Evaluation of a switched reluctance motor for solar vehicle application J Maré orcid.org/0000-0002-4970-6106 Dissertation accepted in fulfilment of the requirements for the degree Master of Engineering in Electrical and Electronic Engineering at the North-West University Supervisor: Dr MG Botha Co-supervisor: Dr JJ Bosman Co-supervisor: Mr JD Human Graduation: August 2023 Student number: 27000729 ABSTRACT The impact of global warming forces the world to develop environmentally sustainable solutions. Common practices for sustainable machines include renewable energy sources and biofuels. The automotive industry is determined to combat environmental problems by investing significantly in the research and development of electric vehicles. The development of electric vehicles using renewable energy sources are promoted by various universities competing in solar races. Solar racing uses vehicles powered from the sun to propel the vehicle. Solar energy is used as an alternative fuel source to charge a battery that provides energy for the electric motor. The first solar race was the Tour the Sol in Switzerland held in 1985 which led to several similar races. Today, solar racing is a highly competitive sport entered by universities to develop the engineering and technological skills of their students. The North-West University frequently competes in the Sasol Solar Challenge; therefore, this study aims to evaluate a switched reluctance motor for solar vehicle application. The switched reluctance motor is believed to be a possible candidate for the next-generation traction motor in electric vehicles. Although the switch reluctance motor originated in the 1850s, the 20th century brought revival to the switched reluctance motor with the improvements made in power electronics, power switches, magnetic materials, and various electric motor design simulation tools and methods. In this study, an un-optimised exploratory development model of a modular switched reluctance motor was designed instead of evaluating an off the shelf switched reluctance motor. The idea of using a modular structure instead of a conventional structure was chosen on the basis of performance and efficiency. The exploratory development model of the modular switched reluctance motor was simulated using numerical simulation software. Using the numerical simulation software, an efficiency map was constructed to evaluate the motor model using a drive cycle. The drive cycle was constructed to typically represent a solar race. The drive cycle consisted of a closed-loop route, in which the traction motor propelled the solar vehicle for eight hours using only the energy from the sun. Solar energy was extracted from the sun using a photovoltaic array. By driving the solar vehicle through the drive cycle, the total driving distance was evaluated for the eight-hour operating period. i To justify the switched reluctance motor as a possible candidate for solar vehicle application, a brushless direct current motor, currently used as the traction motor in the solar vehicle of the North-West University was evaluated as the expected reference point for motor performance. When comparing the switched reluctance motor with the brushless direct current motor, the switched reluctance motor managed a total driving distance of 375.98 km, 23 km less than the total driving distance achieved by the brushless direct current motor. Therefore, the switched reluctance motor operated at lower efficiency. Thus, more energy was used by the switched reluctance motor to maintain the same torque and speed operations as the brushless direct current motor. Although the modular switched reluctance motor did not improve the travelling distance set by the brushless direct current motor, the proposed switched reluctance motor has future potential. The modular switched reluctance motor can be designed for optimised efficiency when modifying the construction, geometric parameters or magnetic materials. Another method is to use a motor controller, designed to work with the modular switched reluctance motor that can improve efficiency over its operating range. In the conclusion of this study it was shown that an un-optimised exploratory development model of a switched reluctance motor used as a traction motor for solar vehicle application is justified for future development studies. Optimising and improving the exploratory development model of the switched reluctance motor will improve its torque, speed and efficiency, such that the achievable total driving distance could be equivalent or extended when compared to the brushless direct current motor. Only after a design is obtained that shows improved efficiency compared to the brushless direct current motor shall the manufacturing of a prototype be justified. Keywords: Switched reluctance motor, Motor efficiency, Solar vehicle, Drive cycle ii TABLE OF CONTENTS ABSTRACT ............................................................................................................................... I LIST OF FIGURES .................................................................................................................... X LIST OF TABLES ................................................................................................................... XV ABBREVIATIONS AND ACRONYMNS ................................................................................. XVI SYMBOLOGY ........................................................................................................................ XIX CHAPTER 1 INTRODUCTION ................................................................................................. 1 1.1 Environmental sustainability ........................................................................... 1 1.2 Electric vehicles ............................................................................................... 2 1.3 Solar vehicle races ........................................................................................... 4 1.4 Traction motors ................................................................................................ 5 1.4.1 Direct current motor ............................................................................................ 5 1.4.2 Induction motor ................................................................................................... 6 1.4.3 Permanent magnet synchronous motor .............................................................. 6 1.4.4 Brushless direct current motor ............................................................................ 7 1.4.5 Switched reluctance motor ................................................................................. 8 1.5 Purpose of the research ................................................................................... 9 1.5.1 Research problem .............................................................................................. 9 1.5.2 Research scope .................................................................................................. 9 1.5.3 Research limitations ......................................................................................... 10 1.5.4 Research assumptions ..................................................................................... 11 1.6 Dissertation outline ........................................................................................ 11 iii CHAPTER 2 THE SWITCHED RELUCTANCE MOTOR ........................................................ 13 2.1 Overview ......................................................................................................... 13 2.1.1 Mathematical model of an SRM ........................................................................ 15 2.1.2 Principle of operation ........................................................................................ 17 2.1.3 Motor operation ................................................................................................ 22 2.1.4 Losses .............................................................................................................. 24 2.2 Propulsion of electric vehicles ...................................................................... 25 2.3 Design considerations ................................................................................... 28 2.3.1 Structure ........................................................................................................... 29 2.3.2 Phases ............................................................................................................. 30 2.3.3 Pole configuration ............................................................................................. 31 2.3.4 Pole embrace ................................................................................................... 32 2.3.5 Pole height ....................................................................................................... 34 2.3.6 Wire and slot factor ........................................................................................... 35 2.3.7 Magnetic material ............................................................................................. 35 2.3.8 Stacking factor .................................................................................................. 36 2.4 Performance Improvements .......................................................................... 36 2.4.1 Modular construction ........................................................................................ 36 2.4.2 Multilayer construction ...................................................................................... 42 2.4.3 Hybrid construction ........................................................................................... 42 2.4.4 Transverse construction ................................................................................... 44 2.5 Summary of the literature .............................................................................. 44 2.6 The proposed switched reluctance motor .................................................... 45 iv CHAPTER 3 ELECTROMAGNETIC MODELLING ................................................................ 48 3.1 Electrical machine analysis ........................................................................... 48 3.1.1 Modelling methods ........................................................................................... 49 3.1.2 Simulation software .......................................................................................... 49 3.2 Finite element analysis .................................................................................. 50 3.2.1 Maxwell’s equations.......................................................................................... 51 3.2.2 Ansys® Maxwell ................................................................................................ 52 3.2.3 Geometry .......................................................................................................... 53 3.2.4 Domain partitions .............................................................................................. 53 3.2.5 Magnetic solvers ............................................................................................... 55 3.2.6 Post-processing ................................................................................................ 60 3.3 Summary of electromagnetic modelling ....................................................... 60 CHAPTER 4 ELECTROMAGNETIC SIMULATION VALIDATION AND VERIFICATION ...... 62 4.1 Validation and verification ............................................................................. 63 4.2 Geometry of the validation model ................................................................. 64 4.3 Magnetostatic validation ................................................................................ 66 4.3.1 Magnetostatic simulation setup ......................................................................... 66 4.3.2 Magnetostatic simulation procedure ................................................................. 69 4.3.3 Magnetostatic simulation results ....................................................................... 71 4.3.4 Magnetostatic simulation summary ................................................................... 75 4.4 Transient validation ........................................................................................ 76 4.4.1 Transient simulation setup ................................................................................ 76 4.4.2 Transient simulation procedure ......................................................................... 80 v 4.4.3 Transient simulation results .............................................................................. 81 4.4.4 Transient simulation summary .......................................................................... 88 4.5 Summary of the electromagnetic simulation validation .............................. 88 CHAPTER 5 DESIGN OF A SWITCHED RELUCTANCE MOTOR ........................................ 89 5.1 Motor specifications ....................................................................................... 89 5.1.1 Motor sizing ...................................................................................................... 90 5.1.2 Motor performance ........................................................................................... 93 5.2 Motor design ................................................................................................... 94 5.2.1 Geometry .......................................................................................................... 97 5.2.2 Magnetic material ........................................................................................... 107 5.2.3 Windings ......................................................................................................... 109 5.2.4 Thermal considerations .................................................................................. 112 5.3 Finite element analysis ................................................................................ 113 5.3.1 Static analysis................................................................................................. 114 5.3.2 Transient analysis ........................................................................................... 115 5.3.3 Conduction angles .......................................................................................... 117 5.4 Performance characteristics ........................................................................ 119 5.4.1 Torque-speed characteristics .......................................................................... 120 5.4.2 Efficiency map ................................................................................................ 120 5.5 Summary of the motor design ..................................................................... 122 vi CHAPTER 6 EVALUATION OF A TRACTION MOTOR ...................................................... 124 6.1 Drive cycle as a method of evaluation ........................................................ 124 6.1.1 Construction of a drive cycle ........................................................................... 125 6.1.2 Drive cycle procedure ..................................................................................... 134 6.2 The Mitsuba M2096-DII ................................................................................. 135 6.2.1 Characteristics ................................................................................................ 136 6.2.2 Evaluation results ........................................................................................... 138 6.2.3 Summary of the Mitsuba M2096-DII ............................................................... 140 6.3 The proposed modular switched reluctance motor ................................... 140 6.3.1 Characteristics ................................................................................................ 140 6.3.2 Evaluation results ........................................................................................... 141 6.3.3 Summary of the proposed modular switched reluctance motor ....................... 143 6.4 Evaluation of the two traction motors ......................................................... 143 6.5 Summary of the traction motor evaluations ............................................... 144 CHAPTER 7 CONCLUSION ................................................................................................ 146 7.1 Literature review ........................................................................................... 146 7.2 Validation of the electromagnetic simulation methods ............................. 146 7.3 Design of the proposed modular switched reluctance motor ................... 147 7.4 Construction of a drive cycle ....................................................................... 148 7.5 Testing and evaluation of the Mitsuba M2096-DII....................................... 148 7.6 Evaluation of the modular switched reluctance motor for solar vehicle application .................................................................................................... 148 7.7 Recommendations for future studies .......................................................... 149 vii 7.7.1 Numerical methods ......................................................................................... 149 7.7.2 Alternative motor design considerations ......................................................... 149 7.7.3 Thermal assessment ...................................................................................... 151 7.7.4 Design optimisation ........................................................................................ 151 7.7.5 Motor controller design ................................................................................... 151 7.7.6 Creating an efficiency map ............................................................................. 151 7.7.7 Prototype manufacturing and experimental testing ......................................... 152 7.7.8 Drive cycles for solar races ............................................................................. 152 7.8 Final thoughts ............................................................................................... 153 BIBLIOGRAPHY ................................................................................................................... 154 APPENDIX A MOTOR TESTING METHODOLOGY ............................................................. 168 A.1 Methodology of motor testing ...................................................................................... 168 A.1.1 Laboratory setup .......................................................................................................... 168 A.1.2 Reliability and validity of the experimental data ............................................................ 169 A.1.3 Experimental data and analysis .................................................................................... 170 A.2 Summary of motor tests ............................................................................................... 170 APPENDIX B VALIDATION OF A MODULAR SWITCHED RELUCTANCE MOTOR .......... 171 B.1 Two-dimensional validation ......................................................................................... 171 B.2 Three-dimensional validation....................................................................................... 173 B.3 Summary of the validation ........................................................................................... 174 APPENDIX C DESIGN OF A MODULAR SWITCHED RELUCTANCE MOTOR .................. 175 viii C.1 Modular switched reluctance motor transient mesh .................................................. 175 C.2 Thermal validation and analysis .................................................................................. 176 C.2.1 Thermal validation ........................................................................................................ 176 C.2.2 Thermal procedure ....................................................................................................... 177 C.2.3 Thermal analysis results .............................................................................................. 178 C.2.4 Thermal distribution of the validated model .................................................................. 178 C.2.5 Thermal distribution of the proposed modular switched reluctance motor .................... 178 C.3 Torque-speed characteristics ...................................................................................... 179 C.4 Summary of the modular switched reluctance motor design .................................... 180 APPENDIX D EVALUATION ................................................................................................ 181 D.1 The Mitsuba M2096-DII ................................................................................................. 181 D.2 The proposed modular switched reluctance motor ................................................... 189 ix LIST OF FIGURES Figure 2-1: Attractive forces between an electromagnet and magnetic material in the: (a) Unaligned position; (b) Aligned position; (c) Continuous motion .......................... 14 Figure 2-2: Equivalent circuit of an SRM ................................................................................. 16 Figure 2-3: A 6/4 SRM in the: (a) Aligned position; (b) Misaligned position; (c) Unaligned position ............................................................................................................... 17 Figure 2-4: Magnetic characteristic relationship between energy (𝑾𝒔) and co-energy (𝑾𝒄) .... 19 Figure 2-5: Magnetic characteristics of an SRM under operation ............................................. 20 Figure 2-6: Desired torque-speed characteristics of an SRM ................................................... 22 Figure 2-7: Phase excitation of a three-phase SRM ................................................................ 23 Figure 2-8: Losses in an SRM ................................................................................................. 24 Figure 2-9: SRM structures: (a) Axial flux; (b) Radial flux [80].................................................. 29 Figure 2-10: Illustration of pole embrace ................................................................................. 32 Figure 2-11: Feasibility triangle of a 6/4 SRM .......................................................................... 34 Figure 2-12: Segmented stator MSRM of (a) Outer rotor of E-core stator segments; (b) Inner rotor of C-core segments [101] .................................................................. 38 Figure 2-13: Magnetic flux path of phase A in a segmented rotor MSRM [104] ....................... 39 Figure 2-14: Double-segmented MSRMs of C-core stators. (a) Axial flux motor; (b) Radial flux motor [77, 74] ............................................................................................... 40 Figure 2-15: Double-segmented MSRMs of E-core stators [96] ............................................... 41 Figure 2-16: Multilayer SRM with rotor stack rotation [112] ...................................................... 42 Figure 2-17: Conventional SRM with (a) Pole permanent magnets; (b) Yoke permanent magnets [113] ..................................................................................................... 43 Figure 2-18: C-core MSRM with permanent magnet-assisted poled in the aligned position under; (a) No excitation current; (b) Excitation current [108] ............................... 43 x Figure 2-19: Single stack of a transverse SRM [114] ............................................................... 44 Figure 2-20: Flux paths of a C-core, E-core, and IIII-core ........................................................ 46 Figure 2-21: Efficiency map of an SRM [116, 117] ................................................................... 47 Figure 3-1: Analysis Procedure in Ansys® Maxwell .................................................................. 52 Figure 3-2: The tetrahedron as a finite element ....................................................................... 54 Figure 3-3: Magnetostatic solver diagram ................................................................................ 56 Figure 3-4: Eddy-current solver diagram ................................................................................. 58 Figure 3-5: Transient solver diagram ....................................................................................... 59 Figure 4-1: Basic structure of the MSRM. (a) Cut front view of one-phase and (b) Top view of the three-phase MSRM ................................................................................... 64 Figure 4-2: Geometry parameters of the MSRM: (a) One stator core; (b) The rotor core (top view); (c) The winding connection of one phase. .......................................... 65 Figure 4-3: (a) The adaptive mesh method used by Ansys®; (b) 3D FEA mesh model. ........... 68 Figure 4-4: Typical monitoring of a solution convergence provided by Ansys® Maxwell. .......... 69 Figure 4-5: Magnetic characteristics for validation: (a) Flux linkage; (b) Winding inductance. ......................................................................................................... 70 Figure 4-6: Static torque characteristics for validation. ............................................................ 70 Figure 4-7: Flux distribution at the aligned position when one phase is excited. ...................... 72 Figure 4-8: Magnetic characteristics by variation of the cross-sectional coil area: (a) Flux linkage; (b) Static torque. .................................................................................... 73 Figure 4-9: Magnetic characteristics by variation of stacking factor: (a) Flux linkage; (b) Static torque. ....................................................................................................... 74 Figure 4-10: Magnetic characteristics by variation of pole width: (a) Flux linkage; (b) Static torque. ................................................................................................................ 75 Figure 4-11: Drive circuit for three-phase SRM. ....................................................................... 77 xi Figure 4-12: 3D FEA mesh model of the transient solution. ..................................................... 79 Figure 4-13: Sensitivity analysis with no clone mesh mapping angle: (a) Phase torque; (b) Phase current. .................................................................................................... 82 Figure 4-14: Sensitivity analysis of 1˚ mapping angle: (a) Phase torque; (b) Phase current. .... 82 Figure 4-15: Sensitivity analysis of mapping angle at a 0.055 ms time step: (a) Phase torque; (b) Phase current. ................................................................................... 83 Figure 4-16: Sensitivity analysis of the stacking factor: (a) Phase torque; (b) Phase current. ............................................................................................................... 84 Figure 4-17: Simulated steady-state torque and phase current waveforms: (a) Current chopping control operation at 40 V and 700 rpm (b); Single pulse control operation at 35 V and 1500 rpm. ......................................................................... 85 Figure 4-18: Simulated steady-state torque and phase current waveforms compared to experimental data using single pulse operation at 25V and 1000 rpm. ................ 87 Figure 5-1: The proposed MSRM ............................................................................................ 89 Figure 5-2: Cross-sectional view of a wheel rim....................................................................... 91 Figure 5-3: Demonstration of the 'breakpoint' of the motor diameter where the torque/ volume increases ................................................................................................ 92 Figure 5-4: The anticipated torque-speed characteristics and power-speed characteristics of the proposed MSRM ....................................................................................... 94 Figure 5-5: Flow diagram of the design procedure ................................................................... 96 Figure 5-6: Magnetic flux linkage characteristics of a C-core, E-core, and IIII-core MSRM ...... 98 Figure 5-7: Simulated steady-state torque and phase current waveforms for speeds of (a) 550 rpm; (b) 800 rpm .......................................................................................... 99 Figure 5-8: Predicted torque-speed characteristics of a C-core, E-core, and IIII-core MSRM ............................................................................................................... 100 Figure 5-9: Idealistic inductance-rotor angle profile of a 12/16 and 12/20 MSRM .................. 101 xii Figure 5-10: Magnetic flux linkage characteristics of the 12/16 and 12/20 MSRM ................. 