaidi, "5MW Direct Drive Wind Turbine Generator

Design," IEEE, Aalbrog , 2012.

[44] H. P. A. v. d. B. Dimitris Kostopoulos, High Temperature Superconducting Generators for Direct-drive

Wind Turbines: A review, Delft: Delft University of Technology.

[45] N. Maki, "Design Study of High-Temperature Superconducting Generators for Wind Power

Systems," IOP Publishing Ltd, 2008.

[46] Y. N. &. N. Maki, "Fundamental Design and Parameter Optimization Study of HTS Generatorsfor Co-

Generation Systems," IEEE, Hiratsuka-shi, 2006.

[47] N. Maki, "Fundamental Electrical Design Method for Superconducting Synchronous Generators,"

IOP Publishing Ltd, 2006.


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[48] I. M. T. H. T. N. S.-W. K. M.-H. S.-K. K. &. K.-S. R. Hyun-Man Jang, "Design and Electrical

Characteristics Analysis of 100 HP HTS Synchronous Motor in 21st Century Frontier Project, Korea,"

IEEE, 2003.

[49] J. Z. T. J. F. X. X. H. F. &. M. D. A. Di Hu, "Analysis of fields in an air-cored superconducting

synchronous motor with an HTS racetrack field winding".

[50] T. J. &. V. H. Juha Pyrhonen, Design of Electrical Rotating Machines (online copy), West Sussex: John

Wiley & Sons Ltd, 2008.

[51] W. G. Q. P. &. L. F. Cheng Pang, "Design and Simulation Analysis of HTS Wind Generator," Trans

Tech Publications, Zurich-Durnten, 2013.

Appendix A: Project Plan


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Appendix B: Project SpecificationThe aim of the project was to conduct a conceptual design and performance analysis of a 3MW HTS

synchronous machine for wind energy applications, in order to show the viability of such machines for

wind energy applications.


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Appendix C: Outcomes Compliance

C.1 Problem Solving

The main problem in this project was to develop a design method for an HTS synchronous wind turbine

generator that produced optimum dimensions. Chapter 2 was dedicated to solving this problem.

Another problem identified was how to select the optimum generator topology to be modeled, taking

into account both the machine performance and economic costs. This was dealt with in section 1.5 of

the report.

C.2 Application of Scientific and Engineering Knowledge

Section 2.1 outlined the mathematical formulae obtained from different references were used as a

starting point to model the basic generator dimensions. Graphical interpretation was used to determine

the rated field current of the generator field windings in section 1.4.

C.3 Engineering Design

A flow chart was used to write a piece of code that provided generator dimensions which were theninserted into the FEM model. The code and flowchart were documented in Appendix D and section 2.1

of the report respectively. Certain machine design variables were varied over a pre-determined range

(set by general electrical machine constraints) in section 2.2 of the report, in order to find the optimum

value of the particular variable in question.

C.4 Investigations, Experiments and Data Analysis

The solutions that were obtained from the code were used in section 2.2 to vary the design variables

and decide on the optimum value. ANSOFT Maxwell was also used to model and optimize the generator

in order to provide the desired performance. The FEM model, optimization and performance analysis

results of the generator were documented in chapter 3 of the report.

C.5 Engineering Methods, Skills and Tools, including Information Technology

Matlab was used to write the generator design code. The ANSOFT Maxwell software package was used

to model, optimize and test the performance of the generator.

C.6 Professional and Technical Communication

This skill was displayed throughout the entire report.

C.7 Independent Learning Ability

Superconductivity and its application in electrical machine design were studied and the operation point

determined in section 1.4 of the report. The decision that was made in section 1.7.1 was also a personal

undertaking, as well as the FEM modeling and analysis that was documented in chapter 3.


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Appendix D: Machine Design Codeformat long;close all

tic;

tw = 65;%operating temperature is 65Kp = 20;%pole numbernm = 15;%rpmMu = 4*pi*10^(-7);%permeability of airf = nm*p/120; %pi*nm*p/60;%pole number = 20, rpm = 15 (in Hz)sigma = 5.9*10^7;%electrical conductivity of copper (in S/m)Kt = (234 + 293)/(234 + tw);%dimensionlessJ = 5000000;%current density of copper in Amps per meter squaredKfull = 0.7;Kiso = 0.9;Ksup = 0.8;h_pole = 0.012;h_arc = 0.005;L_max = 0.6;%800mm is the max acceptable lengthnn = 0;Vgen_prime = 1.2*pi*2.^2;

mech_clearance = 0.003;ac = 45000; %30000;R_ir = 1.75; %1.4:0.1:1.8;Kp = 0.6; %0.4:0.1:0.7;ns = nm/60;%rotational speed in rpsa = 1;%number of parallel current pathsq = 4;%slots per pole per phaseJ_HTS = 250; %rated current density of HTS Field Windingsmm = 3; %number of phasesPout = 3000000; % rated output powerkw = 0.95; % winding factorIf = 88; % critical current HTS

%beginning of iteration and generator sizing processBag = 1.65;%starting valueforn = 1:500

form = 1:500%airgap design%vaccum vessel: set value


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d_vv = 0.004;%metres

%damper layerd_damper = 0.8/(sqrt(pi*(Mu)*f*(sigma)*Kt));%stator winding layer depthd_wst = ac/(J*Kfull*Kiso*Ksup);%summing them up to find Ag ("total airgap length")Ag = d_vv + d_damper + mech_clearance + d_wst;

%metresAg_no_stator_teeth = d_vv + d_damper + mech_clearance;

