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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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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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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));