102 Figure 5-11: Simulated steady-state torque and phase current waveforms of the 12/16 and 12/20 MSRMs ................................................................................................... 102 Figure 5-12: Feasibility triangle of the proposed MSRM ........................................................ 104 Figure 5-13: Geometry parameters of the proposed MSRM .................................................. 106 Figure 5-14: B235-35A B-H characteristics ............................................................................ 108 Figure 5-15: Winding slot area for a single E-core ................................................................. 109 Figure 5-16: Torque and single-phase current waveforms when the number of winding turns is changed. .............................................................................................. 111 Figure 5-17: Steady-state thermal simulation ........................................................................ 113 Figure 5-18: Flux distribution in an E-core at aligned position under excitation of (a) 23 A; (b) 40 A ............................................................................................................. 114 Figure 5-19: Magnetic characteristics of the proposed MSRM. (a) Flux linkage; (b) Static torque ............................................................................................................... 115 Figure 5-20: Simulated steady-state torque and phase current waveforms: (a) Current chopping control operation at 400 rpm; (b) Single pulse control operation at 750 rpm ............................................................................................................ 116 Figure 5-21: Simulated steady-state torque and phase current waveforms when changing the conduction angles at 750 rpm ..................................................................... 117 Figure 5-22: Torque-speed characteristics of the proposed MSRM ....................................... 120 Figure 5-23: The constructed efficiency map of the proposed MSRM .................................... 122 Figure 6-1: The pre-defined and simplified route profile and route gradient ........................... 126 Figure 6-2: Free body diagram of the longitudinal forces acting on the vehicle ...................... 127 Figure 6-3: Solar path and position at Potchefstroom [169] ................................................... 131 Figure 6-4: Radiation over time on the 14th September at Potchefstroom .............................. 133 xiii Figure 6-5: Energy accumulation throughout the day ............................................................ 134 Figure 6-6: Mitsuba M2096-DII characteristics from datasheet and experimental tests.......... 136 Figure 6-7: Mitsuba M2096-DII characteristics from Wye and Delta circuit configurations ..... 137 Figure 6-8: Mitsuba M2096-DII efficiency map ...................................................................... 138 Figure 6-9: The Mitsuba M2096-DII energy usage through the drive cycle ............................ 139 Figure 6-10: The Mitsuba M2096-DII drive distance and speed through the drive cycle ........ 139 Figure 6-11: Proposed MSRM efficiency map ....................................................................... 141 Figure 6-12: The proposed MSRM energy usage through the drive cycle compared to the Mitsuba M2096-DII BLDC ................................................................................. 142 Figure 6-13: The proposed MSRM drive distance and speed through the drive cycle compared to the Mitsuba M2096-DII BLDC ....................................................... 143 Figure 6-14: Operating torque-speed characteristics through the drive cycle ......................... 144 Figure A-1: Motor testing setup in the laboratory ................................................................... 169 Figure B-1: Flux distribution at an aligned position for a 2D model in Ansys® Maxwell ........... 171 Figure B-2: Magnetic characteristics of the 2D MSRM model. (a) Flux linkage; (b) Inductance ........................................................................................................ 172 Figure B-3: Magnetic characteristics by variation of the coil shape: (a) Flux linkage; (b) Static torque. ..................................................................................................... 173 Figure B-4: Magnetic characteristics by variation of the coil fillet: (a) Flux linkage; (b) Static torque. .............................................................................................................. 174 Figure C-1: 3D FEA mesh model of the proposed MSRM ..................................................... 176 Figure C-2: Temperature distribution of a C-core coil under 40 A excitation .......................... 178 Figure C-3: Temperature distribution of the proposed E-core coils under 20 A excitation ...... 179 Figure C-4: Torque-speed characteristics of the proposed MSRM ........................................ 179 Figure D-1: Mitsuba M2096-DII motor characteristics as from the datasheet ......................... 181 xiv LIST OF TABLES Table 2-1: Control strategies of an SRM .................................................................................. 24 Table 3-1: Numerical methods used to solve electromagnetic problems ................................. 49 Table 4-1: Geometry parameters of the MSRM. ...................................................................... 66 Table 4-2: Transient solution setups. ....................................................................................... 80 Table 4-3: FEA comparison of dynamic performance. ............................................................. 86 Table 4-4: Experimental comparison of dynamic performance. ............................................... 87 Table 5-1: Design constraints .................................................................................................. 90 Table 5-2: Design specifications .............................................................................................. 95 Table 5-3: Dynamic performance of a C-core, E-core, and IIII-core MSRM ........................... 100 Table 5-4: Dynamic performance of a 12/16 and 12/20 MSRM ............................................. 103 Table 5-5: Geometry parameters of the proposed MSRM ..................................................... 107 Table 5-6: Magnetic properties of the shortlisted magnetic material ...................................... 107 Table 5-7: Performance characteristics when changing the conduction angles at 750 rpm ... 118 Table 5-8: Ratings of the proposed MSRM ............................................................................ 119 Table 6-1: Solar vehicle characteristics ................................................................................. 129 Table 6-2: Solar vehicle PV array characteristics................................................................... 131 Table 6-3: Drive cycle comparison ........................................................................................ 145 Table D-1: Analytical evaluation of the Mitsuba M2096-DII through the drive cycle ............... 182 Table D-2: Analytical evaluation of the proposed MSRM through the drive cycle................... 189 xv ABBREVIATIONS AND ACRONYMNS 2D Two Dimensional 3D Three Dimensional AC Alternating Current AIAA American Institute of Aeronautics and Astronautics ASC American Solar Challenge AWG American Wire Gauge BLDC Brushless Direct Current Motor BWSC Bridgestone World Solar Challenge CCC Chopped Current Control CFD Computational Fluid Dynamics CPU Central Processing Unit CSIRO Commonwealth Scientific and Industrial Research Organisation DC Direct Current DCC Dependent Current Control E East EMF Electromotive Force EU European Union EV Electric Vehicle FD-TD Finite-Difference Time-Domain FEA Finite Element Analysis FTP-72 Federal Test Procedure-72 xvi GHG Green House Gasses GPU Graphics Processing Unit HEV Hybrid Electric Vehicle HWFET Highway Fuel Economy Test ICE Internal Combustion Engine IDC Indian Driving Cycle IEC International Electrotechnical Commission IEEE Institute of Electrical and Electronics Engineering IM Induction Motor ISO International Organization for Standardization MEC Magnetic Equivalent Circuit MMF Magnetomotive Force MoM Method of Moments MOT Marching-On-in-Time MSRM Modular Switched Reluctance Motor NEDC New European Driving Cycle NWU North-West University PMSM Permanent Magnet Synchronous Motor PM-SRM Permanent Magnet Assisted Switched Reluctance Motor PV Photovoltaic R&D Research RAM Random Access Memory RMS Root Mean Square xvii S South SA South Africa SESC Somabay Egyptian Solar Challenge SPC Single Point Control SRM Switched Reluctance Motor SSC Sasol Solar Challenge Std Standard SynRM Synchronous Reluctance Motor UN United Nations V&V Validation and Verification WCED World Commission on Environmental and Development XDM Exploratory Development Model xviii SYMBOLOGY 𝑎 Acceleration, [m/s2] 𝐴 Frontal area of a vehicle, [m2] 𝐴 2𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 Cross sectional area of a conductor, [mm ] 𝐴𝑠𝑠 Slot area, [mm 2] 𝑏 Tyre pressure bar, [bar] 𝐵 Magnetic flux density [T] 𝐵𝑠 Stator flux density, [T] 𝐵𝑚𝑎𝑥 Maximum flux density, [T] 𝐶𝑑 Aerodynamic drag coefficient, [-] 𝐶𝐻 Coil height, [mm] 𝐷𝑐 Damping coefficient, [-] 𝐷 Electric flux density, [T] 𝑑𝑠 Stator pole length, [mm] 𝐷𝑟𝑜 Rotor outer diameter, [mm] 𝐷𝑆 Inner stator diameter, [mm] 𝐸𝑓 Electric field density, [V/m] 𝐸 Energy, [Wh] 𝐸𝑏𝑎𝑙𝑎𝑛𝑐𝑒 Energy balance, [Wh] 𝐸𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 Available energy, [Wh] 𝐸𝑢𝑠𝑒𝑑 Used energy, [Wh] 𝐸𝑀𝑒𝑐ℎ Mechanical output energy, [Wh] xix 𝐹 Force, [N] 𝐹𝑎 Acceleration force, [N] 𝐹𝑑𝑟𝑎𝑔 Aerodynamic drag force, [N] 𝐹𝑠𝑙𝑜𝑝𝑒 Slope force, [N] 𝐹𝑇𝑟𝑎𝑐𝑡𝑖𝑜𝑛 Traction force, [N] 𝐹𝑡𝑦𝑟𝑒 Tyre friction force, [N] 𝐹𝐹 Fill factor, [%] 𝑔 Air gap length, [mm] 𝑔𝑎 Gravitational acceleration, [m/s 2] 𝐻 Magnetic field strength, [A/m] 𝐼 Current, [A] 𝐼𝑅𝑀𝑆_𝑐𝑜𝑖𝑙 RMS current of coil, [A] 𝐼𝑅𝑀𝑆_𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 RMS current of a single conductor, [A] 𝐼𝑝 Maximum peak current, [A] 𝐽 Current density, [A/mm2] 𝐽𝑟𝑜𝑡𝑜𝑟 Rotor inertia, [kgm 2] 𝐿 Inductance, [H] 𝐿𝑠 Stator total length, [mm] 𝐿𝑠1 Upper stator pole length, [mm] 𝐿𝑠2 Middle stator pole length, [mm] 𝐿𝑠3 Lower Stator pole length, [mm] 𝑀 Mass, [kg] xx 𝑁 Number of conductor turns, [-] 𝑁𝑏 Base speed, [rpm] 𝑁𝑟𝑝 Number of rotor poles, [-] 𝑁𝑟 Rotor speed, [rpm] 𝑃 Power, [W] 𝑃𝑐𝑢 Copper loss, [W] 𝑃𝐻 Pole height, [mm] 𝑃𝑜𝑢𝑡 Output power, [W] 𝑃𝑖𝑛 Input power, [W] 𝑃𝑓+𝑤 Friction and windage losses, [W] 𝑃𝑠𝑡𝑒𝑒𝑙 Iron losses, [W] 𝑞 Number of phases, [-] 𝑟 Radius, [m] 𝑅 Resistance, [Ω] 𝑟𝑟𝑜 Rotor outer radius, [mm] 𝑟𝑠ℎ Shaft outer radius, [mm] 𝑟𝑠𝑜 Stator outer radius, [mm] 𝑡 Time, [h] 𝑇𝑏 Rated torque, [Nm] 𝑇𝑠 Period, [s] 𝑇𝐿 Load torque, [Nm] 𝑣 Vehicle speed, [m/s] xxi 𝑉 Voltage, [V] 𝑊𝑐 Co-energy, [-] 𝑊𝑒 Input energy, [W] 𝑊𝑚 Mechanical work, [W] 𝑊𝑙𝑜𝑠𝑠𝑒𝑠 Energy losses, [W] 𝑊𝑚2 Magnetic field energy, [-] 𝑊𝑠 Stored magnetic energy, [-] 𝑦𝑟 Rotor yoke width, [mm] 𝑦𝑠 Stator outer yoke width, [mm] ∇ Nabla, [-] ∇ × Curl operator, [-] ∇ ∙ Divergence operator, [-] 𝜇 Permeability of a vacuum, [H/m] 0 𝜇 Relative permeability, [H/m] 𝑟 𝜇 Absolute magnetic permeability, [H/m] 𝑀𝑝 Permanent magnetisation, [A/m] 𝑇𝑠 Switching time, [s] Greek and special symbols 𝛽𝑟 Rotor pole arc angle, [˚] 𝛽𝑠 Stator pole arc angle, [˚] 𝜀 Step angle, [˚] 𝜀𝑏 Back EMF, [V] xxii 𝜂 Efficiency, [%] 𝜃𝑠 Angle of slope, [˚] 𝜃 Rotor position, [˚] 𝜆 Flux linkage, [Wb] 𝜌 Air density, [kg/m3] 𝜌𝑐 Charge density, [C/m 3] 𝜏 Torque, [Nm] 𝜏𝑒 Electromagnetic torque, [Nm] 𝜏𝑟 Rotor pole width, [mm] 𝜏𝑠 Stator pole width, [mm] 𝜔 Angular velocity, [rad/s] 𝜔𝑓 Angular frequency 𝜔𝑏 Base speed, [rad/s] 𝜔𝑝 Peak speed, [rad/s] ∅ Equivalent flux , [Wb] ℱ Magnetomotive force, [AT] ℛ Reluctance, [AT/Wb] 𝜎 Conductivity, [S/m] xxiii CHAPTER 1 INTRODUCTION "The switched reluctance motor is a potential contender for the next generation electric vehicle traction motor due to its low cost, high efficiency, and ability to operate at higher temperatures and in other harsh environments" [1]. The invention of the tyre, that made travel and movement easier led to the development of a steam engine and internal combustion engine, able to propel a vehicle. However, these developments brought a few unwanted features, i.e., carbon emissions. Thus, the concern for an electric and hybrid vehicle is brought forth. The 21st century is progressively searching for improved technology in conventional electric motors to use in electric vehicles. With all the technological improvements made, it is considered a suitable time to use a special electric machine, namely a switched reluctance motor [2]. 1.1 Environmental sustainability There are many interpretations of the meaning of sustainability. In the most likely sense, sustainability refers to the ability of something to maintain or "sustain" itself over time [3]. The interpretation of environmental sustainability according to the United Nations (UN) and World Commission on Environment and Development (WCED) stated that environmental sustainability is about acting in such a manner that ensures future generations have natural resources available to live an equal, if not better, way of life as current generations [4, 5]. The definition of environmental sustainability leads to question what part people should play, i.e., as evolutionary species. Thus, in what way must humans change the way they live and develop science and engineering on this planet to assure the environmental sustainability for future generations? [6] Since ecological conditions as well as economic and social systems differ in each country, there is no single proposal for how sustainability must be implemented. Each country has to propose and execute its own strategy to ensure that sustainable development is performed as a worldwide objective. Due to the impact of global warming, glaciers and polar ice are melting at rates two to three times higher than the last century. The earth is going through one of the largest biodiversity losses of unforeseen and unpredictable impact. The human-caused rate of extinction is hundreds of times higher than the natural rate in the past. As the situation turns out, it could be a thousand times higher in the near future. Therefore, environmental sustainability is one of the main areas of 1 attention for researchers, academicians, scholars, governments, and nongovernmental organisations that involve individuals, communities, countries, continents, and the world [7]. Some issues that pose major environmental sustainability complications listed in [8] include:  The destruction of living environments from native species.  The discharge of polluting chemicals and materials into the environment.  Emissions of greenhouse gasses (GHG) into the atmosphere causing climate changes.  Depletion of oil and fossil fuels. These environmental sustainability problems are combatted by promoting sustainable environmental practices, i.e., moving to renewable energy sources, biofuels, and reducing waste. The transport sector is responsible for 27% and 14% of all fossil fuel emissions in the European Union (EU) and South Africa (SA) [9, 10, 11]. With the determination to combat the abovementioned environmental sustainability problems, the automotive industry is a sector that has significant investments in research and development (R&D). Electric vehicles (EVs) have tremendous potential to drastically minimise emissions, which is a tactical path for environmental sustainability growth. Definition 1 (Automotive): Automotive pertain to the design, operation, manufacture, or sale of automobiles. Definition 2 (Automobile): The automobile, also called a motorcar, is usually a four- wheeled vehicle designed primarily for personal or passenger transportation. 1.2 Electric vehicles The Benz patent motorwagen, built in 1885 by Karl Benz, is widely regarded as the first true automobile. However, unlike other major inventions, the original idea of the vehicle cannot be attributed to a single individual. The idea of a self-propelled vehicle was first formulated in the 13th century by the English philosopher Roger Bacon. In his letter 'De mirabile potestate artis et natura' ('On the Marvellous Power of Art and Nature'). Roger Bacon wrote the following: "It is possible that a car shall be made which will move with inestimable speed, and the motion will be without the help of any living creature" [12]. Likewise, Giovanni Fontana and Leonardo da Vinci were the first to introduce a design of a vehicle. Around 1420, Fontana drew a self-propelled vehicle in his technological treatise 'Bellicorum instrumentorum liber' ('Book on the instruments of war'), while Leonardo da Vinci drew a self-propelled vehicle around the year of 1478 that can be found in his 'Codice Atlantico' ('Atlantic Codex'). 2 During the Renaissance period, the word 'Disegno' that translates to ‘design’ was only an 'Idea', and therefore it was not essential to build the invention. For this reason, most inventions, such as the case of the automobile or vehicle as referred to in this dissertation, remained on paper. It was not until the 19th century, when the development of the internal combustion engine (ICE) took place, that the idea of a self-propelled vehicle started to development [13, 14]. Today, a vehicle is propelled mostly by an ICE, an electric motor or a combination of both. Research and development of electric vehicles started in 1827 when a Slovak-Hungarian priest Ányos Jedlik built the first crude but viable electric motor. The electric motor was using a stator, rotor, and commutator. Robert Anderson of Scotland is reported to have constructed a crude electric carriage in 1832 but it wasn't until the 1870s that EVs became somewhat practical. In 1873, Robert Davidson built an electric vehicle that is referred to as the first working electric road vehicle. Inventors have explored many ways to improve the technology of EVs. For example, Ferdinand Porsche developed the P1 in 1898, the world's first hybrid vehicle powered by electricity and gasoline. In 1914, Henry Ford partnered with Thomas Alva Edison to explore options for low-cost EVs [14]. At the beginning of the 20th century, almost a third of American automobiles were electric, as it offered attractive selling points such as instant self-starting, silent operation, minimal maintenance, and higher reliability than the ICE. However, Henry Ford's mass-produced Model T dealt a blow to EVs. This was the cause of Charles Kettering, who introduced the electric starter for the ICE. Simultaneously, ICE vehicles became more reliable and comfortable [14, 15]. The ICE is recognised as one of the greatest inventions of the 20th century and remains popular for the same reason that it became a success, namely, high power density, low cost, rapid refuelling, convenience, high speed operation and long travelling distances [16]. Though, the combustion of fossil fuels is the primary contributor to carbon dioxide production. Carbon dioxide is believed to contribute to climate change, and transport systems alone have doubled the contribution to climate change since 1970 [17]. Technological advances have been made to reduce GHG emissions. In 1980 the catalytic converter was introduced. In the early 2000s, European vehicle manufacturers switched to diesel- powered engines to reduce emissions, although it was later proven that diesel is not more climate- friendly than petrol [18]. Re-evaluation of EVs began at the end of the 20th century. The start of the 21st century brought revival to EVs for many of the same reasons they were first popular, namely, quiet operation, easy to operate, and no pollution. The interest in reviving EVs is said to originate from the introduction of the Toyota Prius in 2000 and the Tesla Roadster in 2008 [15]. The world’s first mass-produced hybrid electric vehicle was the Toyota Prius. The Tesla 3 Roadster was the first-ever high-end, all-electric, highway-legal vehicle that could travel more than 320 km on a single battery charge, a range unprecedented for a production EV at that time [19, 20]. The achieved travelling distance persuaded many other vehicle manufacturers to accelerate work on their electric vehicle line-ups. The European Union suggested an effective ban on the sale of new petrol and diesel vehicles from 2035 onwards. The ban on ICE vehicles effectively forces vehicle manufacturers to invest in alternative energy sources. Along with the development of electric vehicles, the quest to develop an everlasting, cleaner, and environmentally friendly fuel is never ending to progress the development of environmental sustainability. The best alternative to current fuels are renewable energy sources such as the wind, tides, the sun, hydropower, and biomass. The cleanest sustainable energy for the longest time is solar energy. The dream of driving a vehicle without environmental sustainability problems would come true at the time we drive solar powered [21]. 1.3 Solar vehicle races The Tour de Sol in Switzerland was the first race for solar powered vehicles. The first class of vehicles was powered exclusively by direct on-board solar power. The second class of vehicles was allowed direct human power with attached pedals in the vehicle. The race winners were regarded as those who have travelled the least amount of time for the set course each day. The course was on undisclosed roads where drivers were obliged to obey all traffic rules and speed limits [22]. Today, these solar challenges include the Bridgestone World Solar Challenge (BWSC, Australia), the Somabay Egyptian Solar Challenge (SESC Egypt), the American Solar Challenge (ASC, America), the Sasol Solar Challenge (SSC, South Africa) and many more [23]. Even though many solar challenges exist globally, the South African based Sasol Solar Challenge is a notoriously challenging race. This race provides varying weather conditions and extreme landscape topographies such as severe road gradients along the entire route. Solar racing is a highly competitive sport and a test arena for tomorrow's renewable energy applications. The competitive nature leads teams to design solar vehicles for efficiency rather than practicality under the imposed race regulations [24]. These rules limit the energy used to only the energy extracted from solar radiation, although starting with a fully charged battery. Energy consumption is a vital part of the design when striving to improve race performance. It is not uncommon to see teams design solar vehicles with similar aerodynamic characteristics in order to reduce energy consumption [23, 24]. Solar vehicles rely on a photovoltaic (PV) cell array to convert solar radiation into electrical energy. Electrical energy is stored in the battery and used by the electric motor to propel the vehicle, 4 similar to an EV. In this instance, the electric motor, called a traction motor, converts the electrical energy into mechanical energy to overcome rolling resistance, aerodynamic drag, and slope resistance during hill climbs. Definition 3 (Traction motor): A traction motor is an electric motor used for the propulsion of a vehicle, such as an electric locomotive or electric roadway vehicle [25]. 1.4 Traction motors A wide range of electric motors exists, but only a few are used as traction motors. The most common electric motors used as traction motors in EVs are the induction motor (IM), permanent magnet synchronous motor (PMSM), switched reluctance motor (SRM), brushless DC motor (BLDC) and direct current (DC) motor. The DC motor is the oldest type of traction motor. The other named electric motors became available as traction motor options in the past four decades. This is due to advancements in electric motors, power electronics, microelectronics, and control strategies. The PMSM, IM, and SRM are listed as the three most popular electric motors employed in EVs and heavy electric vehicles (HEVs) [26]. These traction motors exhibit the following qualities: high efficiency, high power density, effective regenerative braking, robustness, and good reliability. Each electric motor features different operating principles. The difference in operating principles can be either an advantage or disadvantage in EV applications. The following sections provide background to each traction motor by; a basic description, efficiency of the motor, EV use, the expected torque and speed of the motor and the cost associated with the electric motor. 1.4.1 Direct current motor The DC motor works on the principle of Faraday's law, whereby the current-carrying conductor, when placed in a magnetic field, will experience a torque and tend to move, or in this case, rotate. The efficiency of a DC motor is expected to be around 80%. Motor losses is predominantly in the rotor, known as copper loss. The copper loss occurs as a result of current flow in the windings, as in the case of other electric motors. The copper losses of a DC motor are categorised into three parts, armature loss, field winding loss and brush contact resistance loss. Controlling the DC motor is straightforward. The DC motor does not require complex power electronics and allows the motor to be coupled directly to a battery. However, showing low efficiency, low power density, and the risk of premature wear and tear of the brushes make the DC motor no longer a choice as a traction motor [27, 28]. 5 The DC motor was a good solution as an electric motor up to the 1990s, before power electronics became affordable. Since then, AC electric motors are preferred in the industry. 1.4.2 Induction motor The IM is a commonly used alternating current (AC) motor. Torque is produced by the reaction between a rotating magnetic field generated in the stator windings and the current induced in the coils of the rotor. No induced current will result at synchronous speed; therefore, the IM rotates slower than the magnetic field in the stator windings. Thus, the IM is also referred to as an asynchronous motor. Definition 4 (Coil): The coil in an electric motor is one or more turns, usually cylindrical, of current-carrying wire that is designed to produce a magnetic field or to provide electrical resistance or inductance. Definition 5 (Winding): A winding in an electric motor is the connection of several coils, either in parallel or in series. Assuming that the stator copper loss is negligible and the rotational loss is zero, the IM efficiency under ideal conditions operating at 5% slip can theoretically have an efficiency of 95% [29]. Shahria Sharifan et al. obtained a simulated efficiency of 86% for an IM drive that included both the motor and motor controller [30]. David Dorrel et al. designed an eight-pole, 48-slot IM that achieved efficiencies of 83.1% and 95.2% at speeds of 1500 rpm and 6000 rpm [16]. Nasser Hashernnia and Asaei Behzad state that an IM is usually considered the best candidate for EV applications even though an IM is usually larger and heavier than a PMSM [31]. The Tesla Model S and Mahindra Revo e2o use an IM as the traction motor. T Selvathai et al. chose an IM instead of an PMSM despite the advantages offered by an PMSM [32]. The primary decision to choose an IM was that the flux weakening operation is better controlled since no permanent magnets are in an IM. Therefore, allowing for higher overload capability. The IM requires little to no maintenance with the advantage of using matured technology, making the IM inexpensive compared to other electric motors [33]. 1.4.3 Permanent magnet synchronous motor The PMSM is an AC synchronous motor. The field excitation is provided by the permanent magnets in the rotor and has a sinusoidal back electromotive force (EMF). When the rotor synchronises with the rotating magnetic field in the stator windings, synchronous speed is obtained. 6 The efficiency of the 2004 Toyota Prius hybrid EV achieved an efficiency of 91.3% and 96.1% at speeds of 1500 rpm and 6000 rpm. It has been stated that PMSMs, compared to IMs of the same size, have higher efficiency [16]. Permanent magnets eliminate field excitation losses and enable the motor to be designed to be more compact and lighter [34]. However, a PMSM operating with poor thermal dissipation poses a risk of demagnetising the permanent magnets in the motor that would result in a decrease of performance [35]. Operating at high temperature influences the magnetic properties of the magnetic material which in turn reduces the maximum output torque of the motor. This adds to the already reduced performance of demagnetised permanent magnets [36]. Permanent magnet synchronous motors are serious competitors against IMs. They are widely used by automotive manufacturers and are the traction motor choice in the Formula E motorsport series [37, 38]. The PMSM have faster acceleration, greater efficiency-torque-speed characteristics and higher power density compared to an IM [30]. When the construction of a PMSM is considered, the axial flux PMSM, compared to the radial flux PMSM, has the benefit of a higher power-to-weight ratio, less noise, and less vibration [39]. However, the PMSM does not allow for the overload capability of an IM but offers quite an extensive torque overload capability over a wide speed range when flux weakening methods or custom control algorithms are used under the thermal limitations of the permanent magnets [28]. The cost of PMSM is steadily increasing with the reduced availability of permanent magnets. Thermal prediction is also an important part of the design to avoid irreversible demagnetisation that would result in decreased motor efficiency and performance [34, 40]. 