%rotor and HTS coils design%ratio of pole body angle to pole pitch angle (??)Theta_p = 2*pi/p;k_leak = 0.03;Theta_tp = Kp*(Theta_p);%arc length of the rotor bodytp = Theta_tp.*R_ir./(1-Theta_tp.*0.3);d_yr = tp * 0.3;R_or = R_ir + d_yr + h_pole + h_arc;s_yr = d_yr;

%stator yoke thickness assumed equal to rotor yoke thickness%inner stator radiusR_is = R_ir + d_yr + h_pole + h_arc + Ag;R_is_2 = R_or + Ag_no_stator_teeth;%Average flux density of pole bodyBtp = (2/pi)*Bag*((Theta_p*R_is)/(tp*(1-k_leak)));%required mmf per poleMMF =(((1-k_leak)*Btp*tp*Ag)/(Mu*((Theta_p+Theta_tp)/2).*(R_is-

Ag/2))); %fieldcurrent of HTS coils

%number of turns in the field winding per poleNf = MMF/If;

%minimum cross-section area of HTS Field Coils in sq-mm before%optimizationA_min = MMF/J_HTS;Height_coil = sqrt(A_min);Width_coil = Height_coil;

%assuming square coil manufacture%rotor inner radius optimizationaa = (0.2*10^(-3)*Nf)/3;

%metersbb = (Theta_p - Theta_tp)/2;

%radianscc = R_ir + d_yr;

%metersifaa > (bb*cc);

R_ir = R_ir + 0.01;end

%stator and armature winding designV_rms = 6600/sqrt(3);

%voltspf = 1;Iph = Pout/(3*V_rms*pf);

%amps


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Nph = (pi*(2*R_is)*ac)/(2*mm*Iph);ac_prime = (2*mm*Iph*Nph)/(pi*2*R_is);Vt = V_rms;Ef = 1.027*Vt;

%armature-induced voltageFlux_P = Ef./(4.44*f*Nph*kw);

%flux per poleL = Flux_P/((1-k_leak)*tp*Btp);

%axial lengthR_os = R_is + s_yr; %R_is + Ag + d_wst + s_yr;

%stator outer radiusR_os_2 = R_is_2 + d_wst + s_yr;Vgen = L*R_os.^2*pi;

%volume of the generator%HTS Field Winding lengthHTS_Wire_Length = 2*(L+(Theta_p+Theta_tp)/2*(R_ir+d_yr))*Nf*p;%electrical loading iteration processifVgen > Vgen_prime;

ac = ac + 100;else

ac = ac - 100;endPden = Pout./Vgen;

end

ifBtp > 2.5;Bag = Bag - 0.01;

elseBag = Bag + 0.01;

end

R_av = (R_is+R_is_2)/2;n_conductors = (sqrt(2)*Ef)/(2*pi*ns*kw*R_av*Bag*L*q*(p/2)*(1/a));

%number of copper conductors in each stator slotend

fprintf('Parameters:\n');fprintf('Air gap flux density (Bag): %.2f\n',Bag);fprintf('Electrical loading parameter (ac): %.2f\n',ac);

fprintf('\nAir Gap Design Results:\n');fprintf('Damper shield thickness (d_damper): %.4f\n',d_damper);fprintf('Stator winding layer depth (d_wst): %.4f\n',d_wst);fprintf('Total airgap length: %.4f meters\n',Ag);fprintf('Total airgap length without stator winding layer depth: %.4fmeters\n',Ag_no_stator_teeth);

fprintf('\nRotor and HTS Coils Design Results:\n');fprintf('Rotor Inner Radius: %.4f\n',R_ir);fprintf('Arc length of the rotor body (tp): %.4f\n',tp);fprintf('Rotor yoke thickness (d_yr): %.4f\n',d_yr);fprintf('Rotor Outer Radius: %.4f\n',R_or);fprintf('Average flux density of pole body (Btp): %.4f\n',Btp);fprintf('Required MMF per pole: %.4f\n',MMF);fprintf('Number of turns in field winding per pole (Nf): %.4f\n',Nf);


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fprintf('Minimum Crosssectional Area of HTS Field Coils (A_min):%.4f\n',A_min);fprintf('Height of HTS Field Coils (Height_coil): %.4f\n',Height_coil);fprintf('Width of HTS Field Coils (Width_coil): %.4f\n',Width_coil);

fprintf('\nStator and Armature Winding Design Results:\n');

fprintf('Rated phase current: %.4f Amps\n',Iph);fprintf('Inner Stator Radius (Ris): %.4f\n',R_is);fprintf('Inner Stator Radius before the stator teeth(R_is_2):%.4f\n',R_is_2);fprintf('Stator outer radius (R_os): %.4f\n',R_os);fprintf('Stator outer radius (R_os_2): %.4f\n',R_os_2);fprintf('Number of stator winding turns in series (Nph): %.4f\n',Nph);fprintf('Electrical loading paramater on stator (ac): %.f\n',ac_prime);fprintf('Number of conductors in each stator slot: %.f\n',n_conductors);

fprintf('\nAxial Length Design Results:\n');fprintf('Machine Axial Length : %.4f m\n',L);fprintf('HTS Tape Length required: %.4f km\n',(HTS_Wire_Length/1000));fprintf('Power density (MW/m^3) : %.4f \n',Pout/Vgen/10^6);fprintf('Induced Voltage (EMF) (V) : %.4f \n',Ef*sqrt(2));fprintf('Armature Current (A) : %.4f \n',Iph*sqrt(2));

conceptual design and performance analysis

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