1.4.4 Brushless direct current motor The BLDC motor is an electrically commutated DC motor with the exclusion of brushes. Like the PMSM, the field excitation is provided by the permanent magnets in the rotor, but the BLDC motor has a trapezoidal back EMF instead of a sinusoidal back EMF [41]. Another difference is that concentrated windings are used in BLDC motors, and lap wave windings are used in PMSMs. The efficiency of a BLDC motor is typically within the range of 85% to 90%. In 2009 a research group from Tokai University achieved efficiency in the range of 93% to 96% under various operating conditions. When comparing a BLDC motor against an SRM in [42], the BLDC has only a 1% efficiency improvement compared to the SRM. It should be noted that both motors were designed for the same output power and same outer diameter. 7 Similar to the PMSM, the BLDC motor is preferred in EVs. Their power-to-volume ratio makes them a popular choice in Japan, with their small, lightweight, and more compact vehicles [44]. From the comparison between a BLDC motor and a PMSM in [45], it is concluded that the BLDC has a lower power and torque density than a PMSM. For both these permanent magnet motors, an outer rotor radial flux motor is the preferred choice in high-power and torque-density applications. As in the case of the PMSM, the BLDC motor is expensive and risks demagnetising the permanent magnets when operating above the thermal limitation. 1.4.5 Switched reluctance motor The SRM is a double salient pole motor with phase coils wound on the stator poles. An inherent advantage of the motor is that there are no windings or magnets on the rotor. The rotor consists only of stacked laminated magnetic material. The SRM operates on the principle of magnetic reluctance between the aligned and unaligned pole positions. The efficiencies of 85.2% and 88.2% are achieved at speeds of 1500 rpm and 6000 rpm in [16]. By comparing the efficiency with the efficiency of the IM and PMSM, it is observed that the efficiency is almost 7% lower than the PMSM. A 12/26 SRM simulated in [42] shows an efficiency of 90.4%, only 1% lower than the compared BLDC motor of the same output power. Concluded in [46], the implementation of a dependent current control (DCC) strategy at low speeds and high torque operation can increase efficiency. Motor losses are significantly reduced, along with heat generation and overall weight, since no windings or permanent magnets are in the rotor. The SRM is making a prominent role in appliances, industrial equipment, commercial and vehicular applications in the 21st century, even though the SRM was developed in the 1800s. Optimum operation depend on relatively sophisticated control. Control of an SRM is made possible by the advent of improved switching devices and power electronics [47]. Tesla and Holden already use a permanent magnet-assisted SRM (PM-SRM) in their electric vehicle line- up [42, 48]. The SRM is gaining major attraction given its simple, robust, and inexpensive construction. Control of an SRM is more complex than three-phase sinusoidal excitation [35]. Due to the complexity of the control strategy, the cost of the motor often increases to the range of other electric motors. Another disadvantage of an SRM include torque ripple, vibrations, and strong acoustic noise [49, 27, 44]. M. Yildirim et al. has the state that torque ripple and acoustic noise are not considered a crucial problem in traction motors [50]. This is not always the case, as torque ripple is considered a crucial issue in SRMs that leads to vibrations, premature wear and ultimately failure of the drivetrain system [48]. Therefore, many mitigations methods have to be incorporated when designing or controlling a traction motor. 8 Comparing an SRM to other electric motors, i.e., BLDC and PMSMs found that an SRM offer a wider speed range when operating at constant power. When comparing torque of an SRM, an SRM typically has less torque when operating at low speeds, though more torque at higher speeds when compared to an IM and PMSM. With the absence of rotor windings and permanent magnets, the SRM is inexpensive compared to other electric motors. The absence of the windings and permanent magnets provides a simpler, more rugged rotor that provides high reliability and enables the electric motor to continue operation under open-circuit fault conditions [28, 32]. 1.5 Purpose of the research The Sasol Solar Challenge is the South African solar race. The goal of the Sasol Solar Challenge is to maximise the driving distance each day. Efficiency is the pillar of solar vehicle design. Traditionally, design improvements have focused on reducing mass and aerodynamic drag. The next attempt to improve efficiency of a solar vehicle is to use or design an improved traction motor. 1.5.1 Research problem A traction motor is an essential part of a solar vehicle. Currently, the North-West University (NWU) and competitors in solar races have the option of buying a traction motor, specifically designed for solar racing from two manufacturers. Each of the two manufacturers, namely, Mitsuba and Marand offer a permanent magnet type motor. Marand offer a single motor whilst Mitsuba offer a motor with a list of modification options to improve its performance. However, these traction motors are expensive and bought standard off the shelf. From the opinion of Nir Vaks and Nyah Zarante in [1], the SRM is a potential candidate for the next-generation traction motor in EVs. But the problem is that no SRM is available as a traction motor for solar vehicle application, since no SRM has been adequately evaluated against a PMSM. Since no SRM has been adequately evaluated against a permanent magnet motor (BLDC or PMSM), the research problem manifests that the potential of an SRM for solar vehicle application should be justified by evaluating an SRM as a traction motor in a solar vehicle. 1.5.2 Research scope To evaluate an SRM for solar vehicle application, a suitable SRM for the solar vehicle of the NWU is required. Therefore, an SRM should be designed. The design specifications for the SRM are obtained by evaluating the Mitsuba M2096-DII BLDC, currently the traction motor in the solar vehicle of the NWU. The SRM design follows the same procedures found in [51, 52, 53]. To justify the use of an SRM for solar vehicle application, the scope of this study is limited to a first 9 experimental development model (XDM) and does not follow an iterative design process to find the most optimised motor design. Thus, the most optimised SRM design will not be evaluated for solar vehicle application. Thus, the designed SRM, however not optimised, can be evaluated and provide sense to the hypothesis "The SRM is a potential contender for the next generation traction motor in EVs ". Note that the motor controller is not part of the scope of the study, although a motor controller circuit is required during transient simulations. Therefore, an optimised motor controller or design is not used to simulate the SRM. The conclusion of the evaluated SRM will justify future development and studies to provide an optimal SRM design that can be developed as a manufactured prototype. Definition 6 (Exploratory development model): The exploratory model is an experimental research-based system development method used to develop and redesign a system or product. The exploratory model is based on planning and reviewing potential scenarios and approaches until the one that appears to be optimal is selected. However, this method is essentially a form of educated guesswork. The exploratory model is a type of prototyping model, but it is much more open-ended and less formal than other systems. As such, there is a risk that the results of the exploratory model will be less than optimal [54]. 1.5.3 Research limitations The following research limitations were imposed or identified:  Manufacturing and financial constraints: Manufacturing an electric motor is expensive. Due to the financial costs involved with manufacturing, the switched reluctance motor in this study is modelled using finite element analysis (FEA) software rather than manufacturing the electric motor.  Validation and verification constraints: the validation process cannot be performed on a physical electric motor since the switched reluctance motor is modelled rather than manufactured. Validation and verification are mainly performed by simulating a similar motor to ensure the correct setup and modelling process is followed when analysing an SRM. This requires motor and experimental data from a similar SRM.  Computer resource constraints: Simulations of finite element analysis require extensive computing resources. The simulations of the study were limited to two computers with the following hardware: o Computer 1: Intel i7-5500 CPU, 8GB RAM, NVIDIA GeForce 840M GPU o Computer 2: AMD Ryzen 7-3700X CPU, 64GB RAM, Quadro P2200 GPU 10  Software constraints: Many numerical simulation software are used in the industry. Thus, many software is available to analyse electrical machines, listed in §3.1.2, p.49. The simulation software is expensive. However, the NWU has licenses to the simulation software of Ansys®.  Simulation accuracy constraint: An engineering project is based on financial limitations. In this study for a Master of Engineering degree, the limitations can be divided between time and energy, therefore, limiting the degree of accuracy when simulating. A trade-off between simulation time and the model accuracy is necessary.  Design constraints: The study is not based on the design of an SRM but on the evaluation of an SRM. Design is not part of the scope of the study. However, a random SRM cannot just be evaluated. Thus, some design, based on the specifications of the solar vehicle is necessary. The design is not the best or an optimised design, but merely an un-optimised XDM, as explained in §1.5.2.  Drive cycle constraints: The scope of this study does not focus on the accurate setup of a drive cycle to evaluate a traction motor. A simplified drive cycle does not provide the most accurate evaluation of a traction motor, but uses the procedure to evaluate different traction motors for comparison against each other. 1.5.4 Research assumptions  It is assumed that the magnetic material properties and characteristics provided in the material database of Ansys® are accurate and correct.  The drive cycle setup assumes assumptions of solar radiation and road and route conditions. An accurate setup of the drive cycle is not part of the scope of this study. Therefore, assumptions were made to simplify and demonstrate the evaluation process. All assumptions are set out in chapter 6.  Following the definition of an XDM during the design process, the switched reluctance motor design in chapter 5 is assumed from previous research and literature, i.e., the efficiency of an SRM design is based on the static flux linkages. 1.6 Dissertation outline The dissertation consists of seven chapters, a bibliography, and four appendices. All chapters are provided in logical order. However, during the study, the work is not completed in the particular order of the chapters. Chapter 1 is an introduction. A background on solar races and traction motors used for EVs is discussed, providing an overview of the research topic. The purpose of the research is provided, which includes the research problem, scope, limitations, and assumptions. 11 Chapter 2 provides a literature review on topics related to the research. Relevant background on the SRM and the operating principles of an SRM is provided. Thereafter, the chapter focuses on design considerations of an SRM, including geometrical structures that improve the performance and efficiency of an SRM. Following the conclusion, an SRM is proposed as an XDM. Chapter 3 provides a literature review on the topics of numerical simulations. Relevant background on the numerical simulation methods used in Ansys® Maxwell is discussed. The literature review provides a better understanding of the different types of solvers, solutions, and setups during the analysis of an electromagnetic machine, i.e., an electric motor or transformer. This chapter also summarises different electromagnetic simulation software. Chapter 4 validates the FEA method for analysing a modular switched reluctance motor (MSRM). Replicating the MSRM of Wen Ding et al. is used to validate the FEA methods. Replicating a model instead of comparing data against experimental data is due to financial limitations that prohibit the manufacturing of a switched reluctance motor. The experimental tests of the Mitsuba M2096-DII BLDC used to create an efficiency map for evaluation purposes would have been perfect to validate the FEA method. However, because of the difference in operation by flux production and excitation methods, it is suggested to validate an SRM instead of a BLDC. Chapter 5 presents the steps to design the proposed SRM. Design specifications are obtained by analysing the operating points of the Mitsuba M2096-DII when evaluated using the drive cycle. Design analysis of the geometric structure, windings, and thermal considerations and the constructed efficiency map are provided. Chapter 6 provides an evaluation of an SRM for solar vehicle application. This chapter also evaluates the Mitsuba M2096-DII as a reference. A drive cycle is constructed to evaluate a traction motor. The conclusion compares the results of the proposed SRM with those of the Mitsuba M2096-DII. Evaluating the Mitsuba M2096-DII was completed before starting with chapter 5 to specify performance requirements the design should adhere to. Chapter 7 provides the conclusion of this study. Recommendations for further work and possible design alterations that could improve the proposed SRM are identified for future development studies. The appendices consist of the following:  A methodology to experimentally test a traction motor.  Additional FEA data obtained from the validation study (chapter 4).  Thermal validation and analysis of an MSRM.  Analysis data of the drive cycle evaluation. 12 CHAPTER 2 THE SWITCHED RELUCTANCE MOTOR Today, almost every automotive manufacturer has an EV or HEV in their fleet. The European Union suggested an effective ban on the sale of new ICE vehicles from 2035 onward. The ban on ICE vehicles forces automotive manufacturers to invest in alternative energy sources. As such, electric motors will be used in transport systems at an increasing rate. The largest consumer of electrical energy is electrical motors and therefore an electrical motor plays a vital part in the growing market of electrification. Switched reluctance motors are becoming an exceptionally attractive choice for use in the industrial, residential, commercial, and transportation sectors [55]. This chapter discusses the overview and principles of an SRM. Furthermore, designs of SRMs with similar specifications to the Mitsuba M2096-DII are reviewed. Subsequently, the most important design considerations when designing an SRM are discussed. The design considerations are followed by a review of modular SRM structures that provide improved motor efficiency. This chapter concludes with a summary and a proposed SRM design for evaluation. 2.1 Overview The SRM represents one of the oldest electric motor designs. This motor design originated around the 1830s to the 1850s. The origin of the motor lies in the horseshoe electromagnet of William Sturgeon in an attempt to convert the “once only” attraction of an iron armature into an oscillatory or continuous motion. A piece of soft magnetic material is fastened to a lever and placed near an electromagnet, as shown in Figure 2-1a. The force of the electromagnet tends to attract the piece of magnetic material. The attraction force is divided into a radial and a tangential component. The tangential force attempts to move the piece of magnetic material into the so-called aligned position, shown in Figure 2-1b. With the lever fastened at some central point, the tangential force creates torque, and rotation of the magnetic material occurs. 13 (a) (b) (c) Figure 2-1: Attractive forces between an electromagnet and magnetic material in the: (a) Unaligned position; (b) Aligned position; (c) Continuous motion The rotation of a piece of magnetic material around the centre is based on the principle of mechanical construction. There should always be at least one electromagnet per piece of magnetic material in the unaligned position, as shown in Figure 2-1a. For continuous rotation, a pair of electromagnets must be energised sequentially according to a prescribed energising pattern. The anticlockwise rotation of the magnetic material piece shown in Figure 2-1c is achieved by energising the electromagnet when the magnetic material piece is near and on the right-hand side of the electromagnet. After the de-energisation of the electromagnet, the next electromagnet is energised, similarly, the next phase and so forth. For anti-clockwise rotation, a clockwise excitation pattern is followed. The basic operation highlights that current polarity has nothing to do with the direction of rotation but is determined instead by the excitation sequence of the electromagnet coils [56]. The direct ancestor of the SRM, or the so-called ‘electromagnetic engine’, patented by WH Taylor in 1838, was based on the principle of the horseshoe electromagnet. However, the SRM required mechanical switches that were inefficient that resulted in the SRM suffering from torque pulsations and low reliability. The SRM lost all attention and was soon replaced by DC and AC motors. With the improvement in power electronics, power switches, and advancements in magnetic materials and motor design principles, the SRM was brought into the variable speed market. 14 2.1.1 Mathematical model of an SRM The SRM is a non-linear control structure and therefore it is vital to develop a relevant model. An elementary equivalent circuit, as shown in Figure 2-2 can be derived when neglecting the mutual inductance between the phases as follows [57]: The instantaneous voltage, according to Faraday’s law, is equal to the sum of the resistive voltage drop and the flux linkage derivative as a function of rotor position and the current, provided as [58]: 𝑑𝜆(𝜃, 𝐼) 𝑉 = 𝐼𝑅 + 𝑑𝑡 (1) Where 𝑉 is the phase voltage, 𝐼 the phase current, 𝑅 the phase resistance, 𝜃 the rotor position, and 𝜆 the flux linkage per phase given by: 𝜆 = 𝜆(𝜃, 𝐼) (2) The flux linkage is a function of the rotor position and phase current and by neglecting magnetic saturation in the equivalent circuit, flux linkage is redefined as: 𝜆 = 𝐿(𝜃, 𝐼)𝐼 (3) Where 𝐿 is the dynamic winding inductance dependent on the position of the rotor and the phase excitation current. Differentiating equation (1), the instantaneous voltage equation is: 𝜕𝜆(𝜃, 𝐼) 𝑑𝐼 𝜕𝜆(𝜃, 𝐼) 𝑑𝜃 𝑑𝐼 𝑑𝐿(𝜃, 𝐼) 𝑉 = 𝐼𝑅 + + = 𝐼𝑅 + 𝐿(𝜃, 𝐼) + 𝐼 𝜔 𝜕𝑖 𝑑𝑡 𝜕𝜃 𝑑𝑡 𝑑𝑡 𝑑𝑡 (4) Where 𝜔 is the angular velocity. In this equation, the third term on the right-hand side represents the back EMF, 𝜀𝑏, and is obtained as: 𝑑𝐿(𝜃, 𝐼) 𝜀𝑏 = 𝐼 𝜔 𝑑𝑡 (5) Note that the back EMF is dependent on the operating point and is obtained at the rated torque- speed operating point. 15 Figure 2-2: Equivalent circuit of an SRM Furthermore, the power conversion process of an SRM can be derived by multiplying both sides of equation (4) with the phase current. 𝑑𝐼 𝑑𝐿(𝜃, 𝐼) 𝑉 = 𝐼2𝑅 + 𝐿(𝜃, 𝐼)𝐼 + 𝐼2 𝜔 𝑑𝑡 𝑑𝑡 (6) Assuming the SRM is operating in the magnetic linear region, the second term on the right-hand side can be expressed further using the product rule for differentiation. 𝑑𝐼 𝑑𝐼 1 1 𝑑𝐿(𝜃, 𝐼) 𝐼𝐿(𝜃, 𝐼) = ( 𝐿(𝜃, 𝐼)𝐼2) − 𝐼2 𝜔 𝑑𝑡 𝑑𝑡 2 2 𝑑𝑡 (7) Substituting equation (7) into equation (6), the power equation of an SRM is calculated as: 𝑑𝐼 1 1 𝑑𝐿(𝜃, 𝐼) 𝑃 = 𝑉𝐼 = 𝐼2𝑅 + ( 𝐿(𝜃, 𝐼)𝐼2) + 𝐼2 𝜔 𝑑𝑡 2 2 𝑑𝑡 (8) It can be seen that the input electrical power on the left-hand side is converted, respectively, to electrical, magnetic, and mechanical power on the right-hand side. The electrical power on the right-hand side is dissipated as heat in terms of copper losses. The magnetic power is stored in the magnetic field energy of the magnetic core and the mechanical energy is in terms of torque production. The torque production (𝜏) in the linear region is given by: 𝐼2 𝑑𝐿(𝜃, 𝐼) 𝜏 = 2 𝑑𝑡 (9) It is seen that the direction of torque is independent of current polarity, due to the square of the current. The next section will demonstrate how the torque equation of an SRM is derived using co-energy. Co-energy is a non-physical quantity used in extensively in the analysis of non-linear systems, such as electrical machines and electromechanical devices [55]. 16 2.1.2 Principle of operation An SRM is identified by the number of stator poles and number of rotor poles. As shown in Figure 2-3, an SRM with 6 stator poles and 4 rotor poles, called a 6/4 SRM is shown to describe the basic principles of an SRM. Figure 2-3 shows a 6/4 conventional SRM in its aligned position, misaligned position, and unaligned position with respect to the coils [59]. The following parameters are shown in Figure 2-3: pole height, pole arc, and pole pitch, which applies to both the stator and the rotor. Also, a non-magnetic spacer shown, explained in §2.1.4 is used to minimise windage losses. Pole arc Nonmagnetic spacer Pole pitch (a) (b) (c) Figure 2-3: A 6/4 SRM in the: (a) Aligned position; (b) Misaligned position; (c) Unaligned position The operation of a motor relies on torque production to achieve the desired rotational speed. Torque production is a function of inductance in an SRM. Inductance is derived from the magnetomotive force (MMF), ℱ, in a magnetic circuit [29]. MMF is given by: ℱ = ∅ℛ = 𝑁𝐼 (10) Where 𝑁 is the number of conductor turns, 𝐼 is the current, ℛ is the magnetic reluctance, ∅ is the equivalent flux and is given by: 𝜆 ∅ = 𝑁 (11) Where 𝜆 is flux linkage, given by 𝜆 = 𝐿𝐼, with 𝐿 as inductance. 17 Pole height Rearranging the equations, we can obtain the following: 𝑁2 𝐿 = ℛ (12) Thus, the phase inductance of a coil is inversely proportional to the magnetic reluctance in the magnetic circuit of an SRM. The three relative positions of an SRM described by inductance and reluctance are as follows:  An aligned position where the rotor poles are aligned with the stator poles. During this instance, the phase inductance of the winding is at a maximum and the magnetic reluctance at a minimum.  A misaligned position where rotor poles are not fully aligned with the stator poles, nor unaligned with two stator poles. Moving from the unaligned position to the aligned position, the phase inductance of the winding is gradually increasing, and the magnetic reluctance gradually decreases. When moving from the aligned position to the unaligned position, the phase inductance of the winding is gradually decreasing, and the magnetic reluctance gradually increasing; and  An unaligned position where the rotor poles are exactly between two stator poles. During this instance, the phase inductance of the winding is at a minimum and the magnetic reluctance at a maximum. A magnetic circuit, similar to an electrical circuit can be used to analyse an SRM. The biggest difference in the analogy is that a resistor in an electric circuit dissipates electrical energy, whereas reluctance stores magnetic energy as discussed in the operating principles of an SRM. The operating principles of an SRM for torque production are described in the following sections. The operating principles of an SRM are divided into its electromechanical energy conversion and its torque production. 2.1.2.1 Electromechanical energy conversion Electromechanical energy conversion is the consecutive transformation of electrical energy into magnetic energy and magnetic energy into mechanical energy, or mechanical energy into magnetic energy and magnetic energy into electrical energy. An SRM is a single electromechanical system in which the electrical energy is converted into mechanical energy [60, 55]. Non-linear analysis of an SRM takes into account the saturation of the magnetic circuit to fully understand the electromagnetic energy conversion for motor operation. To understand the electromechanical energy conversion process of a non-linear system, a non-linear magnetisation curve is used, shown in Figure 2-4. 18 𝑊𝑠 𝑊𝑐 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 (𝐴) Figure 2-4: Magnetic characteristic relationship between energy (𝑾𝒔) and co-energy (𝑾𝒄) The magnetisation curve in Figure 2-4 plot the flux linkage versus current for a fixed rotor position of the SRM, shown in Figure 2-4. The magnetisation curve shows the stored magnetic energy, 𝑊𝑠, and the magnetic co-energy, 𝑊𝑐. The stored magnetic energy and co-energy is given by equations (13) and (14) respectively: (13) 𝑊𝑠 = ∫ 𝐼𝑑𝜆 𝑊𝑐 = ∫ 𝜆𝑑𝐼 (14) When the rotor reaches the turn-on position, the phase switches are turned and the phase voltage starts to build up phase current. A part of the energy is stored in the magnetic field at this stage, called the magnetic field energy. The magnetic field energy will increase with the rotating rotor until the position where the current excitation, known as the turn-off position is reached and the phase winding switches are turned off [61]. The other part of the input energy, 𝑊𝑒, is dissipated by mechanical work, 𝑊𝑚 , and losses, 𝑊𝑙𝑜𝑠𝑠𝑒𝑠. Thus, the energy conversion is given by: 𝑊𝑒 = 𝑊𝑠 + 𝑊𝑚 + 𝑊𝑙𝑜𝑠𝑠𝑒𝑠 (15) The flux linkage of an SRM during operation is not constant, as shown in Figure 2-5. Nevertheless, a uniform flux distribution is crucial to obtain smooth torque. Note that the conversion of electromagnetic energy is explained on the basis of constant supply voltage and fixed rotor speed. The mechanical work produced during the magnetisation process is known as the co-energy in the electromechanical energy conversion. The input energy starts at the turn-on position, taken as the unaligned position and stops at the turn-off position. The turn-off position, is some time 19 𝐹𝑙𝑢𝑥 𝐿𝑖𝑛𝑘𝑎𝑔𝑒 (𝜆) before the aligned position. Once the turn-off position is reached, the magnetic energy at that moment is 𝐹 + 𝑊𝑚2. At this stage, the magnetic field energy, 𝑊𝑚2 is converted into mechanical work and losses [61]. The surplus of field energy, 𝐹, are fed back to the power source. 𝐴𝑙𝑖𝑔𝑛𝑒𝑑 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝐹 𝑊𝑚2 𝑇𝑢𝑟𝑛 − 𝑜𝑓𝑓 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑊𝑚 𝑈𝑛𝑎𝑙𝑖𝑔𝑛𝑒𝑑 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 (𝐴) Figure 2-5: Magnetic characteristics of an SRM under operation The aligned position of an SRM in saturation has higher stored energy than an SRM not in saturation for the same current magnitude. Significant magnetic saturation of a motor has an influence on the torque producing capability and power factor, equal to about twice that of a motor not in magnetic saturation [55]. The degree of saturation influences the choice of motor and inverter design. Thus, magnetic saturation is a desirable characteristic for SRM operations but must be localised to the pole tips since electromagnetic energy conversion occurs in the air gap [62]. 2.1.2.2 Torque production The torque production of an electric machine is mainly of two types; electromagnetic torque and reluctance torque [56]. Electromagnetic torque is produced with the interaction of the magnetic fields between the stator and rotor poles and the reluctance torque is produced by the variable air gap between the stator and rotor poles. The torque of an SRM can be calculated by applying the principles described in the previous section. Using the flux linkage curve of Figure 2-5, the electromagnetic torque of a non-linear magnetic system can be calculated in terms of the co-energy [55, 58]. The electromagnetic torque equation is given by: 20 𝐹𝑙𝑢𝑥 𝐿𝑖𝑛𝑘𝑎𝑔𝑒 (𝜆) 𝜕𝑊𝑐(𝜃, 𝐼) 𝜏𝑒(𝜃, 𝐼) = 𝜕𝜃 (16) Rewriting equation (14), the co-energy can be expressed at any rotor angle, 𝜃, as given by: 𝐼 𝑊𝑐 = ∫ 𝜆(𝜃, 𝐼)𝑑𝐼 (17) 0 If a linear magnetic model is assumed, the co-energy and torque equations, using the relationship between flux linkage and current can be rewritten as: 𝐼 𝑊𝑐 = ∫ 𝐿(𝜃)𝐼 𝑑𝐼 (18) 0 𝐼2 𝑊𝑐 = 𝐿(𝜃) 2 (19) 𝐼2 𝑑𝐿 𝜏𝑒 = ∗ 2 𝑑𝜃 (20) 𝑑𝐿 The absolute value of contribute to the amount of mechanical torque, and therefore SRM 𝑑𝜃 𝐿 𝑑𝐿 designs require large 𝑚𝑎𝑥 ratios, hence the large absolute value of to obtain the high torque. 𝐿𝑚𝑖𝑛 𝑑𝜃 The equation of motion torque for an SRM is given by: 𝜕𝜔 𝜏 = 𝐽𝑟𝑜𝑡𝑜𝑟 + 𝐷𝜔 + 𝑇𝐿 𝜕𝑡 (21) Where 𝐽𝑟𝑜𝑡𝑜𝑟 is rotor inertia, 𝐷𝑐 is the damping coefficient and 𝑇𝐿 is the load torque. Angular velocity can be written as a function of the rotor speed, 𝑁𝑟, as: 𝜔 = 2𝜋𝑁𝑟 (22) In this section, it is shown that a simple equivalent circuit, as shown in Figure 2-2 cannot be used to represent an SRM. However, an equivalent circuit can only be used under the assumption of unsaturated, linear operating conditions and is only an approximation of reality. To accurately predict the characteristics of an SRM, the saturation and non-linear effects should be included. Therefore, FEA software is used to consider all these effects when analysing an SRM [63]. §3.1.2, p.49, offers a review of the different FEA software for electromagnetic systems. 21 2.1.3 Motor operation Depending on the applications, an electric motor can operate under different load conditions. For an industrial motor, some priority is given to the operating region. An industrial motor operates more frequently near a single operating point than the rest of the points in its torque-speed profile. However, for traction, its operating region is constantly changing [61]. Therefore, a traction motor must meet all operating requirements. Obtaining a better understanding of motor usage and operational changes under different driving cycles will be required. A driving cycle is used to assess the performance of a vehicle, refer to chapter 6. The expected operating regions when using an SRM as a traction motor are mapped by its torque-speed characteristics as shown in Figure 2-6. 2.1.3.1 Torque-speed characteristics 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑇𝑜𝑟𝑞𝑢𝑒 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑃𝑜𝑤𝑒𝑟 𝐹𝑎𝑙𝑙𝑖𝑛𝑔 𝑃𝑜𝑤𝑒𝑟 𝜔𝑏 𝑆𝑝𝑒𝑒𝑑 𝜔𝑝 Figure 2-6: Desired torque-speed characteristics of an SRM The typical torque-speed characteristics of an SRM are shown in Figure 2-6. Torque-speed characteristics can be divided into three visible operating regions. The three operating regions are the constant torque, constant power, and falling power regions. The constant torque operation occurs between the zero speed and the base speed (𝜔𝑏). The base speed is the maximum speed at which the current rises almost instantly as the generated voltage is higher than the back EMF. The current should be limited to achieve constant torque. An increase in back EMF also occurs at speeds above the base speed. At speeds above the base speed, the conduction angle of the motor should be increased to reach the desired current level before the motor reaches an aligned position. In the region of constant power, the torque 22 𝑇𝑜𝑟𝑞𝑢𝑒 decreases with the increase of speed until the maximum speed of constant power, 𝜔𝑝, is reached. At speeds beyond the maximum speed of constant power, the conduction angle cannot be increased, such that the torque decreases more rapidly with the increase of speed. This is known as the region of falling power. In the falling power region, constant power is no longer achievable [61]. A motor control strategy is used to operate in each of these three operating regions. 2.1.3.2 Control strategies To operate an SRM a certain amount of control and power electronics is necessary, unlike an IM or DC motor which can run directly from a DC or AC power supply. Torque of an SRM is produced in impulses, flux is built from zero and has to return to zero in each stroke. The orthogonality of the flux and current as found in DC machines or employed in AC machines is not present in an SRM. As torque is produced in impulses, a certain amount of control and power electronics is necessary to control an SRM. For the operation of an SRM, only one phase should be excited at a time. Another phase is then activated and so forth to generate continuous torque. The switching of a three-phase SRM is shown in Figure 2-7. Figure 2-7: Phase excitation of a three-phase SRM The different operating regions shown in Figure 2-6 are usually controlled by different motor control strategies. The control strategies are current control and single-point control (SPC). The back EMF is very small at low speeds; therefore, the phase current rapidly increases. A hysteresis band is used to maintain the current within a reference value. The current is maintained within the hysteresis band of the reference value, and the semiconductor switches act as a current chopper. This control strategy is known as chopped current control (CCC). The conduction angle (turn-on and turn-off angles) usually stays constant for CCC unless the motor is optimised for efficiency, torque ripple, or acoustic noise. SPC is used to operate the SRM above its base speed. For constant torque operations, the conduction angles are adapted to their torque and speed requirements until the conduction angles can no longer be adapted, therefore 23 staying constant and operating in the falling power region [64]. The control operation of an SRM is summarised in Table 2-1. Table 2-1: Control strategies of an SRM Control Operation Variables Constants CCC Constant torque Reference current Conduction angle SPC Constant power Conduction angle Supply voltage 2.1.4 Losses In §2.1.2.1, the review of electromagnetic energy conversion, copper loss in the windings, core losses in the iron core, and mechanical losses in the rotor are neglected. When considering the losses in an electrical motor, the energy balance can be categorised as shown in Figure 2-8 [55]. Figure 2-8: Losses in an SRM When all losses are subtracted from the input power, the mechanical output power is obtained. Mechanical output power divided by the electrical input power gives efficiency. In an electric motor, efficiency is considered an important aspect during the development process to maximise the amount of output power when providing a set amount of input power [65]. The mechanical loss of an electric motor originates from the bearing friction and wind resistance opposing the rotor. Bearing losses depend mainly on the bearing load, bearing type, bearing lubricant, and lubricant characteristic properties. When the rotor of an SRM is rotating, the rotor work like a fan, which generate windage loss. To reduce the windage losses, the air gap between the rotor poles and the rotor structure, referred to as the back iron should be a cylindrical shape obtained by filling epoxy resin or using non- magnetic spacers, creating a smooth rotor surface, as shown in Figure 2-3. These mechanical 24 losses often present much higher losses at high speeds, since the mechanical losses are a cubic function of rotor velocity, rather than a linear function [66]. Electrical losses of an electric motor are divided into two categories. The two categories are copper losses and iron losses. Copper losses is used to describe the resistance in the wire used to wind a coil, which means that even conductors made of aluminium account for copper losses, or more specifically resistive losses. Copper losses in an SRM are due to the electrical resistivity of the stator windings and are usually the most significant energy loss of the motor, predominantly active at low-speed and high-current operating conditions. Copper is relatively heavy, therefore in the development of an electric motor, as little as possible copper usage is desired to minimise motor mass. However, minimising the cross-sectional area of copper in the motor leads to an increase in resistance and therefore an increase in copper losses [67]. Thus, a trade-off between motor mass and motor performance is expected when limited by constraints. Iron losses, also known as core losses, consists of eddy current losses and hysteresis losses. The eddy current losses are produced by parasitic current through the magnetic core of an electric motor and are dependent on the lamination thickness, motor operating frequency, flux density, and material resistivity. The hysteresis losses are the resistance to a directional change from the magnetisation, frequency or flux density in the magnetic core and are mainly dependent on the hysteresis loop of the material [68, 69]. Determining core losses in an electrical motor is a significant part of the development process of an electric motor. However, it is a complicated process to accurately predict the core losses in an SRM when following an analytical approach. The difficulty of the analytical approach is a consequence of the flux linkage waveforms and flux densities that differ in each part of an SRM [55, 70]. An analytical procedure often does not account for the difference between the flux linkage and the flux densities in the motor. Due to distorted and non-sinusoidal flux and magnetic saturation in different parts of the stator and rotor, calculating core losses is very complicated [71]. Analytical models and lookup tables are a fast approach to determine losses, however have reduced accuracy. Empirical formulas are usually considered in core loss estimation, but are insufficient for SRMs [72]. Therefore, the best alternative method to accurately determine core losses is to use FEA [73]. 2.2 Propulsion of electric vehicles Traction motors play a crucial role in an EV. The purpose of an electric motor is to propel the vehicle using energy extracted from the battery. The purpose of this study is to evaluate an SRM for solar vehicle application. A suitable SRM should be selected to evaluate. In this section, four SRM designs found in literature, exhibiting similar power ratings as the Mitsuba M2096-DII were 25 reviewed as the Mitsuba M2096-DII is currently used as the traction motor in the solar vehicle of the NWU. However, per the scope of this study (§1.5.2, p.9), an SRM best suited for the solar vehicle characteristics would need to be designed to justify the use and future development of an SRM for solar vehicle application. Nikunj Ramabhai Patel et al. designed a 12/16 C-core radial flux modular SRM [74, 75]. The motor is designed to propel a vehicle, having a total mass of 120 kg, 0.6 m2 frontal area, and 0.7 drag coefficient. These vehicle characteristics resulted in the motor specifications of 26 Nm at a rated speed of 600 rpm when considering acceleration of 0-50 km/h in 20 seconds and speeds of roughly 60 km/h. The design process is divided into three steps. The first is to derive the required torque and power using vehicle dynamic equations. The second part is to fulfil the three basic SRM conditions using the feasibility triangle (refer to §2.3.4, p.32). The third part was to calculate the excitation parameters and torque using magnetic analysis and Ansys Maxwell to analyse the static and dynamic characteristics. When comparing the analysis results against a 12/16 conventional SRM, Nikunj Ramabhai Patel et al. concluded that when comparing magnetic characteristics of a conventional radial flux SRM and the designed C-core radial flux modular SRM, that less magnetic material was required for the C-core design [74, 75]. The C-core radial flux modular SRM offered higher torque and efficiency than the conventional SRM at rated current and at the rated operating condition. This C-core radial flux modular SRM proved a viable contender to use for evaluation purposes based on its rated operating condition. However, not enough information was provided to construct and verify the design using Ansys Maxwell. Also, the study did not provide an efficiency map for the designed motor that could be used for evaluation purposes. Jeanin Lin designed a 6/10 conventional SRM [56]. The motor was designed to propel a bicycle, with total mass of 100kg (mass of the cyclist and the bicycle), 0.5 m2 frontal area, and 0.5 drag coefficient. These characteristics resulted in motor specifications of 9.5 Nm at a rated speed of 500 rpm. Using a reduction gear ratio of 3:1 and a wheel radius of 0.33 m, 500 rpm equalled 20 km/h as the rated speed. The configuration of an electric bicycle system was constraint by the legislation of Ontario, Canada, which limits the output power of electric bicycles to be within 500 Watt with the maximum speed not exceeding 32 km/h while the bicycle is only propelled by the electric motor. The design process started with the requirements obtained by analysing a typical velocity profile of an electric bicycle. SPEED PC-SRD, a commercial machine design software was used to assist in SRM 26 geometry analysis, where after Flux 2D from Magsoft was used to obtain a detailed design analysis. Jeanin Lin concluded that the motor exhibits higher torque compared to a conventional 6/4 SRM, and that an alternate pole configuration (NSNSNS) compared to a traditional pole configuration (NNNSSS) in an SRM proved to have higher and more consistent output torque. It was concluded from experimental testing that the difference between 2D FEA and test results showed that the end winding effects needs to be considered for small thickness machines. This SRM design lacked performance characteristics, not only when compared to the Mitsuba M2096-DII (§6.2.1, p.136), but also when considering the design constraints as the motor was only designed to assist the cyclist when pedalling. Saurabh Prakash Nikam et al. designed a conventional SRM [43]. The motor was designed for a two-wheeler vehicle with a total mass of 120 kg (mass of the driver and the vehicle). The maximum speed of 30 km/h and an acceleration target of 0 to 20 km/h in 5 seconds was required. The characteristics resulted in motor specifications of 36 Nm at rated power of 500 W whilst using a gear ratio of 6:1. Both a three phase 6/4 pole SRM, a three phase 6/8 and a four phase 8/6 pole SRM was considered during the design process. The rotor poles were increased from four to eight for the three phase motor to reduce the magnetic flux paths. However, with the rotor poles close to one another, the motor exhibited low field weakening capabilities. Therefore, a four phase 8/6 pole SRM was proposed to improve the field weakening capabilities, that could lead to increased efficiency. Even though the different designs were discussed, the studies did not discuss the design processes. Considering the motor specifications, the motor designed by Saurabh Prakash Nikam et al. without the gear ratio will be rated for a torque of 4 Nm, and speed of 1200 rpm. These characteristics were not sufficient to propel the solar vehicle. Vandana Rallabandi and Baylon Godfrey Fernandes designed a 12/26 segmented rotor SRM [76]. The motor was designed for direct drive applications with the performance characteristics of 24 Nm and 600 rpm for maximum torque and speed. The motor was chosen as a 12/26 segmented rotor SRM to demonstrate tight torque, low speed and high efficiency operations. The effects of the number of rotor poles, pole arc angles and the geometric dimensions of the stator was analysed using FEA. Flux 2D, developed by Cedrat is used to analyse this SRM design. 27 Comparing the design with that of a 6/10 SRM and 12/16 segmented rotor SRM with equal dimensions, it was shown that the design exhibited significantly higher efficiency and a higher torque to weight ratio. Efficiency was 2 to 4% higher, whilst the torque to weight ratio was roughly 1 Nm/kg more than the other SRMs. The increase in efficiency was due to lower copper losses, with copper losses almost a third to half the losses compared to the other two SRMs. This design exhibited good performance characteristic, however, the maximum performance characteristics of this design was roughly the required rated performance characteristics for evaluation purposes. The four SRM designs were briefly discussed in order of their designed performance characteristics, design process, modelling tool, results and a quick summary. Though, none of these motor designs offered the required performance ratings, as specified in §5.1, p.89. If an SRM was found with the required performance characteristics and enough data to replicate the design using FEA software and thereafter validate the design to provided experimental data (i.e. torque-speed characteristics, efficiency map, operating currents), the SRM design could have been used for evaluation purposes in this study. Thus, as no design was found with the required performance characteristics, an XDM of an SRM was required, as per the scope of this study (§1.5.2, p.9). 2.3 Design considerations The geometric dimensions of an SRM are the main contributing factor to its magnetic characteristics, and therefore its electromagnetic energy conversion as reviewed in §2.1.2.1. Specifying the desired performance characteristics, such as the torque-speed profile, the SRM design can begin. The design considers the aspects of geometric dimensions, pole configurations, and the winding parameters as discussed in this section. Anas Labak has shown that an SRM with increased reluctance improves the magnetic flux characteristics. A significant improvement in the aligned position of magnetic flux is seen when observing the magnetic flux characteristics. This improvement in magnetic flux relate to improved dynamic torque operations, resulting in higher output performance. Assuming the input power is constant, an SRM of high efficiency can roughly be estimated during the design stage using magnetic flux characteristics. However, magnetic flux characteristics are not always a guarantee of an optimal and high efficient SRM design [55, 77]. The motor controller and conduction angles, shown in §2.1.3, p.22 and §5.3.3, p.117 also have a major effect on the performance and efficiency of an SRM [55, 78]. 28 2.3.1 Structure Switched reluctance motors fall into three classifications based on the direction of flux through the air gap. The three classifications are the transverse, axial, and radial flux motors [55]. The basics of the radial and axial flux directions are explained from the coordinate system in Figure 2-9. Both the radial and axial flux motors lie centralised around the z-axis, also called the axial direction. As observed in Figure 2-9, the axial flux motor is where the magnetic flux path in the air gap is parallel to the axis of rotation and the radial flux motor is where the magnetic flux path in the air gap is perpendicular to the axis of rotation. The transverse-flux motor has the magnetic flux path predominantly tangential to the relative axis of rotation. A transverse flux motor is complex and very rarely found [79]. The basic principles of the transverse flux motor are further discussed in §2.4.4. X Z Y Figure 2-9: SRM structures: (a) Axial flux; (b) Radial flux [80] An axial and radial flux SRM is compared in [81]. Both the axial and the radial flux motors consist of the same volume, resulting in the radial flux motor offering more torque. This is mainly due to the fact that magnetic flux crosses the air gap twice in a radial flux motor compared to four times in the double-sided axial flux motor. To obtain the same torque as the radial flux motor, the diameter of the axial flux motor has to be increased beyond the diameter of the radial flux motor. It is often difficult to obtain the same amount of torque when the diameter is constrained. Manufacturing an axial flux motor is also a difficult process. Another method to manufacture an axial flux motor is shown in [82], where the complex structure is machined from a block of soft magnetic material instead of laminations. An outer rotor radial flux SRM is an appealing choice when mounting the rim of the wheel directly to the traction motor, commonly referred to as an in-wheel traction motor [55, 83]. An outer rotor configuration offers higher torque capability due to its extended air gap diameter and larger rotor 29 inertia. An outer rotor motor can be coupled directly to a wheel rim, eliminating the use of mechanical gears, and can reduce the overall drive efficiency by around 20-30%. Due to the larger inertia of the rotor, the torque ripple is damped, making for smooth and stable low-speed operation [55]. Quite a few topological variations of SRMs have emerged over the years to improve their performance. The main considerations include the number of phases, pole configurations, pole and winding designs, and the magnetic material. However, segmented pole configurations offered an alternative way to improve motor performance. These performance improvements are reviewed in §2.3.8. 2.3.2 Phases Common industry practice is to use a three-phase motor [55]. For an electric motor, at least two phases are needed to maintain torque and rotational capability. In an SRM, increasing the number of phases reduces the root mean square (RMS) current of each phase for the same amount of torque capability. However, increasing the number of phases also adds to the reliability of the motor, so that when one phase fails, the other phases will still allow the motor to operate at a lower performance rating. Increasing the number of phases also has its drawback. The major drawback of increasing the phases is the increase of electronic switches and converters in the motor controller. In low and medium-power motors, the increase in switches and converters significantly increases the cost of the motor drive system [84]. Also, a higher number of phases requires a higher number of poles. A larger number of poles will reduce the available space for coils if the outer diameter of the motor is constrained. Therefore, increasing phases is not always a practical solution [55]. During the design of an SRM, the following factors are usually the deciding factors when specifying the number of phases [85]:  The starting capability of the motor  The directional capability of the motor  The reliability of the motor  The cost of the motor  The power density of the motor  The efficiency of the motor Efficiency is a crucial aspect of an electric motor and is enhanced by reducing losses. For an SRM, the decrease in the number of stator phases and the number of phases switching per revolution reduces the core losses at high-speed operations. Therefore, three phases are 30 preferred over four phases in an aircraft starter/generator with the requirement of very low losses [85]. This is because the starter/generator of small size requires a reduction in losses to maintain thermal robustness when operating at high speeds. 2.3.3 Pole configuration An SRM is identified by the number of stator poles and the number of rotor poles. The number of poles has a significant effect on the operational and performance requirements of the motor. The pole configuration requires a correct selection during the design process so that the condition of balanced operation is satisfied. Balanced motor operation is obtained by symmetry of the electrical angle between stator poles and the number of stator pole to rotor pole combinations [86, 59]. The well-known SRM combinations are as follows:  Three-phase SRMs: 6/2; 6/4; 6/8; 6/14; 12/8; 18/12; 24/16  Four-phase SRMs: 8/6; 8/10; 16/12; 24/18; 32/24;  Five phase SRMs: 10/4; 10/6; 10/8; 10/12. Note that at a set rotational speed, the increase of a rotor poles will cause the excitation frequency to increase. For an SRM, the phase excitation frequency is determined by the time it takes for one rotor pole to move from one phase to an adjacent phase. The phase excitation frequency can be calculated using equation (46), p.108. Also, when the outer diameter of the motor is a constraint, an increase of poles will reduce the width of the stator teeth and slot areas. A small slot area might be difficult to wind the specified winding, reduce the copper losses, and achieve the required current density. Furthermore, if the width of the stator pole decreases, the core might oversaturate when operating at peak current, which can lead to reduced torque production capability [55]. However, it is known that the torque production of an SRM is improved when operating in the saturation region of its magnetic material. Comparing a 12/16 three-phase SRM with a 12/8 three-phase SRM of the same geometry and magnetic material, it is determined that the 12/16 SRM offers more static torque over its electrical period [86]. The 12/16 SRM has a smaller mechanical angle for its respective electrical period. The 12/16 pole configuration exhibits a good static torque to rotor position shape and is concluded to be advantageous to use for EVs. A 6/10 three-phase SRM is compared to a 6/4 three-phase SRM in [87]. The outer diameter, stack length, and air gap were kept constant between the two motors. The 6/10 SRM configuration showed a significant increase in torque during the comparison. However, it should be noted that, for comparative cases, the stator and rotor arc angles, phase windings, current ratings, and 31 switching frequencies differ. Thus, the comparison between motors is not a direct comparative case. These studies proved that an SRM with a high ratio of stator to rotor poles has higher efficiency, lower torque ripple, and a high torque to weight ratio. Note that the studies focus on inner rotor, radial flux SRMs and not on outer runner SRMs. Furthermore, the losses depend on the electrical frequency and could be intensified at the same operating speed given a higher ratio of poles [55]. 2.3.4 Pole embrace Pole embrace is regarded as a satisfactory performance requirement. The importance of pole embrace is to satisfy the requirements of self-starting, high output torque, and low torque ripple in an SRM [55]. Pole embrace, illustrated in Figure 2-10 is defined as the ratio of the pole arc to pole pitch angle and can be expressed as: 𝑝𝑜𝑙𝑒 𝑎𝑟𝑐 𝐸𝑚𝑏𝑟𝑎𝑐𝑒 = 𝑝𝑜𝑙𝑒 𝑝𝑖𝑡𝑐ℎ (23) Figure 2-10: Illustration of pole embrace Thus, pole arc angles have a significant effect on the operation of the motor. The stator and rotor arc angles are easily obtained from the feasibility triangle, shown in Figure 2-11. The feasibility triangle is constructed for a three-phase, 6/4 SRM that adheres to the requirements of self- starting, high output torque, and low torque ripple. 32 To satisfy the requirement of self-starting capability, the stator arc angle should be greater than the stroke angle, obtained by the following: 2𝜋 𝜀 = < 𝛽 𝑞𝑁 𝑠 (24) 𝑟𝑝 Where 𝜀 is the step angle, 𝑞 is the number of phases, 𝑁𝑟𝑝 is the number of rotor poles, and 𝛽𝑠 is the stator pole arc angle. Keeping the ratio of aligned to unaligned inductance as high as possible is to improve torque production, as discussed in §2.1.2.1, p.18. The stator pole should be smaller than the interpolar arc angle of the rotor, obtained by: 2𝜋 − 𝛽 𝑁 𝑟 > 𝛽𝑠 (25) 𝑟 Where 𝛽𝑟 is the rotor pole arc angle. To further reduce torque ripple, the positive slope of the inductance curve should not overlap the negative slope of the previous shape. Thus, the rotor pole arc angle should be equal to or slightly larger than the stator pole arc angle, shown as: 𝛽𝑟 ≥ 𝛽𝑠 (26) Traditionally, the stator and rotor pole arcs are chosen approximately the same to avoid zero torque zones centred at the aligned position. Choosing the rotor pole arc angle equal to the stator pole arc angle is an effective way to extend the positive torque zone. From these three constraints shown in equations (24), (25) and (26), the stator and rotor pole arc angle possibilities satisfying the three requirements are easily obtainable [88]. However, the use of the feasibility triangle requires the number of phases and pole configuration of the SRM to be known. 33 30 25 20 Feasible region 15 10 5 0 0 5 10 15 20 25 30 35 𝛽𝑟 Figure 2-11: Feasibility triangle of a 6/4 SRM A study of the effect of the pole embrace was carried out in [89]. The pole embrace ranged from a ratio of 0.2 to 0.5. The pole embrace of the stator was kept the same as that of the rotor. The findings showed that an increase of the stator pole arc angle resulted in a lower torque ripple due to minimum inductance at the unaligned position. Another study ranged the pole embrace between the ratio of 0.45 to 0.6 [90]. The results showed that the highest peak torque was obtained at a pole embrace combination of 0.45 for the rotor and 0.5 for the stator. The lowest torque obtained was at a pole embrace combination of 0.6 for the rotor and 0.45 for the stator. It was concluded that the output torque decreased when the rotor embrace increased for the same stator embrace. Thus, the pole embrace by considering the stator and rotor pole arc angles is among the most important geometrical parameters of an SRM [55]. 2.3.5 Pole height The height of the stator pole in an SRM is the height of the coil, as seen in Figure 2-3. Some space at the pole tip must be left for the pole shoe and pole wedge, which ensures that the coil remains in place during operation. If the pole tips are too long, the rotor poles operate like a fan which, in turn, along with the stator poles, generates windage losses, vibrations, and acoustic noise. In critical motor applications, the gaps between poles are filled with epoxy to minimise windage losses [55]. 34 𝛽𝑠 Analysis of pole heights results in the conclusion that an increase in stator pole heights decreases the motor torque. This is because the diameter of the rotor is decreased to satisfy the constraint of the outer diameter of the motor. Therefore, the distance between the air gap and the shaft is decreased [55]. Note that the SRM under investigation is a conventional SRM of the inner rotor structure, as shown in Figure 2-3. In addition to windage losses, a longer pole height increases the amount of magnetic material that has to be saturated, thus affecting the magnetic flux characteristics [55]. 2.3.6 Wire and slot factor Enamelled copper wire, also known as magnet wire is widely used in motor windings and exists of two components, namely the copper strand coated with a very thin layer of insulation material. The insulation material around the bare copper allows the wires to touch each other without causing an electrical short circuit [55]. Magnet wire is standardised and categorised using the American Wire Gauge (AWG). These are different categories of wire classification, but AWG is the most widely known. When winding the magnet wire around a pole, the amount of wire is limited to the available slot area. This restriction is known as the fill factor. The copper fill factor is the amount of copper that can be used in the available slot fill factor. Theoretically, the fill factor is 71.3%, however, in practice, the fill factor is around 35 to 60% and for hand-wound coils, the fill factor is between 35 and 40% [55]. The fill factor is an important parameter for an SRM, given the restrictions in manufacturability, cost, torque density, and thermal considerations. A further review of the fill factor is discussed in §5.2.3.1, p.109. 2.3.7 Magnetic material In contrast to copper losses in low-speed operations, iron losses are predominantly active in high- speed operations. The selection of the magnetic material used for an electric motor can reduce iron losses. The magnetic characteristics are a fundamental characteristic of an SRM as no permanent magnets are used in an SRM. Thus, for an electric motor, the correct choice of magnetic material can achieve characteristic traits of high efficiency or high torque [55]. High power and torque density and low loss standard grade (EN 10106) magnetic material are usually used in traction motors. Some electric steel manufacturers provide specific magnetic materials with characteristics intended for EVs. ArcelorMittal offers its iCARe® range, with low loss levels, high torque, and speed-specific uses [91]. Cogent Power offers its Hi-lite range of advanced thin gauge electrical steel with a specific design to improve the performance of an energy-efficient application system [92]. Thyssenkrupp offers its Powercore® range consisting of magnetic material grades for e-mobility and high frequencies that are ideal for use in highly 35 efficient traction motors [93]. These magnetic materials are offered in very thin lamination sheets to reduce eddy current losses and increase motor efficiency [94]. 2.3.8 Stacking factor Stacking factor of an SRM is defined as the ratio of the total thickness of the lamination sheets to the axial length of the iron core [55]. For an electrical machine, the stacking factor is always less than 100%. The stacking factor typically varies between 80% and 95%. For laminations of 0.1 mm thickness, the stacking factor is around 89.6%, while for 0.2 mm thickness, the stacking factor is around 92.5%. For a lamination thickness of 0.5 mm, the stacking factor is around 95.8%. Thus, as the lamination thickness increases, the stacking factor increases [55]. 2.4 Performance Improvements Various methods are investigated to improve the performance of an SRM. These methods to enhance the performance of an SRM are ultimately divided into two feasible approaches: modifying the magnetic structure or implementing a sophisticated motor controller [1]. The motor controller can significantly affect efficiency. The scope of this study does not include the motor controller; however, because the motor controller can significantly affect efficiency, the effect of the motor controller was briefly shown in §5.3.3, p.117. For the performance improvements of an SRM, this section focused on the magnetic structure of an SRM. Loránd Szabó stated that electrical machines were pushed to their limits by a high market demand in the last decade. As a response to the demanding challenges and high market demands of electric motors, improvements were to made to the design and manufacturing of an electric motor [95]. One of the technology solutions introduced for the magnetic structure of an SRM was the modular structure. The modular structure allowed for fast and easy repairs. The principles of modular construction tend to increase efficiency. This is due to the reduction of magnetic flux paths which tend to minimise iron losses, as well as copper losses, because less magnetisation is needed to operate at certain output power [55]. The different modular constructions and other alternative methods to improve the performance of an SRM are discussed. 2.4.1 Modular construction The modular construction of an SRM is a method to reduce the flux path length. The concept of modular construction initially came as a response to increase the safety and reliability requirements of an electrical motor [64]. For an SRM, modular construction is an approach to increase performance and efficiency [57]. 36 A modular switched reluctance motor (MSRM) eliminates the long magnetic path in the back iron of the stator when a phase is excited. In addition, the modular construction eliminates magnetic flux reversal in the back iron. When flux reversal in the back iron is eliminated, the phase flux linkage is enhanced and the flux leakage is reduced, leading to a reduction of hysteresis losses [96]. When an MSRM is compared to a conventional SRM, performance advantages can be expected [97]. For comparison, a 16/18 four-phase MSRM is compared with a 16/18 four-phase SRM. The MSRM is designed for short flux paths to minimise iron losses without compromising high-power capability. Thus, by comparison, the following advantages are listed [98, 99].  The flux path is independent of the diameter of the rotor, providing the designer with the ability to increase the output torque by increasing the diameter of the rotor. An increase in the diameter of the rotor increases the output torque without increasing the flux paths between the stator and rotor.  The modular construction provides an independent magnetic circuit for each individual phase, unlike a conventional SRM. In a conventional SRM, one magnetic circuit is shared with other phases; and windings of two adjacent phases fitted together in one slot contribute to mutual coupling between phases. Since each phase of an MSRM is separated, the mutual coupling is almost entirely removed.  The flux direction in the back iron of the start and rotor core is always in the same direction. Thus, no flux reversal occurs in an MSRM compared to a conventional SRM. Having no flux reversal in the back iron reduces hysteresis losses as residual magnetism in the back iron is eliminated.  The modular construction allows for an enlarged winding slot space. A larger winding slot space allows for design flexibility in the winding turns, gauge, and coil type.  The modular construction of the rotor allows for lower rotor inertia that allows for high- speed operations. Also, the modular construction of either the stator or rotor provides the benefit of reduced weight and, therefore, costs are reduced as less magnetic material is used.  Greater heat dissipation in the motor structure can occur in a modular structure due to open winding structures compared to a conventional SRM where windings are packed together in slots.  A modular structure allows for easy replacement of an individual stator or rotor core when the core is damaged. The purpose of the comparison by Anas Labak et al. was mainly to provide a solution to improve the torque ripple of an SRM [98]. However, the modular construction approach was found to lead 37 not only to the improvement of torque ripple, but also to increased motor efficiency compared to the conventional SRM. Ultimately, various MSRM structures that consist of segmented stator cores, segmented rotor cores, or both offer a range of advantages when compared to a conventional SRM. Not only is the performance of the motor improved, but also costs are reduced as less magnetic material is used [100]. 2.4.1.1 Segmented stators The simplicity of an SRM allows for modular construction. A modular structure allows easy manufacturing methods [64]. However, the main challenge of a modular structure is to find an effective way to join the modules while maintaining the necessary robustness of the conventional SRM structure [64]. Modular switched reluctance motors of segmented stators usually employ a C-shaped or E- shaped stator segment called a stator core. Segmented stator cores are joined together by plastic fixtures or other non-magnetic permeability materials [101]. As in the case of a conventional SRM, the stator can be placed in the inner or outer region of the motor, as seen in Figure 2-12. However, these figures demonstrate segmented stator cores in a conventional structure. Figure 2-12a represents an E-core and Figure 2-12b represents a C-core MSRM where only the stator cores are segmented. (a) (b) Figure 2-12: Segmented stator MSRM of (a) Outer rotor of E-core stator segments; (b) Inner rotor of C-core segments [101] When comparing the E-core-shaped stator MSRM against a conventional MSRM, it is found that the E-core-shaped MSRM produces 20% higher torque. Furthermore, the same performance as the conventional SRM can be obtained using less iron and copper [102, 103]. The C-core shaped stator MSRM, shown in Figure 2-12b consists of 18 C-shaped stator cores. A coil is wound around 38 the yoke of two stator cores, and adjacent stator core modules are separated with a non-magnetic spacer. The non-magnetic spacer ensures adequate magnetic saturation between the flux paths of phases and stator cores [101]. An MSRM of segmented stator cores offers inexpensive and easy manufacturing methods, low iron losses, high efficiency, and fault-tolerant operation with the benefit of easy stator core replacement if a stator core is damaged [64]. 2.4.1.2 Segmented rotors The inspiration behind segmented rotor cores in an SRM was taken from the synchronous reluctance motor (SynRM) [95]. The development of a SynRM focuses on the magnetic circuit of the rotor. Identical axial laminations of different sized non-magnetic material sheets are interleaved between the core segments as an approach. This approach of a segmented rotor increased the torque output as the magnetic utilization of the magnetic flux carried in the magnetic circuit is enhanced [42]. An SRM with segmented stator cores is shown in Figure 2-13. The 12/8 three-phase SRM is a modified SRM, where the stator has excitation and auxiliary poles along the segmented rotor [104]. The auxiliary stator poles provide a flux return path; therefore, they are not wound. The approach to auxiliary poles in an SRM provides short magnetic paths for one excitation sequence, as two adjacent auxiliary poles form one magnetic circuit, as shown below. Figure 2-13: Magnetic flux path of phase A in a segmented rotor MSRM [104] An MSRM of segmented rotor cores offers increased torque performance compared to a conventional SRM. For the example shown in Figure 2-13, the magnetised stator poles are doubled. Thus, the torque output is increased as the attractive radial force on the rotor is dispersed among the poles. Given its circumferential flux direction, the electromagnetic forces are lower than those of a conventional SRM [105]. 39 2.4.1.3 Double segmentation As mentioned above, an MSRM can consist of segmented stator or rotor cores. However, an MSRM can also consist of a double segmented construction, meaning that the MSRM can consist of both a segmented stator and a segmented rotor. Anas Labak developed an axial flux MSRM consisting of double-segmented cores. The stator of the MSRM has 15 C-cores, each having a concentrated coil wound around its yoke. The rotor poles were embedded in non-magnetic material, as shown in Figure 2-14a [77]. Nikunj Ramanbhai Patel et al. developed a similar MSRM, where the motor was compared to a conventional SRM of the same dimensions. When the two motors were compared, it was evident that the C-core MSRM produced more torque than the conventional SRM for the same current. It was concluded that the MMF in the C-cores had increased, resulting in the reduction of coil length, increased torque, lower current use, and therefore lower copper losses that result in higher efficiency [74]. Additionally, the space available for a coil on the C-core allowed for thicker conductors to be used, which will reduce the copper losses even further as the winding resistance is reduced. Thus, an MSRM allows for a considerable amount of design flexibility [64, 95]. These modular stator and rotor segments allow for design alterations between a radial flux and an axial flux structure, as shown in Figure 2-14. As seen in Figure 2-14b, an MSRM allows a phase winding, depicted by green, yellow, and red coils, to be connected in series or parallel, depending on the performance requirements. With a segmented rotor and stator core, the magnetic characteristics of the entire motor can be generated by analysis of a single stator and rotor core. This analysis of its magnetic characteristics is due to the MSRM symmetry [75, 106]. (a) (b) Figure 2-14: Double-segmented MSRMs of C-core stators. (a) Axial flux motor; (b) Radial flux motor [77, 74] 40 Comparing the 12/16 radial flux MSRM, shown in Figure 2-14a with a conventional motor, the design structure was found to offer minimal axial length, short and independent magnetic flux paths, good heat dissipation and an increase in performance. The torque was increased by 12%, the efficiency by 5% and the magnetic material of the motor was decreased by 20% [74]. A C-core MSRM can easily be augmented by cascading several c-cores on each other for more power [99]. This variant was proposed by Wen Ding et al., consisting of E-cores as shown in Figure 2-15 [96, 97, 107, 108, 109, 110, 111]. Comparing the MSRM with a conventional SRM structure of the same pole configuration, diameter, and axial length, it was found that the MSRM produced higher torque and power. Furthermore, the MSRM had the lowest mass between the two motors, as a result of a segmented stator and rotor. Figure 2-15: Double-segmented MSRMs of E-core stators [96] Wen Ding et al. concluded that such an MSRM can be an outstanding competitor for traction motor applications. Consequently, an MSRM offers excellent performance suitable for in-wheel implementations of EVs [96]. 41 2.4.2 Multilayer construction The multilayer construction of an SRM is a method of reducing torque ripple. However, this approach uses segmented rotors and stators in the axial direction, as shown in Figure 2-16. The multiplayer SRM shown in Figure 2-16 consists of three independent rotor stacks, each identical to one another. However, each rotor stack is placed at a 15˚ mechanical shift to one another. Figure 2-16: Multilayer SRM with rotor stack rotation [112] The multilayer construction significantly reduces torque ripple, which was proven to have the same effect as a skewed rotor. For a multilayer SRM, each rotor pole arrives at the aligned position at different instances. Therefore, three control circuits are required to operate a motor stack. By analysis of the multilayer SRM, it was found that efficiency was improved by almost 10%. The efficiency improvement was due to the reduction of torque ripple and the reduction of eddy current losses [112]. 2.4.3 Hybrid construction The hybrid construction of an SRM aims to increase the power density. The approach to increase the power density is to add permanent magnets to the excitation poles. The simplest way to introduce permanent magnets to the motor structure is to replace the non-magnetic spacers in stator-segmented MSRMs. Adding a permanent magnet to the excitation pole increases MFF. As a result of higher MMF, higher power than a conventional SRM is achieved as the magnetic flux is improved in the motor [113]. Figure 2-17 shows a conventional SRM structure modified as a hybrid construction. Figure 2-17a represents a pole-assisted SRM where the permanent magnet is placed in the excitation pole. Figure 2-17b represents the yoke-assisted SRM where the permanent magnet is placed in the back iron of the SRM [113]. Placing the permanent magnets inside the back iron of the motor provides the benefit of longer, larger, and less thick permanent magnets to be used. Therefore, permanent magnets larger than the pole-assisted SRM can be used. 42 (a) (b) Figure 2-17: Conventional SRM with (a) Pole permanent magnets; (b) Yoke permanent magnets [113] Wen Ding et al. designed and analysed a 12/10 hybrid SRM. The SRM consisted of a segmented stator that contained six C-cores [108]. Each C-core was wound with concentrated coils and a permanent magnet placed between the poles, as shown in Figure 2-18. The permanent magnet enclosed the flux path within the core when the coil was not excited, as shown in Figure 2-18a. When the coil was excited, the flux generated by the permanent magnet added to the flux of the coil. Thus, two flux paths occurred during excitation, as shown in Figure 2-18b. (a) (b) Figure 2-18: C-core MSRM with permanent magnet-assisted poled in the aligned position under; (a) No excitation current; (b) Excitation current [108] Comparing the hybrid C-core SRM with a conventional SRM of the same dimensions, it was concluded that the hybrid SRM were less likely to saturate under the same excitation currents. Therefore, the hybrid SRM achieved higher torque production [108]. 43 2.4.4 Transverse construction The transverse construction of an SRM has one toroidal coil for a single phase, as shown in Figure 2-19. The MM generated by the toroidal coil is homopolar, and the flux path is in a transverse direction. This provides the transverse SRM with high torque density, high efficiency, and low copper losses as end-turn effects are fully eliminated. Figure 2-19: Single stack of a transverse SRM [114] From fundamentals, a transverse construction requires a modular approach due to its complex flux paths. The flux path occurs in a 3D domain, similar to the double-segmented construction shown in Figure 2-14. Unlike the double segmented SRM, the transverse SRM offers an increase in the stator and rotor segments without reducing the MMF [114]. However, considering a three- phase transverse SRM, the motor would consist of three stacks, as shown in Figure 2-16 joined together. Thus, the axial length of the motor would be three times that of a stack, almost similar to multilayer SRMs. 2.5 Summary of the literature From the literature, the overview of an SRM was discussed. This overview included the basic mathematical model and operating principles of an SRM. The operating principles of an SRM clarified how toque was produced from the electromagnetic energy conversion process. Thereafter, the torque-speed characteristics of an SRM were discussed, accompanied by two control strategies used to obtain the constant torque, constant power and falling power torque- speed characteristics. Various SRM designs that could possibly be used to evaluate an SRM for solar vehicle application was reviewed. The SRM designs does not produce the same amount of performance characteristics as the Mitsuba M2096-DII, currently used in the solar vehicle of the NWU. Not enough information was provided to replicate the design successfully. Therefore, an un-optimised 44 XDM of an SRM was designed to justify the development and use of an SRM for solar vehicle application. To design an XDM, the design considerations of an SRM was reviewed. From the design considerations it was found that an SRM of an outer rotor radial flux structure is an appealing choice for in-wheel traction motor applications. Many considerations could be made for the amount of phases in the motor, but increasing the amount of phases increases the overall costs. A three-phase motor is preferred over a motor with more phases. The pole configuration of an SRM can have an effect on the operational and performance characteristics of an SRM, along with the pole arc angles. Once the pole configuration was chosen, a feasibility triangle could be used to evaluate the acceptable pole arc angles adhering to self-starting, high output torque and low torque ripple requirements. High power and torque density and low loss standard grade (EN 10106) magnetic material are usually used in traction motors which are stacked together. The typical stacking factor can range between 80% to 95% depending on the lamination thickness. After the review of the design considerations, the design review was broadened by a review of geometrical variations of an SRM to improve the performance characteristics. These design variations include modular, multilayer, hybrid and transverse constructions. The modular construction offered the best performance improvements without extending the axial length of the motor or adding permanent magnets, which adds thermal limitations to the operating capability. Thus, the literature review provided a broad overview of an SRM, such that an un-optimised XDM of an SRM could be designed for evaluation purposes. Using the design considerations, aspects for the XDM of an SRM could be proposed. 2.6 The proposed switched reluctance motor To evaluate an SRM as a traction motor for solar vehicle application, a suitable SRM should be selected. In this case, as discussed in §2.2, p.25, an SRM should be designed for the required specifications. An MSRM was proposed as the selected XDM. An MSRM was selected to eliminate long flux paths and flux reversal to reduce losses and increase motor efficiency. It was proposed to use a 12/16 pole configuration, similar to the design of Nikunj Ramanbhai Patel et al. [74]. However, an outer rotor motor was proposed for use as a direct drive motor. A segmented E-core stator was selected instead of a C-core. Xinglong Li and Ernest Mendrela found that an E-core in a transverse linear SRM has a higher force-to-mass ratio than a C-core [115]. Winding turns, pole area, and air gap are kept constant in the study. Applying the principle 45 of a linear motor around an axis, a rotary motor was formed. Thus, the torque-to-mass ratio of an E-core MSRM was expected to be higher than that of a C-core MSRM. As stated by Shang-Hsun Mao and Mi-Ching Tsai, C-cores can be mounted on top of each other to increase their power [99]. However, the axial length, winding turns, and input power increases. Considering that short flux paths, as in an MSRM, have high losses, an additional research question was formed. The research question of the flux paths is whether a C-core with a winding is less efficient than an E-core with the same axial length and winding turns. However, the winding constitutes two coils, and the sum of the coil turns is the winding turns. The axial length and winding change are shown in Figure 2-20, where a C-core is changed to an E-core and the E-core to a four-pole stator core (IIII-core). 𝐶𝐻 is the coil height and 𝑃𝐻 the pole height, which is used to demonstrate the geometric effect when more poles are added to a core while keeping the axial length and winding turns constant. Note that the sum of the pole heights and coil height remains the same no matter the number of poles. This research question is not within the scope of the study. However, the effect of pole changes on the core was analysed in §5.2.1.1, p.97 to gain an understanding of whether more poles on a core may lead to a more efficient motor. A future study is recommended to gain a comprehensive understanding of this research question. Figure 2-20: Flux paths of a C-core, E-core, and IIII-core A selection of magnetic material will be limited to lamination thickness of around 0.5 mm, to steel losses and maximising the stacking factor, as a stacking factor of 95.8% was expected for material of a 0.5 mm lamination thickness. 46 When considering the proposed MSRM, an efficiency map was essential to evaluate the proposed motor. An expected efficiency map of an SRM is shown in Figure 2-21. Figure 2-21a shows an efficiency map of an inner rotor double U-core SRM, provided by ePower Motors [116], and Figure 2-21b shows an efficiency map of a three-phase inner rotor 6/4 SRM designed to propel a scooter. Efficiency values are indicated by the legends, which range from a dark blue indicating 75% and 0% efficiency to a yellow and dark red indicating 100% efficiency. (a) (b) Figure 2-21: Efficiency map of an SRM [116, 117] It is unknown whether a similar efficiency map can be expected for the proposed MSRM. Similarity of the efficiency maps is unknown due to the lack of literature providing no efficiency map of an MSRM. An efficiency map of a conventional SRM was rarely obtained, and if an efficiency map was obtained, very little information about the SRM was provided. Therefore, a comparative analysis between the efficiency map of a conventional SRM and an MSRM is proposed as a future study. However, the construction of the proposed MSRM efficiency map will provide some indication of the similarity between the efficiency maps. Furthermore, the verification and validation of the efficiency map are proposed by manufacturing a prototype of the proposed MSRM. To conclude, a 12/16 E-core MSRM was proposed as an un-optimised XDM, which is used to justify future development and utilisation for solar vehicle application. The proposed XDM was designed according to the specified power characteristics and design constraints, listed in Table 5-2, p.95 and Table 5-1, p.90. 47 CHAPTER 3 ELECTROMAGNETIC MODELLING The electromagnetic modelling method is reviewed in this chapter. This chapter focused on the FEA method used to design or analyse an electrical motor. Finite element analysis is a popular solution for electromagnetic modelling. An overview of the simulation software used in this study, Ansys® Maxwell, is presented in this chapter. Ansys® Maxwell is an industry standard electromagnetic modelling software utilised by most designers to analyse an electrical motor, as seen throughout the literature review on the design articles and journals. There is various other simulation software, but in this study, the software is limited to Ansys® Maxwell, as the NWU has license access. 3.1 Electrical machine analysis An electrical machine's design and step-by-step optimisation is often a trial-and-error process. The design and construction of the electrical machine require expensive prototypes to be manufactured. Having to build an iteration of prototypes is time-consuming and expensive, such that numerical methods are suggested to replace the iterative design stage. The same numerical analysis procedure can be used to analyse an electrical machine [118]. Numerical methods became necessary in many electromagnetic applications where the electrical machine operates in the saturated region. The most popular method to solve an electromagnetic problem is the use of FEA [119]. This chapter focuses on the FEA approach in Ansys® Maxwell. Compared to numerical methods, the analytical methods can significantly reduce computational complexity without solving high-dimensional matrixes such as FEA. The magnetic equivalent circuit (MEC) method is popular for electromagnetic analysis. However, the task to solve the MEC is to find as many assumptions, simplifications, and empirical factors as possible, which cannot always be satisfied [118]. The background and solving principle of an MEC are described in [29]. In PMSMs, the permeability of a permanent magnet is close to the permeability of air, allowing the assumption of linear material characteristics. The SRM have non-linear characteristics, and the assumption does not hold when analysing an SRM. Additionally, the flux topology of the SRM changes with the rotor angle. Thus, the MEC structure of an SRM is empirical, and different assumptions on the magnetic flux path, especially the areas and lengths of fringing/ leakage reluctance in the air region that are non-linear, have to be made for the different rotor positions. The assumptions should be based on previous experiences with FEA results, which confine the accuracy and generality applied to the analysis of SRMS with arbitrary geometries. The accuracy of an analytical approach decreases when the machine operates in the saturated region, and 48 even if the MEC considers magnetic saturation using an iterative approach, the solution is not as generic as a numerical solution. Therefore, this study uses a numerical approach of FEA to analyse an SRM. An extended review of analytical methods is not discussed further in the study. 3.1.1 Modelling methods Electromagnetic modelling is the process of modelling the interaction of electromagnetic fields between a physical object and the surrounding environment (e.g. air, vacuum). The process typically involves software to compute the solutions of Maxwell’s equations. The computational numerical technique can overcome the inability to derive closed-form solutions when an analytical method is not solvable. This makes electromagnetic modelling a critical "tool" in the design and analysis procedure of an electrical machine. Any electromagnetic problem can be described using integral and/ or partial differential equations derived from Maxwell’s equations (§3.2.1). Typical problems involve either time-stepping through the equations over the domain of each instant, a matrix inversion when modelled by FEA, or matrix products when using the transfer matrix method, calculating integrals using the method of moments; or using the fast Fourier transform method. The most commonly used numerical methods are shown in Table 3-1 and discussed below: Table 3-1: Numerical methods used to solve electromagnetic problems Time-Domain Frequency-Domain Partial differential Finite-Difference Time- Finite Element Analysis equation formulation Domain (FD-TD) (FEA) Integral formulation Marching-On-in-Time (MOT) Method of Moments (MoM) The different numerical methods used by the simulation software to solve electromagnetic problems are not discussed in detail in this study. More information on the numerical methods can be found in [120, 121, 122]. In this study, FEA is used to analyse an SRM. 3.1.2 Simulation software With the application of highly efficient numerical algorithms running on high-performance computers, it is possible to rapidly design and analyse an electrical machine. At the same time, these numerical algorithms enable the development of ever more complex machine designs. The advanced software offered today can effectively analyse and characterise electrical machines. The software makes solving an electrical machine by its respective equations no longer a challenging, time-consuming process. Quite a number of commercially available simulation 49 software is available for electromagnetic modelling. A non-exhaustive list with relevant web links of the most popular software used to analyse electrical machines is listed below:  Ansys® Maxwell [123];  Altair Flux [124];  Simcenter Magnet [125];  JMag [126];  COMSOL Multiphysics [127];  FEMM [128];  Elmer FEM [129]; The software license, required to use the electromagnetic simulation software are very expensive. Thus, not just any simulation software is readily available for use in this study. As the NWU has license access for students to use Ansys® Maxwell, this study is limited to Ansys® Maxwell. Therefore, Ansys® Maxwell is used to analyse the magnetic characteristics of an SRM in this study. Ansys® Maxwell is compared to Cedrat in [130]. Cedrat was an electromagnetic simulation software acquired by Altair in 2016. The comparison between the simulation software concluded that Maxwell is a convenient choice for young engineers using FEA software for the first time, while Cedrat is more suited for those who desire a more realistic solution. However, the multidisciplinary simulation environment offered by Ansys®, i.e., coupling Ansys® Maxwell to Ansys® Fluent or Ansys® Mechanical, makes it the best solution for professional engineers wanting to analyse the mechanical, structural, and thermal characteristics of an electrical machine whilst the electromagnetic interaction of the machine occurs. 3.2 Finite element analysis The finite element analysis comprises of two fields, namely mathematics and engineering. The first record of differential equations in a surface with a minimum area confined by a closed curve in space was in Schellenbach's study, 1851. In 1943, Courant developed the FEA to what it is known today. In the 1950s, engineers in the aeronautical field made progress in their designs and structural analysis using FEA. During this time, the key contributors to the analysis method were Ton Turner, John Argyris, and Ray Clough with Ray Clough coining the term "finite element" in 1960. Since then, the analysis method spread to all engineering fields [131]. The FEA provides mesh elements to cover the entire solution domain, making the solution process adaptable to any complex or irregular machine geometry. The FEA provides an accurate magnetic field distribution solution with inhomogeneous properties, i.e., the laminated cores with non-linear permeability. Regardless of the adaptations of the model, the solution process remains 50 the same. Additionally, FEA provides an iterative approach to the solution, and using computational resources provides a faster solution time than an analytical approach [132]. Maxwell's equations define the solution of the electromagnetic field. 3.2.1 Maxwell’s equations The study of electromagnetic field phenomena has been developed since the 19th century. Formulations were proposed by scientists like Gauss, Ampère, Faraday, and Lenz, but only completed in 1862 when James Clerk Maxwell added an extra term to Ampere's law. The added addition to the equation allowed for a complete description of electromagnetic field phenomena [131, 133, 134]. The four fundamental equations that define the electromagnetic fields are as follows: 𝜕𝐷 Ampère’s circuital law ∇ × 𝐻 = 𝐽 + (27) 𝜕𝑡 𝜕𝐵 Faraday's law of induction ∇ × 𝐸𝑓 = − (28) 𝜕𝑡 Gauss's law ∇ ∙ 𝐷 = 0 (29) Gauss's law for magnetism: ∇ ∙ 𝐵 = 0 (30) In these equations, J represents the current density, 𝐻 the magnetic field strength, 𝐸𝑓 the electric field density, 𝐵 the magnetic flux density, 𝐷 the electric flux density, and ∇ × and ∇ ∙ the curl and divergence operators. Equation (27) describes Ampère's circuital law in differential form and can also be represented by the integral form, shown in equation (31). The equation states that the line integral of the magnetic field, 𝐻, in a closed path, dl, is equal to the current enclosed in that path. ∮ H ∙ dl = I (31) The time variation section of Ampère's circuital law represents the displacement current effect. The current effect produces a time-varying, non-steady magnetic field as an adequate flow of electrical charges, as proposed by the equation of electrical continuity [133]. ∂𝜌𝑐 ∇ ∙ J = − (32) ∂t 51 Where 𝜌𝑐 is the charge density. The four fundamental equations are linear and may appear relatively easy to solve analytically. However, complex geometries and boundary conditions of an electromagnetic problem make these equations difficult to solve. Therefore, numerical analysis software is used to solve such machines, i.e., an electrical machine. 3.2.2 Ansys® Maxwell Ansys® Maxwell is a low-frequency electromagnetic field simulation solution that uses finite element analysis to solve static, frequency domain, and time-varying electromagnetic and electric fields. When solving an electromagnetic model, the procedure, adapted from the documentation provided by Ansys® in [133], shown in Figure 3-1, is followed. Figure 3-1: Analysis Procedure in Ansys® Maxwell The process of formulating and solving an electromagnetic solution is used in chapter 4 to validate the electromagnetic modelling method of an MSRM. The necessary information about some of the processes is discussed in this section. 52 3.2.3 Geometry Ansys® Maxwell offers 2D and 3D model analysis. A 3D model analysis holds an advantage when exploring the electromagnetic field distribution around a complex domain. When analysing an electric motor, the magnetisation direction of the magnetic field is in the same plane as conventional motor topologies. When ignoring end winding effects, often the case for well established, conventional radial flux motors, Maxwell 2D can obtain an accurate solution. The advantage of a 2D approach is a decrease in mesh elements, allowing for faster simulations [131, 133]. However, the end winding effect considerably influences solution accuracy when modelling electric motors of complex winding distributions, such as an axial flux motor, transverse flux motor, or an MSRM [135]. In the case of an MSRM, the end winding has a winding ratio of roughly 1:1, while the end winding of a conventional SRM is usually around a ratio of 1:8. Thus, the end winding of a conventional SRM constitutes only a tiny fraction of the whole winding when simulated in a 2D domain [52]. A 2D and 3D simulation comparison of an MSRM is shown in Appendix B, p171. Thus, analysing an MSRM (chapter 4 and chapter 5) that utilises a unique magnetic path, field distribution, and magnetic field effects requires Ansys® Maxwell 3D. The consequence of using a 3D solving domain is that a larger number of mesh elements need to be solved. A larger number of mesh elements results in slower simulations [136, 137]. When using a 3D solving domain and restricted by a time constraint, the user is limited to the number of simulations in the study if an accurate motor solution is to be obtained. Therefore, if limited time is available, the user will either use all of the available time for a single simulation, should only a single point of operation be analysed, or the user will split the time for various simulations setups, should different operation points be analysed. 3.2.4 Domain partitions The discretisation of the domain is the stage in which a great number of tetrahedra elements define the model. The assembly of all tetrahedra is referred to as the finite element mesh of the model or simply the mesh. The mesh setup defines the accuracy of the solution by providing a better simulation resolution of the field distributions. Therefore, there is a trade-off between the size of the mesh, the desired level of accuracy, and the number of available computing resources [131]. The precision of the solution depends on the size of each tetrahedron, shown in Figure 3-2. To generate a precise description of the magnetic field quantity, each tetrahedron should occupy a sufficiently small region. A sufficiently small region for the magnetic fields is necessary to adequately interpolate from the nodal values [133]. For the tetrahedron: 53  The magnetic field component, tangential to the element's edges, is explicitly stored at the vertices.  The magnetic field components that are tangential to the face of an element and normal to an edge are explicitly stored at the midpoint of the selected edges.  The value of a vector field at the interior point is interpolated from the nodal values. Figure 3-2: The tetrahedron as a finite element Definition 7 (Tetrahedron): A tetrahedron (plural: tetrahedra or tetrahedrons) is a polyhedron with four faces, six edges, and four vertices, in which all faces are triangles. A regular tetrahedron has equilateral triangles. Therefore, all its interior angles measure 60˚ [138]. The desired field in each element is approximated by the second order quadratic polynomial, shown in equation (33). H𝑋(𝑥, 𝑦, 𝑧) = 𝑎0 + 𝑎1𝑥 + 𝑎2𝑦 + 𝑎3𝑧 + 𝑎4𝑥𝑦 + 𝑎5𝑦𝑧 + 𝑎6𝑥𝑧 + 𝑎7𝑥 2 + 𝑎 𝑦28 + 𝑎9𝑧 2 (33) Solving a magnetic field solution involves the inverting of a matrix with approximately the number of elements of the tetrahedra nodes. For a mesh setup of many tetrahedra elements, inversion of the matrix requires a significant amount of computing resources. Therefore, it is desirable to use a mesh setup that is refined enough to obtain an accurate solution but coarse enough not to overwhelm the available computing resources [133]. The mesh setup used to analyse an MSRM is explained in §4.3.1.3 and §4.4.1.3, using the magnetostatic solver and the transient solver. 54 3.2.5 Magnetic solvers Ansys® Maxwell offers three independent solving approaches to analyse electrical machines related to magnetic magnitudes. The three magnetic solvers include the magnetostatic, eddy- current, and transient solvers. The two solver approaches chosen to validate the model of an electric motor are the magnetostatic solver and the transient solver. The three solvers in a 3D domain are presented in this section. From the documentation of Ansys ® Maxwell, it is clear that the eddy current solver is also a static solver, but is primarily used when analysing electrical transformers [133]. 3.2.5.1 Magnetostatic The magnetostatic solver computes static magnetic field simulations where the source of the static magnetic field is one or more of the following:  DC currents in conductors  Permanent magnets  Static external magnetic fields represented by the boundary conditions The quantities which the magnetostatic solver solves are the magnetic field, 𝐻, the current density distribution, 𝐽, and the magnetic flux density, 𝐵. These fundamental field quantities are used to calculate the force, torque, energy, and inductance. Note that no time variation effects are included in magnetostatic solutions, as the objects are considered stationary. Therefore, the transformation of energy in a magnetostatic solution is only due to ohmic losses associated with currents flowing in real (non-ideal) conductors [133]. Thus, the heating effect is acknowledged in the solver, though the effect of heating has no influence on the simulated. To simulate the effect of heating, the simulation has to be coupled with a temperature simulation. The solution process of the magnetostatic solver is very automated. Once the problem is fully defined, Maxwell automatically runs through several stages of the solution process, as shown in Figure 3-3. When performing domain discretisation, the solver follows an iterative process that involves adaptive mesh refinement (§4.3.1.3, Figure 4-3, p.68 ) until the maximum number of mesh refinement passes is reached or the solution has converged [133, 139]. 55 Figure 3-3: Magnetostatic solver diagram During the solution process, the magnetostatic solver solves the following two Maxwell equations [63]: ∇ × 𝐻 = 𝐽 (34) ∇ ∙ 𝐵 = 0 (35) The following constitutive (material) relationship is also applicable: 𝐵 = 𝜇0(𝐻 + 𝑀) = 𝜇0 ∙ 𝜇𝑟 ∙ 𝐽 + 𝜇0 ∙ 𝑀𝑝 (36) 56 Where 𝐻 is the magnetic field strength, 𝐵 is the magnetic flux density, 𝐽 is the conduction current density, 𝑀𝑝 is the permanent magnetisation, 𝜇0 is the permeability of a vacuum, and 𝜇𝑟 is the relative permeability. 3.2.5.2 Eddy current (static) The eddy-current solver computes electromagnetic field simulations in the frequency domain where the source of the electromagnetic field is one or more of the following:  AC currents in conductors  Time-harmonic external magnetic fields represented by boundary conditions The quantities which the eddy current solver solves are the magnetic field, and the magnetic flux density, 𝐵. Force, torque, energy, and inductance are calculated at the solution frequencies from these fundamental field quantities. The solver assumes that all electromagnetic fields pulse at the same frequency. Note that the eddy-current solver does not allow moving objects or permanent magnets, and that magnetic materials are assumed to be linear. Solutions of non-linear material are based on the fundamental components of B and H at the specified frequency as an approximation [133]. Like the magnetostatic solver, the solution process of the eddy current solver is automated. Once the problem is fully defined, Maxwell automatically runs through several stages of the solution process, as shown in Figure 3-4. When performing the domain discretisation, the solver follows an iterative process involving adaptive mesh refinement, similar to the magnetostatic solver. 57 Figure 3-4: Eddy-current solver diagram During the solution process, the eddy current solver solves the magnetic field equation [63]: 1 ∇ × ( ∇ × 𝐻) = −𝑗 ∙ 𝜔 ∙ 𝜇 ∙ 𝐻 (37) 𝜎 + 𝑗 ∙ 𝜔𝑓 ∙ 𝜖 Where 𝜖 is the absolute permittivity, 𝜔𝑓 the angular frequency at which all quantities oscillate, 𝜎 the conductivity, and 𝜇 the absolute magnetic permeability. 𝑗 indicates an imaginary part of the complex number. 3.2.5.3 Transient The transient solver computes the time-domain magnetic field where the source of the magnetic fields is one or more of the following:  Moving or non-moving time-varying currents and voltages  Moving or non-moving coils and/ or permanent magnets  Moving or non-moving external circuit coupling 58 The quantities which the transient solver solves are the magnetic field, 𝐻, the current distribution, 𝐽, and the magnetic flux density, 𝐵. The quantities of force, torque, energy, speed, position, winding flux linkage, and winding induced voltage are calculated from these fundamental field quantities [133]. In the 3D transient solver, the solver uses the 𝑇 − Ω formulation. The formulation 𝑇 − Ω is said to be a powerful method to solve low frequency electromagnetic problems [133]. This is the only formulation used in Ansys® Maxwell. The solution process is shown in Figure 3-5. For simulations involving rotational motion, i.e., the rotor of a motor, a "sliding band" approach is followed, and thus no re-meshing is done during the simulation. Note that the transient solver does not use adaptive refinement like the above mentioned solvers, and therefore a mesh needs to be defined by the user [133]. Figure 3-5: Transient solver diagram During the solution process, the transient solver solves the following Maxwell equations: 1 𝜕𝐵 ∇ × ∇ × 𝐻 + = 0 (38) 𝜎 𝜕𝑡 59 ∇ ∙ B = 0 (39) Note that, even though the transient solver is used in Ansys® Maxwell, the motion setup offers either a transient or a steady-state solution. When a transient simulation is set up, the solution is automatically set to a steady-state solution. However, if a transient response simulation is required, the mechanical transient selection should be selected in the motion setup before starting the simulation [133]. Thus, for the remainder of this study, when referring to transient simulations, the simulations will provide steady-state solutions. This imply that motor start-up shall not be observed in the simulations. Only steady-state simulations are required to construct an efficiency map, needed to evaluate an SRM through the drive cycle, provided in chapter 6. 3.2.6 Post-processing Post-processing is the last step of the solution. At this step, it is possible to analyse the solution based on the solution data, convergence, mesh statistics, and plot reports of a parameter [133]. The output parameters used to evaluate the results during simulations are summarised as follows:  Solution data: The solution data provide information about the solution process, containing info about the software performance, simulation time, and the computational memory utilised during the simulation. The data can be checked during the simulation process.  Field Overlays: The field overlay is one of the main demonstrative tools to represent the model graphically. The field plot contour or vector plot is used to show the magnetic flux density, magnetic field, current density, and electric field.  Plot reports: The report plotting tool is helpful when analysing graphs of time-varying parameters, such as the current and torque of a transient solution. 3.3 Summary of electromagnetic modelling In many instances, studying a real system can be too complex, expensive, or even dangerous if exposed to electrical hazardous conditions. For this reason, simulation software using FEA (Ansys® Maxwell) is an appropriate solution that can be conducted within cost constraints and without injury. An electromagnetic simulation can be helpful when the machine does not yet exist or is not fully understood. However, a good simulation can ultimately yield wrong solutions, especially when the simulation or simulation method is difficult to understand and implement. This chapter provided a basic understanding of the numerical methods, mainly FEA, used to analyse an electrical machine. The FEA method of Ansys® Maxwell was reviewed to understand the solution process of the software. 60 For this study, in conjunction with the manufacturing & financial constraints (§1.5.3, p.10), validation of the simulation method was finalised before the proposed MSRM was designed. Thus, both the validation of an MSRM and the design of the proposed MSRM form part of the electromagnetic analysis discussed in this chapter. 61 CHAPTER 4 ELECTROMAGNETIC SIMULATION VALIDATION AND VERIFICATION The validation and verification (V&V) of an MSRM in this chapter is based on an E-core MSRM designed by Wen Ding et al. [96, 110, 109, 97, 107, 111]. The simulation and experimental results were compared to the modelled MSRM, using numerical simulation software. The numerical simulation software used to set up and model the MSRM was Ansys® Maxwell. Usually, validation is completed after the prototype is built. In this study, due to limitations (§1.5.3, p.10), no prototype could be manufactured. The design of the E-core MSRM was to be validated following the same procedures as provided in the articles. Following the same procedures, the magnetostatic and transient solution data were used to validate the setup and modelling method of an MSRM. These publications were chosen for validation purposes, not only because an MSRM is analysed, but because the publications offer experimental data. Experimental data for MSRMs, throughout the literature review, were rarely found, and if found the motor analysed constitutes an axial flux SRM. In these publications, it is noted that the E-core MSRM designed by Wen Ding et al. differ in terms of the structure (inner vs outer rotor) and flux path (different rotor segmentation) when compared to the proposed MSRM (§2.6, p.45). In [97], Wen Ding et al. compared the segmented rotor to a conventional rotor. The conventional rotor had four short flux paths, similar to the proposed MSRM, but due to the inner rotor topology, still a yoke on the rotor, that is removed when compared to the I shaped rotor segments of the proposed MSRM. Wen Ding et al. found that the two rotor structures had similar winding flux linkage and electromagnetic torque characteristics. It was also found that the segmented rotor had higher torque density power density and accelerated faster at start-up. Though this was due to the conventional rotor structure having more magnetic material and therefore weighing more. Thus, the flux paths of the E-core MSRM designed by Wen Ding et al. will have no significant influence on operations compared to the flux path of the proposed MSRM. Also, the difference between inner and outer rotor structures will only have an effect on the overall size of the motor and output torque if the air gap diameter differs. When using a double segmented MSRM, flux path is independent of the diameter of the rotor and the structure, i.e., inner or outer rotor. As some difference might have an effect between the two motors, it is proposed as a future study to validate the proposed MSRM against experimental data once a prototype is manufactured. 62 4.1 Validation and verification Many interpretations exist for the meaning of V&V. Some of the interpretations include the IEEE Std 1012, 1998 AIAA, and the ISO/IEC 17027:2019 [140, 141, 142]. The V&V definitions used in this study are adapted from [143]. Definition 8 (Validation): Validation is the process of ensuring that a model, when integrated together with other models, gives the expected behaviour for the application environment it is used in. If the validation process has been finished for a model with no anomalies, then the model has a validated status. Definition 9 (Verification): Verification is the process of making sure that a model has been implemented correctly. If the verification process has been finished for a model with no anomalies, then the model has a verified status. There are many ways of performing V&V, as described in [140]. In this study, the following methods for V&V are applied:  Hand-checking that the calculations used for the drive cycle implementation was correct, i.e. the excel spreadsheet used to calculate the power use at each time iteration.  Analysing an alternative approach to arrive at the expected results of the models and integrated models, i.e. using other simulation software like the 2D simulation model provided in Appendix B, §B.1, p.171  Comparisons to literature, i.e., comparing the model results to published results.  Comparisons with well-defined criteria, i.e., experimental data or other simulation models that have been validated. Ansys® Maxwell provide quality assurance by V&V both existing and new program functions. Both internal and external quality audits were conducted to ensure the software fulfils the requirements of the ISO 9001:2015 standard [144]. Normally, the validation of an electrical motor is performed after the design is finalised. However, due to manufacturing & financial constraints (§1.5.3, p.10), a prototype cannot be built to validate the design. Therefore, the numerical modelling method of an MSRM was validated and verified to ensure that the correct procedures are followed when evaluating the design options and criteria of an MSRM. §4.2 to §4.4 contains the setup of the E-core MSRM described by Wen Ding et al. in [96, 110, 109, 97, 107, 111]. This SRM was simulated using the magnetisation and transient solvers in Ansys® Maxwell to V&V the simulation model setup, simulation methods and simulation post- processed results 63 4.2 Geometry of the validation model The MSRM designed by Wen Ding et al. consists of six independent modular E-shaped stator cores and a segmented rotor, shown in Figure 4-1. The rotor consists of three rotor cores as shown in Figure 4-1a, thus called a segmented rotor. Figure 4-1a and Figure 4-1b shows the magnetic paths of the MSRM when one phase is excited. It is observed that there are two magnetic paths in this MSRM, and the two paths are in the same direction in the middle pole. Unlike a conventional SRM, each phase has independent magnetic paths. Thus, there is no mutual coupling between phases through cross-slot leakage flux [110]. (a) (b) Figure 4-1: Basic structure of the MSRM. (a) Cut front view of one-phase and (b) Top view of the three-phase MSRM The physical parameters and characteristics of the stator and rotor are defined in Figure 4-2a and Figure 4-2b. The geometric parameters are summarised in Table 4-1. Two coils are wound around each stator core and connected to the diametrically opposite stator coils in a series-parallel combination, shown in Figure 4-2c. The four connected coils form one phase winding. 64 𝜏 𝑦𝑠 𝑠 𝑑𝑠 𝛽𝑟 𝑟𝑟𝑜 𝑦𝑟 𝐿𝑠1 𝑟𝑠ℎ 𝛽𝑠 𝑑 𝜏 𝑟 𝐿 𝑟𝑠 (b) 𝐿𝑠2 Winding A1 1 2 𝐿𝑠3 3 4 (a) Winding A2 (c) Figure 4-2: Geometry parameters of the MSRM: (a) One stator core; (b) The rotor core (top view); (c) The winding connection of one phase. The magnetic material, specified by Wen Ding et al. for the stator and rotor was the non-oriented silicon steel DW540-50. All material characteristics were used as provided from the material database of Ansys®. This material database is maintained by Ansys® Granta, providing a broad coverage of material types and key property data for analysis. At the time of publishing articles [109, 110, 111] in 2014, Ansys® Maxwell 2013 was the latest version available. Ansys® Maxwell 2013 required manual allocation of the magnetic material DW540-50. The magnetic material properties and characteristics could differ from the material database of Ansys®. Thus, the simulation results of the motor model might differ from the published results. It was assumed that the magnetic material characteristics provided by Ansys® was correct, thus no difference between the simulated results and experimental data were expected. 65 Table 4-1: Geometry parameters of the MSRM. Geometry Parameters of the SRM (unit: mm) Stator outer radius, 𝑟𝑠𝑜 45 Shaft outer radius, 𝑟𝑠ℎ 6 Rotor outer radius, 𝑟𝑟𝑜 20 Stator total length, 𝐿𝑠 80 Stator yoke width, 𝑦𝑠 9 Upper stator pole length, 𝐿𝑠1 12 Rotor yoke width, 𝑦𝑟 9 Middle stator pole length, 𝐿𝑠2 24 Stator pole arc, 𝛽𝑠 32˚ Lower stator pole length, 𝐿𝑠3 12 Rotor pole arc, 𝛽𝑟 32˚ Stator pole width, 𝜏𝑠 10.73 Air gap length, 𝑔 0.25 Rotor pole width, 𝜏𝑟 10.60 4.3 Magnetostatic validation The magnetostatic solver of Ansys® Maxwell was used to obtain the magnetostatic characteristics of the E-core MSRM, described in §4.2. The magnetostatic characteristics of the MSRM involves the flux linkage, static torque, and winding inductance. The magnetostatic characteristics were obtained over half an electrical period when the rotor moves from the unaligned position to the aligned position, similar to results provided by Wen Ding et al. Refer to Figure 2-3, p.17 for the unaligned and aligned positions of an SRM. Owing to the independent magnetic structure of each motor phase, the magnetostatic structure of one phase was selected as the solving domain. Only two E-shaped stators and the segmented rotor were modelled, as shown in Figure 4-1a. 4.3.1 Magnetostatic simulation setup The model setup should be finalised for the numerical simulation to be solved. The magnetostatic setup involves the excitation, boundary conditions, mesh and the magnetostatic solution and analysis setup, in that particular order. 4.3.1.1 Excitation setup Excitation of the phase winding is done in the following process. Each coil is assigned a current excitation that sets the conduction path. The stranded type wire is selected in the current excitation settings, and the coil number is set to 300 turns. The direction of the current flow is changed to indicate the winding direction of the coil, such that the flux path, shown in Figure 4-1a and Figure 4-7, is achieved. The flux path in the stator is easily known by using Fleming's right- hand rule. Note that in the magnetostatic solver, the MMF is used as the value of current excitation. 66 4.3.1.2 Boundary setup Before a boundary condition is assigned, a solving domain is created. The solving domain involves the construction of a volumetric region around the motor model. The magnetostatic solver automatically assigns two boundary conditions. The boundary conditions are the Neumann and the natural boundary conditions. Neumann boundaries are assigned to the outside surfaces of the solving domain. Natural boundaries are assigned to surfaces between objects, i.e., between the stator and the coils. Additionally, verification of the conduction paths between the coils and the stator cores is applicable. Otherwise, an insulating boundary must be assigned to the coil to exclude excitation interference between the coil and the stator. 4.3.1.3 Mesh configuration An explicit mesh configuration is not applied to the magnetostatic model, but rather an adaptive mesh refinement. The magnetostatic solver customarily uses the adaptive mesh refinement described by the flow chart in Figure 4-3a. The magnetostatic solver creates an initial mesh. The solver then analyses the model. The solution is then analysed by calculating the energy error in each mesh node. When the energy error in certain areas is higher than the specified criteria (§4.3.1.4), the mesh is refined for these areas of unsatisfied energy errors. This refinement process continues until the total energy error is smaller than the specified energy error, or the maximum refinement iterations have been reached. Under ideal conditions, the energy value would be exactly zero, but is not plausible due to some amount of residual current density in FEA solutions. The adaptive mesh refinement allows for mesh independence. Mesh independence means that the mesh is refined until the obtained solution converges. Any further refinement of the mesh would only waste valuable computational time without improving the accuracy of the simulation. 67 (b) (a) Figure 4-3: (a) The adaptive mesh method used by Ansys®; (b) 3D FEA mesh model. 4.3.1.4 Solution and analysis setup Before simulations can be performed, the magnetostatic solution parameters have to be set. The parameters of the magnetostatic solver with their respective values are:  The maximum number of mesh refinement iterations is set to 10.  The maximum percentage error acceptable in the nodes is set to 1%.  The mesh refinement per iteration is set to 35%.  The minimum converged iterations are set to 2. The solution and analysis setup means that a maximum of 20 mesh refinements will be made before the simulation is stopped without obtaining a solution. Each iteration will refine the mesh by 35%, as per the method explained in §4.3.1.2. If a solution with more than 1% energy error is obtained in the nodes, the solution has to undertake another iteration to confirm convergence and stop the simulation. The converged answer is then taken as the solution. The mesh, energy error, and mesh refinement information provided by Ansys® Maxwell is shown in Figure 4-4. This information is provided during a magnetostatic simulation of the E-core MSRM. 68 Energy error is the error energy as a percentage of the total energy calculated at each node. The delta energy is the percentage difference in total energy calculated from the previous simulation. Delta Energy Energy Error 100 10 1 0.1 40000 60000 80000 100000 120000 140000 160000 Tetrahedra Figure 4-4: Typical monitoring of a solution convergence provided by Ansys® Maxwell. 4.3.2 Magnetostatic simulation procedure Obtaining the magnetostatic characteristics from the unaligned position to aligned position requires many simulation setups. These setups require the change of rotor position and excitation current. Thus, a parametric sweep is used to allow the rotor position and excitation current to be swept through a range of values. The rotor position is defined by the angle from the values ranging from 0˚ to 45˚ in steps of 3˚. The excitation current is set to values ranging from 0 to 3.5 A in steps of 0.5 A. The parametric sweep accounts for 128 simulated solutions. Wen Ding et al. provided both experimental data and FEA data in the articles, that was used to validate the magnetostatic simulation method. The experimental data of flux linkage characteristics and the winding inductance were obtained from [96] and [110]. These experimental data were compared to the FEA data, provided in [110]. The experimental data of the two articles and the FEA is shown in Figure 4-5. No experimental data on the static torque characteristics were provided in any of the listed articles (§4, p.63). However, FEA data were provided in [96] and [110], as shown in Figure 4-6. The static torque is shown at excitation currents of 0 to 3 A in steps of 0.5 A. 69 Energy Error (%) Delta Energy (%) Experimental [96] Experimental [110] FEA [110] 0.14 0.12 0.1 Aligned position 0.08 0.06 Unaligned position 0.04 0.02 0 0 0.5 1 1.5 2 2.5 3 3.5 Current (A) (a) 0.09 0.08 0.07 Aligned position 0.06 0.05 0.04 0.03 0.02 Unaligned position 0.01 0 0.5 1 1.5 2 2.5 3 3.5 4 Current (A) (b) Figure 4-5: Magnetic characteristics for validation: (a) Flux linkage; (b) Winding inductance. FEA [96] FEA [110] 0.9 0.8 3 A 0.7 0.6 0.5 0.4 0 A 0.3 0.2 0.1 0 0 5 10 15 20 25 30 35 40 45 Position (˚) Figure 4-6: Static torque characteristics for validation. Observing the flux linkage and winding inductance graphs in Figure 4-5, a contradiction is observed between the experimental data from [96] and [110]. Furthermore, by observing Figure 4-6, the static torque shows some deviation from the FEA data provided in [96] and [110]. These contradictions posed the problem that the experimental test method was not properly 70 Torque (Nm) Inductance (H) Flux linkage (Wb) implemented between tests or that the information about the data was incorrectly implemented during the writing of the article. However, the articles listed (§4, p.63) provide the most information on a radial flux MSRM by FEA data and experimental data. The sequence of validating the magnetic characteristics is set out below. 1. The articles do not provide various geometric parameters of the MSRM model (§4, p.63). Therefore, five geometric parameters are chosen to evaluate. It is necessary to evaluate these parameters' degree of accuracy with respect to the magnetostatic characteristics. The degree of accuracy is achieved by varying the parameters of: a. The cross-sectional coil area. b. The stacking factor of the rotor and stator cores. c. The rotor and stator pole width. d. The radius of the coil fillet when modelling. e. The coil shapes. (From a square to rectangular shape when viewed from the top view. The top view is in reference to Figure 4-2b.) 2. Simulating the flux linkage at each rotor position and excitation current. The results are compared with the experimental data and the FEA data (Figure 4-5). 3. Simulating static torque at each rotor position and excitation current. The results are compared with the FEA data (Figure 4-6). Unfortunately, the static torque characteristics of the MSRM cannot be compared with the experimental data. This is due to the static torque characteristics limited to FEA data in the articles (§4, p.63). It was stated by Wen Ding et al. in [96] that the error margin between FEA and experimental flux linkage at aligned and unaligned positions was 12% and 3.2%. Error margins were said to be within a reasonable amount of error. The error is justified by the B-H characteristics of the material in the FEA software, showing a 5-10% deviation in practice. In addition, there may have been a subtle deviation in the air gap length in the manufactured prototype, which contributed to this error deviation. 4.3.3 Magnetostatic simulation results A series of magnetostatic simulations was constructed for the selected geometric parameters (§4.3.2). Each of these parameters was assigned a variable value, allowing the parametric sweep to account for the variation of these parameters during the simulations. The 3D flux distribution of the hybrid magnetic flux paths in the MSRM can be seen from the simulated solutions. The 3D flux distribution of the MSRM is shown in Figure 4-7. In this simulation, a current excitation of 2.5 A was used. The MSRM is seen to produce around 1.6 T to 2.0 T at an aligned rotor position under current excitation of 2.5 A. 71 Figure 4-7: Flux distribution at the aligned position when one phase is excited. The simulated flux linkage and static torque characteristics, following the procedures in §4.3.2, were compared to the FEA data and the experimental data (Figure 4-5 and Figure 4-6), as obtained from the articles (§4, p.63). The magnetic characteristics by variation of the cross-sectional coil area are compared in Figure 4-8. The width of the coil was changed to change the cross-sectional area, keeping the coil height constant. Note that the legend indicates the coil width value, ‘FEA’ indicates the FEA data simulated by Wen Ding et al. and ‘Experimental’ indicate the experimental data obtained by Wen Ding et al. When the flux linkage is analysed, a 5% deviation occurred between the simulated and experimental data. Observing the static torque graph, a similar shape occurs from 15˚ onward, but the simulated data do not have the same trend between 10˚ and 15˚. It was concluded from the flux linkage that the cross-sectional coil area does not have a major effect on the simulation results due to all the simulating points deviating within 5% from the comparative data. For static torque, a minimal variation is shown, with the exception between 10˚ and 15˚. 72 14mm 11mm 8mm Experimental FEA 0.12 0.1 Aligned position 0.08 0.06 Unaligned position 0.04 0.02 0 0 0.5 1 1.5 2 2.5 3 3.5 Current (A) (a) 1 0.9 3.5 A 0.8 0.7 0.6 0.5 0 A 0.4 0.3 0.2 0.1 0 0 5 10 15 20 25 30 35 40 45 Position (˚) (b) Figure 4-8: Magnetic characteristics by variation of the cross-sectional coil area: (a) Flux linkage; (b) Static torque. The magnetic characteristics by variation of the stacking factor are compared in Figure 4-9. The stacking factor of the rotor and stator were changed in 5% intervals. Note that the stacking factor of the rotor and stator was the same stacking factor value when doing a simulation. When the flux linkage was analysed, a 5% deviation occurred for the aligned position between simulations. A 3% and 5% deviation occurred when compared to the simulation with a 95% stacking factor. Observing the static torque graph (only graphed at current excitation of 0,1,2 and 3 A), the same shape occurrence is seen as in Figure 4-8b. Comparing the static torque data to the FEA data provided by Wen Ding et al., it is visually observed that the static torque with 95% stacking factor have a minor error margin with an excitation current of 3 A. Hence, a stacking factor of 95% with reference to §2.3.8, p.36 can be assumed for the MSRM. Thus, it is clearly seen that the stacking factor of an MSRM have an influence on the magnetostatic results. 73 Torque (Nm) Flux linkage (Wb) 0.75 SF 0.8 SF 0.85 SF 0.9 SF 0.95 SF Experimental FEA 0.12 0.1 Aligned position 0.08 0.06 0.04 Unaligned position 0.02 0 0 0.5 1 1.5 2 2.5 3 3.5 Current (A) (a) 1 0.9 3 A 0.8 0.7 0.6 0.5 0 A 0.4 0.3 0.2 0.1 0 0 5 10 15 20 25 30 35 40 45 Position (˚) (b) Figure 4-9: Magnetic characteristics by variation of stacking factor: (a) Flux linkage; (b) Static torque. The magnetic characteristics by variation of the pole width are compared in Figure 4-10. The rotor and stator pole widths were changed, thus increasing their pole arc angle. Note that the legend refers to the width value of the stator pole. The same ratio changes the width of the rotor pole. The ratio relates to the width value of the pole divided by the original width value of the pole (Table 4-1). By analysing the flux linkage, a 5% deviation occurred between the simulated, experimental, and FEA data. Observing the static torque graph, it is seen that the torque increases more rapidly between 10˚ and 15˚. When excluding the static torque between 10˚ and 15˚, less of a variation between simulated static torque and FEA data is observed. Therefore, it was concluded that pole width has the most influence on static torque when the rotor rotates from an unaligned position to an aligned position. This was most likely due to the magnetic flux path between the stator and rotor cores occuring at an earlier rotor rotational angle. The magnetic flux path started to occur at an earlier rotor rotational angle due to the wider core poles. 74 Torque (Nm) Flux linkage (Wb) 10.6 10.889 11.17 11.469 Experimental FEA 0.14 0.12 0.1 Aligned position 0.08 0.06 Unaligned position 0.04 0.02 0 0 0.5 1 1.5 2 2.5 3 3.5 Current (A) (a) 1 0.9 3.5 A 0.8 0.7 0.6 0.5 0.4 0 A 0.3 0.2 0.1 0 0 5 10 15 20 25 30 35 40 45 Position (˚) (b) Figure 4-10: Magnetic characteristics by variation of pole width: (a) Flux linkage; (b) Static torque. The magnetic characteristics by variation of the coil shape and variation of the coil fillet had no significant effect on the magnetic characteristics. By analysing the flux linkage, a 1% deviation occurred between the simulated, experimental, and FEA data. The simulated data are provided in Appendix B, §B.2, p.173. 4.3.4 Magnetostatic simulation summary The magnetostatic process to replicate the magnetostatic characteristics of the MSRM was provided in §4.3.1 to §4.3.3. The parameters of the cross-sectional coil area, rotor and stator core stacking factor and coil shape were not provided by Wen Ding et al. in [96, 110, 109, 97, 107, 111]. The replication procedure was analysed by a parametric sweep simulation of the geometric parameters to observe the effect on the magnetostatic characteristics. The flux linkage compared well to the experimental data when a stacking factor of 95% was used. This stacking factor coincides with that found in the literature for magnetic material laminations of 75 Torque (Nm) Flux linkage (Wb) 0.5 mm thickness (§2.3.8, p.36). The effect of pole width and coil cross-sectional area had an effect on the solution, and it should be remembered that a manufactured prototype was not produced to the precise dimensional specifications. Thus, there will be some deviation from the prototype. Comparing the simulated static torque to FEA data, provided by Wen Ding et al., a torque characteristic difference was seen when the rotor was between the angles of 10˚ and 15˚. Unfortunately, no experimental data was provided to confirm the correct static torque characteristic graph. Torque production for an SRM, during motoring operation was produced and calculated in terms of co-energy, using a flux linkage curve (§2.1.2.2, p.20). Therefore, the flux linkage characteristics are considered the most important aspect of the magnetostatic simulation. This is because the flux linkage characteristic can be used to calculate the electromagnetic torque of an SRM. 4.4 Transient validation The transient solver of Ansys® Maxwell was used to obtain the dynamic behaviour of the MSRM. The dynamic behaviour observed in this study was the motor speed, shaft torque, phase current, and phase voltage to calculate motor efficiency. The dynamic behaviour was simulated for the amount of time it took one electrical period to complete at the specified motor speed. For an SRM, the mechanical degrees were calculated by dividing the degrees of an electrical period with the number of rotor poles and multiplying the answer by two. Thus, simulating this 4/6 MSRM of Wen Ding et al. over an electrical period resulted in the rotor rotating 90˚ mechanical degrees. Only one electrical period was needed to simulate the motor at steady-state. The post-processed result could then be multiplied to obtain the result over multiple electrical periods. Unlike the magnetostatic validation, the whole motor was constructed for the transient validation. This was because each phase winding was excited one after the other with the dynamic behaviour of a motor. For transient simulations (§4.4.3, p.81), the upper and lower coils of the opposing stators were divided into two windings connected in parallel to form one phase, shown in Figure 4-2. 4.4.1 Transient simulation setup The model setup should be finalised for the numerical simulation to be solved. The transient setup contains the excitation, boundary conditions, mesh, and the transient solution and analysis setup. The setup is discussed in the order listed. 76 4.4.1.1 Excitation simulation setup Excitation of the phase windings is provided in the following process. Each coil in a phase winding is assigned an excitation. The external excitation method is selected, the stranded coil type is selected, and the number of turns is set to 300. The stranded coil type is selected for the excitation method, otherwise the simulation assumes a solid piece of material for the coil geometry. The direction of the current flow is changed to the desired position, so that the flux path of the phase, shown in Figure 4-7, is achieved. The external excitation method is used so that an asymmetric half-bridge circuit can be coupled to the simulation to drive the electric motor. The asymmetric half-bridge converter, shown in Figure 4-11, is one of the most flexible and versatile switching circuits used in SRM drives. Each phase winding is controlled independently and allows three modes of operation, as discussed [55, 58]: 1. Magnetisation mode: The upper and lower switches of a phase are turned on together, exciting the phase by the current flow. 2. Freewheeling mode: Only one pair of the switches is turned on, and the phase winding is not connected to the DC source. Thus, there is no energy flowing back to the DC source. 3. Demagnetisation mode: When both switches are turned off, the current flows through the diodes, transferring trapped magnetic energy from the phase winding back to the DC source. Demagnetisation and magnetisation of the two phases occur simultaneously. Figure 4-11: Drive circuit for three-phase SRM. The asymmetric half-bridge converter is set up in the Ansys® Maxwell circuit. The switches in the circuit are operated by position control, meaning that the switch is turned on and off on the basis 77 of the angle of the rotor during rotation. The turn-on and turn-off angles vary at different motor speeds, as found in §4.4.2. Finalising the asymmetric half-bridge converter requires the winding resistance of each phase. A winding resistance of 1.15 Ω is used to validate the MSRM. The value of 1.15 Ω was obtained using the equation of copper loss in a three-phase motor. Note that the phase resistance is the same as the individual coil resistance due to its series-parallel connection. Copper loss: 𝑃 2𝑐𝑢 = 3𝐼 𝑅 (40) Here, 𝐼 is the root mean square (RMS) current and 𝑅 is the winding resistance. 4.4.1.2 Boundary setup Before a boundary condition is assigned, a solving domain is created. The solving domain consists of two volumetric cylinder regions. The first cylinder is constructed such that the cylindrical area is in between the rotor and stator pole areas. This region is known as the 'Band' and is used as a reference for the motion setup. The motion setup is set to the rotational type and the specified angular velocity (speed in Table 4-2) is assigned. Note that the mechanical transient selection is not selected in the motion setup. Thus, a steady-state solution will be obtained using the transient solver, as discussed in §3.2.5.3, p.58. The second cylinder is constructed around the motor model. The solver automatically assigns natural boundary conditions while an insulating boundary is considered, refer to §4.3.1.2. Transient 3D FEA consumes significant computational time [131]. The motor model is divided into four symmetric quadrants to reduce simulation time. When dividing the motor model into sections, a master and slave symmetry boundary is assigned to the motor model. Thereafter, the motor symmetry is set to the inverse of the modelled section value. Dividing the model saves significant computational time [133, 145]. Verifying the symmetry setup, a full, half, and a quarter motor model was simulated using identical simulation setups, and the results were equivalent whilst saving significant computational time. 4.4.1.3 Mesh configuration The transient solver does not use the adaptive meshing technique. Therefore, manual mesh specifications are required to define the mesh in the important regions of the motor model to achieve the accuracy of the results. The mesh setup is a relatively important aspect when FEA is done. Therefore, the sensitivity to the mesh setup is performed in §4.4.3, following the procedure in §4.4.2. 78 The mesh generated in Ansys® Maxwell of half of the motor model is shown in Figure 4-12. Note that the setup of a rotary region around the rotor automatically assigns a cylindrical gap mesh to the 'band' (§4.4.1.2). Figure 4-12: 3D FEA mesh model of the transient solution. The mesh setup assigned to validate the transient behaviour of the MSRM in §4.4.3 consists of the following mesh selection for each geometric aspect:  Band o Cylindrical gap mesh with clone mesh mapping angle assigned at 0.5˚ o Inside selection length-based mesh of 5 mm  Rotor core segments o Inside selection length-based mesh of 5 mm o Clone mesh density of 15 layers  Stator core segment o Inside selection mesh of 5 mm o Clone mesh density of 15 layers  Coils o Inside selection length-based mesh of 4 mm 79 4.4.1.4 Solution and analysis setup Before a simulation can be performed, the parameters of the transient solution must be set. The parameters of the transient solver are as follows:  The simulation stepping time is set to 0.055 ms, chosen from the sensitivity analysis in §4.4.3.  The simulation stopping is set to the time it would take the motor to rotate 90˚ at the specified speed, shown in Table 4-2. This means that the simulation performs one complete electrical period.  The non-linear residuals of the transient solver are set to 0.0001, and the option of a smooth B-H curve is selected to improve the accuracy of material characteristics during a simulation.  The second-order potential solver is selected as the standard used in the transient solver.  The rotational speed, DC source voltage and conduction angles (turn-on and turn-off angles) are assigned for three simulations, shown in Table 4-2. Table 4-2: Transient solution setups. Speed (rpm) DC voltage (V) Turn-on; Turn off angles Stop time (s) 1500 35 0˚; 33˚ 0.01 1000 25 5˚; 35˚ 0.015 700 40 0˚; 30˚ 0.02143 4.4.2 Transient simulation procedure Minimal experimental data of dynamic operation were provided in the articles (§4, p.63). However, the articles provided most experimental data when considering other MSRMs found in literature. Therefore, the transient solutions were compared with the FEA and experimental data obtained from the articles. Comparing the solution data to experimental data ensured that the transient setup and procedures were performed correctly. Confidence in using the transient magnetic solver will be obtained when the transient solution is replicated within an acceptable error margin of the article data. The sequence of validating the transient operation is set out below. 1. The complete setup of the transient operation is not provided in the articles (§4, p.63). The data not provided in the articles include the mesh setup and the solution setup. Therefore, 80 it is necessary to determine the influence of these parameters. The influence of these parameters is called a sensitivity analysis. The solver time steps and mapping angles of the cylindrical gap mesh are chosen as the two most important parameters [133, 137]. Both the phase current and torque solutions are compared as indications of the parameter effects. These simulations of the sensitivity analysis consist of: a. The variation of time steps with no clone mesh mapping angle is assigned. b. Assigning a clone mesh mapping angle under the variation of time steps. c. Keeping the time steps constant under a variety of mapping angles, and d. Keeping the exact setup and only changing the stacking factors of the cores between 95% and 100%. 2. Simulating the MSRM at steady-state speeds of 700, 1000 and 1500 rpm. Simulations are carried out for a single electrical period. The solution data for each electrical period are equivalent. Thus, saving valuable computational time. The post-processed results, including the phase currents and shaft torque, are compared with the experimental and FEA data. Note that all simulations were based on single-phase excitations. This is credible because the magnetic poles of an SRM can be generated with non-coupled coil configurations. Therefore, the mutual coupling between phases becomes negligible, and the flux linkage characteristics for a single phase can be used to model the other phases. Additionally, during commutation between phases, two phases are conducting simultaneously. This is mutual coupling, but since it occurs very briefly in each cycle, the effect can be neglected when modelling an SRM [55]. If adequate spacing between any two spaces is provided, the mutual coupling in an MSRM is negligible [146]. 4.4.3 Transient simulation results A series of transient simulations were conducted to conclude the sensitivity analysis. Each of these parameters was evaluated during the sensitivity analysis to understand and set up a transient simulation in order to obtain the best post-processed solution data. An in depth understanding of all equations, methods, processes and procedures can be found in [133]. As observed in Figure 4-16, the post-processed torque and current data of the simulations represented graphically better than those shown in Figure 4-13. Note that the torque and current graph colours are represented by the legend on the right-hand side. The transient results by variation of time steps with no clone mesh mapping angles are compared in Figure 4-13. The time steps of the simulations were changed between 0.555 ms, 0.111 ms, and 0.055 ms. It is observed from Figure 4-13 that the visual waveform of torque increased with 81 the decrease of time steps. This was due to more simulations being carried out within the same simulation time period when rotating between 0˚ and 70˚. Thus, smaller simulation stepping times resulted in more simulations, therefore increasing simulation time but also the accuracy of the post-processed results. The elapsed simulation time for each of these simulations ranged between 3 to 8 hours, depending on the simulation setup and computer resource availability. 0.6 8 0.5 6 0.4 0.3 4 0.2 2 0.1 0 0 -0.1 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 Position (˚) Position (˚) 0.555ms 0.111ms 0.055ms (a) (b) Figure 4-13: Sensitivity analysis with no clone mesh mapping angle: (a) Phase torque; (b) Phase current. The transient results by variation of time steps with a 1˚ clone mesh mapping angle are compared in Figure 4-14. The time steps of the simulations were changed between 0.222 ms, 0.111 ms, and 0.055 ms. The waveform resolution was observed to increase with decreasing time steps, as observed in Figure 4-14. When comparing the waveforms (0.055 ms and 0.111 ms) of no clone mesh mapping angles with the waveforms of a 1˚ clone mesh mapping angle (0.055 ms and 0.111 ms) in Figure 4-13, it is visually observed that the use of a clone mesh mapping angle improves the current post-processed results. However, the torque waveform still shows acoustical noise at the top of the torque waveform. 0.6 8 0.5 6 0.4 0.3 4 0.2 2 0.1 0 0 -0.1 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 Position (˚) Position (˚) 0.222ms 0.111ms 0.055ms (a) (b) Figure 4-14: Sensitivity analysis of 1˚ mapping angle: (a) Phase torque; (b) Phase current. 82 Torque (Nm) Torque (Nm) Current (A) Current (A) From the above simulation results, it was chosen to use 0.055 ms time steps for further sensitivity analysis. Note that the torque shapes in Figure 4-13 and Figure 4-14 differ from one another. This was because the torque simulations shown in Figure 4-13 were simulated using a stacking factor of 100% and the torque simulations in Figure 4-14 were simulated using a stacking factor of 95%. The effect the stacking factor has on the torque and current waveforms are shown in Figure 4-16. The transient results by variation of mapping angles with 0.055 ms time steps are compared in Figure 4-15. The clone mesh mapping angles were changed between 0.5˚, 1˚ and 2˚. The waveform resolution is observed to increase with the decrease of the mapping angle, as observed. Decreasing the mapping angle would increase the simulation time and the visual accuracy of the post-processed simulation results as the acoustic noise is eliminated. 0.6 8 0.5 6 0.4 0.3 4 0.2 2 0.1 0 0 -0.1 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 Poistion (˚) Position (˚) 0.5deg 1deg 2deg (a) (b) Figure 4-15: Sensitivity analysis of mapping angle at a 0.055 ms time step: (a) Phase torque; (b) Phase current. The transient results by variation of the stacking factor with 0.055 ms time steps and a 0.5˚ clone mesh mapping angle are compared in Figure 4-16. It is observed that the torque shape differs. For solid cores, the torque shape rises to a peak and descent faster than cores with a 95% stacking factors, as observed between Figure 4-13 and Figure 4-14. It is also observed that more current is drawn when cores of a 95% stacking factor are used. Thus, it was concluded that the use of the highest stacking factor in an electrical motor was to minimise losses, as the excitation current would be less and therefore less copper losses can be expected in the motor. 83 Torque (Nm) Current (A) 0.6 8 0.5 6 0.4 0.3 4 0.2 2 0.1 0 0 -0.1 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 Poistion (˚) Position (˚) 0.95 Solid (a) (b) Figure 4-16: Sensitivity analysis of the stacking factor: (a) Phase torque; (b) Phase current. In finalising the sensitivity analysis, it was concluded that different setup options affect the post- processed results. Setup values that result in the best post-processed solutions were applied to the simulations to finalise the transient validation. Steady-state transient solutions of 700 rpm and 1500 rpm were compared to FEA data, and the solution of 1000 rpm was compared with experimental data obtained in the articles (§4, p.63). Note that the experimental data of the MSRM were conducted under closed-loop control. The turn-on and turn-off angles were assumed to be the same as those of the 1000 rpm simulation in [110]. However, the provided simulation used a 24 V DC source, as specified by Wen Ding et al. in the articles and does not provide further solution data. The post-processed solution data of 700 rpm and 1500 rpm are shown in Figure 4-17. The difference in shaft torque and phase current was due not only to the difference in speed but also to the different control methodology used by the motor controller. At 700 rpm, the motor uses current chopping control and at 1500 rpm, the motor uses single pulse control, as explained in §2.1.3, p22. Both the shaft torque and phase torque are represented in the torque waveforms. The shaft torque is indicated by the solid line and the phase torque is represented by the dotted lines, often times overlapped by the shaft torque. 84 Torque (Nm) Current (A) 0.55 0.45 0.35 0.25 0.15 0.05 -0.05 6 4 2 0 5 7 9 11 13 15 17 19 21 23 25 Time (ms) (a) 0.55 0.45 0.35 0.25 0.15 0.05 -0.05 8 6 4 2 0 5 7 9 11 13 15 17 19 21 23 25 Time (ms) (b) Figure 4-17: Simulated steady-state torque and phase current waveforms: (a) Current chopping control operation at 40 V and 700 rpm (b); Single pulse control operation at 35 V and 1500 rpm. A comparison between the post-processed simulation data and the FEA data provided in the articles is summarised in Table 4-3. It is shown that the simulated solution has a deviation of 13.45% for the copper loss at 1500 rpm. As per equation (40), the copper loss is a function of the RMS current and winding resistance. Phase current is subject to winding resistance and magnetic core stacking factor, as seen in Figure 4-16. The stacking factor was shown to be around 95% in §4.3.3, p.71, and supported from literature (§2.3.8, p.36). The coil resistance was calculated using the provided copper loss and RMS phase current. Since these parameters, along with the mesh setup was not provided by Wen Ding et al., an error margin was expected between the comparisons of the simulated and provided FEA data. 85 Current (A) Torque (Nm) Current (A) Torque (Nm) Table 4-3: FEA comparison of dynamic performance. Speed (rpm) 700 700 - 1500 1500 - RMS phase current (A) 1.83 1.89 2.89 2.11 1.98 6.52 Maximum phase current 4.68 - - 7.56 6.85 10.38 (A) Average torque (Nm) 0.26 0.26 1.94 0.410 0.43 5.72 Maximum torque (Nm) 0.51 0.48 5.58 0.496 0.53 7.61 Copper loss (W) 11.65 7.61 7.00 15.44 13.61 13.45 The error differences at the solution of 700 rpm were smaller than those at the solution of 1500 rpm. An explanation for this phenomenon is that more simulations were conducted in an electrical period at slow speed than in high-speed operation because of the solution and analysis setup. Thus, acquiring a lower solution error in high-speed simulation requires smaller time steps in the solution setup, therefore allowing the same number of simulations during an electrical period. The steady-state transient solution of 1000 rpm was compared to the experimental data obtained in the article [109]. The motor simulation used single pulse control, a 25 V DC source and turn- on and turn-off angles of 5˚ and 35˚. A 25 V DC source voltage was chosen for the simulation of a 1000 rpm, as provided by Wen Ding et al. in [109]. Figure 4-18 shows the shaft torque and phase current waveforms compared to the experimental data. 86 Simulated FEA data Error (%) Simulated FEA data Error (%) Shaft torque Experimental [109] 0.55 0.45 0.35 0.25 0.15 0.05 -0.05 6 4 2 0 5 10 15 20 25 30 35 40 Time (ms) Figure 4-18: Simulated steady-state torque and phase current waveforms compared to experimental data using single pulse operation at 25V and 1000 rpm. The post-processed solution data are summarised in Table 4-4. Note that only the average torque and maximum phase current of the experimental data are provided in the article. Table 4-4: Experimental comparison of dynamic performance. Speed (rpm) 1000 1000 - RMS phase current (A) 1.637 - - Maximum phase current (A) 5.604 5.108 9.71 Average torque (Nm) 0.285 0.328 13.11 Maximum torque (Nm) 0.362 - - Copper loss (W) 9.243 - - The simulated solution has a deviation of 13.11% for the average shaft torque and a deviation of 9.73% for the maximum phase current. This deviation could be due to numerous factors the simulation had compared to the experimental motor, i.e., the stacking factor, the motor controller, geometric deviation, material characteristic deviations, measuring equipment accuracy, and operating conditions. A quick solution to improve the accuracy of the solution was to increase the 87 Current (A) Torque (Nm) Simulated Experimental data Error (%) stacking factors of the magnetic cores. However, increasing the stacking factor was not very practical as the maximum stacking factor for thin gauge silicon steel is 97% [147]. 4.4.4 Transient simulation summary The transient process to replicate the dynamic behaviour of the MSRM was provided in §4.4. The replication procedure was analysed by performing a sensitivity analysis of the post-processing solutions. The sensitivity analysis included the solution time steps, the clone mesh mapping angle, and the stacking factor. During the simulations, the coil resistance and stacking factors were unknown. The resistance obtained by equation (40) and the stacking factor of 95% were used, provided from the magnetostatic validation summary of the stacking factor (§4.3.4, p.75). The predicted performance of the simulations compared well with the FEA data and the experimental data provided in the articles (§4, p.63). Given the unknown resistance of the coil and the stacking factor of the magnetic material, a maximum deviation of 13.11% and 12.884% occurred for the experimental data and the FEA data. Provided a more refined mesh, solution setup, or exact parameters were used during a simulation, the maximum deviation was expected to decrease. However, this might not always be the result for FEA. 4.5 Summary of the electromagnetic simulation validation The process to set up, construct, and analyse an electromagnetic model of an MSRM was accomplished following the procedures in this chapter. Following the procedures, both the magnetostatic and transient behaviour of the MSRM was validated. The MSRM was replicated within a 5% and 13% deviation from the experimental data. The articles state a 7.5% maximum deviation between the FEA and the experimental data. Given the unknown motor parameters of the stacking factor, coil resistance, mesh and simulation setup that was not provided in the article data, along with the possibility of different material characteristics between Maxwell 2013 and Ansys® Maxwell 2021 and time and computing power limitations (§1.5.3, p.10), the simulation accuracy was limited. Therefore, the deviation of the solution data was considered acceptable when demostrating the simulation methods. Thus, the same simulation methods could be used to design an MSRM. For future studies, it is proposed to validate the MSRM using different simulation software, i.e. JMAG or Altair Flux, listed in §3.1.2, p.49. 88 CHAPTER 5 DESIGN OF A SWITCHED RELUCTANCE MOTOR This design of a three-phase MSRM, proposed in §2.6, p.45, is provided in this chapter. The conceptual diagram of the proposed MSRM is shown in Figure 5-1. The stator comprises of 12 E-cores with a coil wound on the upper and lower yoke of each core. Eight coils are connected in series to form a phase winding, shown in Figure 5-1 as blue, red, and yellow. Figure 5-1: The proposed MSRM This chapter focused on an electromagnetic design using FEA, as the manufacture of a prototype is unfeasible due to financial limitations (§1.5.3, p.10). The electromagnetic design of the proposed MSRM used the design principles of Vanessa Siqueira De Castro Teixeira et al. [51], Nikunj R Patel et al. [75, 106, 74, 53], and Anas Labak [52, 57] with the addition of the literature review (chapter 2) to construct an XDM. The MSRM was designed according to the specified power characteristics. Thereafter, an efficiency map of the proposed MSRM was constructed for use in the drive cycle. Refer to chapter 6 for the evaluation of a traction motor. 5.1 Motor specifications The design specifications of AC machines are usually provided in terms of their torque-speed characteristic curve. The designed motor is expected to provide constant torque below rated speed and constant power above rated speed [148]. The torque-speed characteristic curve of the proposed MSRM was determined in this section while considering the motor size before the design of the proposed MSRM commenced. 89 The MSRM, proposed in §2.6, p.45 was constrained to the parameters listed in Table 5-1. The outer diameter of the motor, considering that the proposed MSRM is a direct drive motor, is constrained by the rim of the solar vehicle. The axial length of the motor was restricted to ensure that the motor uses minimal space. The design of the mechanical housing for the motor is not part of this study, therefore the mechanical housing will increase the axial length of the motor to some extent. In this study, the focus was only on the electromagnetic design of the motor, as provided in this chapter. The maximum peak current was restricted by the battery of the solar vehicle, and a three-phase motor is specified, keeping to the most commonly used industry practice of using a three-phase motor. Furthermore, specifying a three-phase SRM ensures that electric switches and converters do not increase, thus keeping the cost of the motor controller minimal if it should be considered to manufacture a prototype of the proposed MSRM in the future. Table 5-1: Design constraints Motor structure Radial flux Rotor outer diameter, 𝐷𝑟𝑜 𝐷𝑟𝑜 ≤ 14" (355.6 𝑚𝑚) Inner stator diameter, 𝐷𝑆 𝐷𝑆 > 𝐷𝑠ℎ𝑎𝑓𝑡 Axial length, 𝐿𝑠 𝐿𝑠 ≤ 150 𝑚𝑚 Maximum peak current, 𝐼𝑝 𝐼𝑝 < 80 𝐴 Phases, 𝑞 𝑞 = 3 5.1.1 Motor sizing The proposed MSRM is a direct drive motor, similar to the Mitsuba M2096-DII. For a direct drive motor, the diameter is limited to the size of the tyre. Thus, a tyre incorporates a rim and therefore sets the constraint of the outer diameter of the motor, such that the outer diameter cannot be selected as an optimised parameter [149]. The overall dimensions of a direct drive motor are limited to the space available inside a rim. Due to of the profile of a rim cross section, shown in Figure 5-2, only 80% of the rim diameter is available to insert the motor. Generally, for lightweight vehicles that use tyre size R13 (330.2 mm) and R14 (355.6 mm), an outer diameter of 290 mm is used as a design constraint. Keeping the diameter constraint in mind, the rules of thumb are followed to size the proposed MSRM [83]. 90 Figure 5-2: Cross-sectional view of a wheel rim Generally, a given air gap at the greatest radius will produce the greatest torque. Similarly, the torque will require lower field strength when the air gap is at a larger radius, and energising the windings will therefore require less current. Lower current will provide lower thermal losses, better efficiency, and greater continuous performance in a traction motor [55]. Thus, the consideration can be represented by the following. 𝑇𝑜𝑟𝑞𝑢𝑒 ∝ (𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟2 (41) 𝐴𝐺 ∗ 𝐿𝑒𝑛𝑔𝑡ℎ) Where 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟𝐴𝐺 is the average air gap diameter. For the rule of thumb to size an electric motor, the difference between the inner and outer air gap diameter is negligible. From equation (41) it is observed that by doubling the diameter of the air gap, both the distance of the tangential forces and the air gap shear area are doubled. This results in doubling the tangential forces and therefore quadrupling the torque. If only the length of the motor is doubled, only the air gap shear area is doubled, and therefore the torque is only doubled [83]. Assuming a cylindrical machine, the equation is provided as: 𝑉𝑜𝑙𝑢𝑚𝑒𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 ∝ (𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 2 𝑂 ∗ 𝐿𝑒𝑛𝑔𝑡ℎ) (42) Where 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟𝑂 is the outer diameter of the machine. By accepting that 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟𝑂 = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟𝐴𝐺 for an outer rotor radial flux machine, dividing equation (41) by equation (42) gives the following approximate relationship: 𝑇𝑜𝑟𝑞𝑢𝑒 ∝ ~𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (43) 𝑉𝑜𝑙𝑢𝑚𝑒𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 91 Fundamentally, no matter what parameter of a cylindrical, outer-rotor, radial flux machine is altered, the machine will still require the same amount of volume to produce the required torque. However, energising the air gap requires only a certain radial depth. Thus, once the motor reaches a diameter where the inner diameter of the stator is large enough, the motor can essentially take on a toroidal form, and the rules that govern the occupied volume significantly change [83]. Assuming that the radial depth is constant and the diameter and length are free to scale, the volume of a toroid is proportional to that shown in equation (44). 𝑉𝑜𝑙𝑢𝑚𝑒𝑡𝑜𝑟𝑜𝑖𝑑 ∝ (𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟𝐴𝐺 ∗ 𝐿𝑒𝑛𝑔𝑡ℎ) (44) The approximate relationship of a toroidal motor, provided in equation (45) is obtained when dividing equation (43) by equation (44). 𝑇𝑜𝑟𝑞𝑢𝑒 ∝ ~𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 (45) 𝑉𝑜𝑙𝑢𝑚𝑒𝑡𝑜𝑟𝑜𝑖𝑑 Thus, as the outer diameter of the motor increases, the motor can transition from a cylindrical motor shape to a toroidal motor shape, and the torque per volume performance changes from an essentially constant value to an approximately linear proportion to the diameter of the motor, as demonstrated in Figure 5-3. Cylindrical Toroidal Machine Diameter Figure 5-3: Demonstration of the 'breakpoint' of the motor diameter where the torque/ volume increases From these approximate scaling factors, a large diameter, short axial length, toroidal shaped motor will most likely meet the performance requirements. However, the large diameter of the motor is limited by the rim. The constraint allows for a maximum diameter of 370 mm, measured inside the rim of the solar vehicle. This will allow future considerations where the outer rotor is 92 Potential Torque/Volume used as a rim hub for the tyre, similar to the case of the Commonwealth Scientific and Industrial Research Organisation (CSIRO) motor, implemented by the Aurora and Nuna solar teams [150]. 5.1.2 Motor performance The required performance characteristics of the proposed MSRM were obtained by evaluating the Mitsuba M2096-DII in §6.2.2, p.138 as the current traction motor of the NWU solar vehicle after following a similar approach as discussed by Amir Ahmed and Dikki Bhutia in [151]. Evaluating the Mitsuba M2096-DII was carried out using the drive cycle developed in §6.1.1, p.125. Using the evaluated data, a scatter plot of instantaneous torque and speed throughout the drive cycle is plotted in Figure 5-4. The instantaneous torque and speed are known as the operating points, plotted as blue dots. A similar approach as in [151] was used to specify the performance parameters of the proposed MSRM. This approach is discussed in this section. The transient torque-speed characteristics of a motor are constructed from the rated torque-speed parameters. However, the transient torque-speed characteristics of a motor are greater than the continuous operating capability. Thus, the operating capability of an electric motor can be extended for a period of time. The operating time beyond the transient limits, otherwise known as the overload torque-speed characteristics, is a function of thermal constraints. Effective thermal management of an electric motor will improve its performance and ensure reliable operation, while poor thermal management will result in performance degradation and accelerated machine wear that may eventually cause motor failure. The SRM, compared to other electric motors, does not have additional losses generated in the rotor by windings or permanent magnets. Therefore, concerns of demagnetisation of permanent magnets or excessive thermal heat are non-existent in SRMs. Thus, an SRM is only limited by the thermal limits of the stator windings and therefore offers the highest temperature operation capacity [55]. Following a similar approach to the one used in [151], the rated torque-speed characteristics and the overload torque-speed characteristics were chosen. The rated torque-speed characteristics were chosen where the power under evaluation (the operating points) is constant with the increase of speed. However, it was observed from the power-speed operating points that the torque falls linearly above 525 rpm. This was due to the torque-speed characteristics of the Mitsuba M2096-DII, which cannot be operated at extended torque for high speeds. Given the torque-speed characteristics of an SRM, a decreasing power-speed relation will likely not be the case. The approach in [151] did not include an overload torque-speed characteristic. Thus, the approach was altered to include both the rated torque-speed characteristics and the overload torque-speed characteristics, as shown in Figure 5-4. 93 Operating Points Rated Performance Overload Performance 45 40 35 30 25 20 15 10 5 0 2500 2000 1500 1000 500 0 200 300 400 500 600 700 800 900 Speed (rpm) Figure 5-4: The anticipated torque-speed characteristics and power-speed characteristics of the proposed MSRM The rated torque-speed characteristics were chosen to include the most frequent operating points of the Mitsuba M2096-DII, according to the evaluation of the Mitsuba M2096-DII (§6.2.2, p.138). A minor number of operating points was excluded from the rated torque-speed characteristics. The excluded operating points will be achieved under overload operations. Thus, the torque- speed characteristics were chosen at 30 Nm and 550 rpm, which equate to an output power of 1.73 kW. The overload parameters offer an output power of around 2.1 kW. 5.2 Motor design The objective of the design was to provide an XDM of an SRM. The XDM was evaluated for solar vehicle application to justify the use of an SRM as a traction motor in solar vehicle races. The required design characteristics of the proposed MSRM are summarised in Table 5-7. Some margin for the speed specification was provided. The margin was provided as the intersection between the operating regions from constant torque to constant power that is not a definite point, as observed in Figure 5-22. Wen Ding et al. showed the difference when constructing the torque- speed characteristics of an MSRM in [97]. 94 Power (W) Torque (Nm) Table 5-2: Design specifications Rated Torque, 𝑇𝑏 30 𝑁𝑚 ≤ 𝑇𝑏 ≤ 35 𝑁𝑚 Base speed, 𝑁𝑏 500 𝑟𝑝𝑚 < 𝑁𝑏 < 600 𝑟𝑝𝑚 The outer diameter of the MSRM is set to the maximum allowable value within the constraints listed in Table 5-1 to provide the maximum electromagnetic torque in the air gap of the motor. The rotor and stator cores are segmented so that the flux path length is minimised. Thus, high efficiency is achievable [77, 74]. The performance of an SRM depends mainly on the dimensions of the stator and rotor core, pole configuration, pole arc angles, and its phase windings [148]. The design of the proposed MSRM was divided into three sections namely: geometry, magnetic material, and windings. These sections were intertwined with each other during the design and was not a straightforward process. A flow diagram summarising the design procedures is shown in Figure 5-5. The flow diagram shows the iterative design procedure between the start and end of the design process. After the design is completed, the flow diagram continues with additional procedures. These extra procedures were included to indicate the process of evaluating the designed motor. Note that after the construction of the efficiency map, the flow splits into two with different coloured arrows. In this study, the red arrow was followed to evaluate the proposed MSRM. Evaluation of the proposed MSRM is done in §6.3, p.140. The green arrow indicates the design process when the most efficient SRM is desired. However, this process is a time-consuming design process, as each motor design has to be analysed on the basis of its efficiency map. The construction of an efficiency map required a lot of simulation time and computer resources. Note that this is the idealised design process to obtain an SRM for the solar vehicle of the NWU. However, due to time and resource constraints (§1.5.3, p.10), this design process could not be accomplished. 95 Figure 5-5: Flow diagram of the design procedure 96 5.2.1 Geometry Following the design procedures shown in Figure 5-5, the geometry of the proposed MSRM was defined. An MSRM of segmented stators and rotors was proposed because of its short flux paths. The proposed MSRM allows for a large diameter motor with short flux paths to increase motor efficiency. This section discusses the geometric design procedures, where the design variables corresponding to the geometry have the following parameters:  Stator pole width, 𝜏𝑠  Rotor pole width, 𝜏𝑟 𝐿  Stator pole length, 𝐿 = 𝑠2𝑠1 = 𝐿2 𝑠3  Stator total length, 𝐿𝑠 Note that because an E-core-shaped stator was used, the stator consisted of three poles. The middle pole is twice the volume of an outer pole to carry the flux density of both, as graphically shown in Figure 5-18, p.114. Thus, the total length of the stator was not equal to the sum of the three lengths of the poles. In a conventional SRM, the pole length would be the length of the stator, also known as the axial length. The initial geometry values used are those of a C-core MSRM, designed by Anas Labak [77], and Nikunj Ramanbhai Patel et al. [53]. The C-core MSRM was designed for a rated performance of 28 Nm and 600 rpm. The C-core MSRM, although an axial flux motor was easily modifiable to use as a radial flux motor, while obtaining the same rotor diameter. 5.2.1.1 Core shape The stator pole shape of the proposed MSRM consists of an E-core. An E-core was chosen on the basis of the study of Xinglong Li and Ernest Mendrela [115]. Xinglong Li and Ernest Mendrela found that an E-core has a higher force-to-mass ratio than a C-core linear SRM [115]. Applying the principle of a linear motor around an axis, a rotary motor can be formed. Thus, a higher torque- to-mass ratio can be expected for an E-core MSRM. During the proposal of the SRM in §2.6, p.45, a research question was formed from the literature. The research question formulated the idea that a core with more poles while keeping the core length, width, and winding turns constant will result in higher efficiency as the flux paths are shorter. The research question was based on Figure 2-20, p.46, showing the flux paths and parameters of a C-core, E-core, and IIII-core. The C-core consists of two poles, the E-core consists of three poles, and the IIII-core consists of four poles. The poles of these cores are otherwise known as pole teeth [152]. Even though the research question did not form part of the 97 scope of this study, the effect of the core shapes was analysed using magnetostatic and transient simulations to justify selecting an E-core over a C-core and to gain a basic understanding of the effect of having more poles on the core. The C-core, E-core and IIII-core MSRM geometry parameters consist of a total core length of 80 mm, pole arc angle of 9° and a total of 80 winding turns. Note that with the addition of poles, the pole height and winding height decreased. However, the sum of pole heights and winding heights remained constant. The magnetic flux characteristics of the C-core, E-core, and IIII-core MSRM are shown in Figure 5-6. It is observed that the magnetic flux characteristics (aligned and unaligned flux linkage curves) of each core shape differ from each other. As discussed in §2.1.2.1, p.18, the core shape with the highest energy area will produce the highest amount of torque given a constant excitation current. However, in a transient operation, the excitation current will not be a constant variable. Thus, a transient simulation is required. C-core E-core IIII-core 0.25 0.2 Aligned positions 0.15 0.1 Unaligned positions 0.05 0 0 5 10 15 20 25 30 35 40 45 50 Current (A) Figure 5-6: Magnetic flux linkage characteristics of a C-core, E-core, and IIII-core MSRM Steady-state transient solutions of 550 rpm and 800 rpm of each core shape were completed. These simulations used a 100 V DC source voltage and turn-on and off-angles of 0˚ and 6˚. Figure 5-7a shows the shaft torque and phase current waveforms at a steady-state speed of 550 rpm. It is observed that the C-core operated with SPC, while the E-core and the IIII-core operated with CCC. Thus, both the C-core and the E-core operated in the constant torque region, while the IIII- core was already operating in the constant power region. Figure 5-7b shows the shaft torque and phase current waveforms at a steady-state speed of 800 rpm. It is observed that the C-core and E-core were operating with SPC while the IIII-core was 98 Flux linkage (Wb) still operating with CCC. Thus, the IIII-core was still in the constant torque operating region, whereas both the C-core and the E-core operated in the constant power region. C-core E-core IIII-core 50.00 40.00 30.00 20.00 10.00 0.00 60.00 40.00 20.00 0.00 7 9 11 13 15 17 19 21 23 25 Time (ms) (a) 30 20 10 0 60 40 20 0 5 7 9 11 13 15 17 19 21 23 25 Time (ms) (b) Figure 5-7: Simulated steady-state torque and phase current waveforms for speeds of (a) 550 rpm; (b) 800 rpm The post-processed solution data are summarised in Table 5-3. The post-processed torque- speed operating points of the simulations are plotted and the predicted torque-speed characteristics of each core shape are graphed, as shown in Figure 5-8. Observing the torque-speed characteristics of the core shapes, it was seen that the torque-speed characteristics of the C-core are not on the same constant power curve, as expected from 99 Current (A) Torque (Nm) Current (A) Torque (Nm) literature (§2.1.3.1, p.22). Thus, the operating point at 800 rpm was expected to already be in the falling power region. Therefore, a faster torque decrease was expected. However, as discussed in §5.4.1, p.120, this was due to the use of the same conduction angles at different operating speeds. To obtain a torque-speed characteristic with a constant power region, optimal conduction angles should be used at each operating point. The operating point in which both the C-core and the IIII-core transition from a constant torque to a constant power region is unknown from these simulations. However, the difference in the torque-speed characteristics shows a difference between the core shape operations. Table 5-3: Dynamic performance of a C-core, E-core, and IIII-core MSRM C-core E-core IIII-core Speed (rpm) 550 800 550 800 550 800 Average torque (Nm) 9.15 3.565 30.46 20.234 18.50 17.663 Output power (W) 527.28 298.65 1754.2 1695.1 1065.7 1479.7 RMS phase current (A) 7.253 3.603 25.478 18.017 27.283 25.759 Copper loss (W) 3.8089 1.892 13.379 9.461 14.327 13.527 C-core (Predicted) E-core (Predicted) IIII-core (Predicted) C-core E-core IIII-core 50 40 30 20 10 0 0 100 200 300 400 500 600 700 800 900 1000 Speed(rpm) Figure 5-8: Predicted torque-speed characteristics of a C-core, E-core, and IIII-core MSRM The three core shapes are not a direct comparison. Therefore, a conclusive assessment was not necessary for the purpose of the research question. However, it is still unknown whether one core shape is more efficient than the other, even though a core with more poles has shorter flux paths. For a conclusive evaluation of motor efficiency, the torque-speed characteristics have to be 100 Torque (Nm) similar. This research question is proposed as a future study to fully understand the efficiency effect when having a core with more poles while keeping the core length, width and winding turns constant. 5.2.1.2 Pole configuration Two pole configuration options were considered for the proposed MSRM. A 12/16 and 12/20 pole configuration was considered. From literature, it is known that an SRM with more rotor poles exhibits higher static torque over an electrical period and produced more torque during operations, which is advantageous for EVs. However, maintaining the rotor and stator diameter, the pole arc angles and phase winding turns differ between the comparative SRMs. Thus, this section compares a 12/16 MSRM to a 12/20 MSRM, keeping all dimensions and operating conditions equal. A 12/16 and 12/20 MSRM consisting of the same geometric parameters, magnetic material, and winding turns were analysed. The only difference between the configurations of the comparative motors was the rotor poles. Note that the number of rotor poles required the conduction angles of the motor controller to be different. The difference in conduction angles was demonstrated by the ideal inductance-rotor angle graph in Figure 5-9. The difference in the inductance profile was due to the rotor pole pitch. The 12/16 MSRM has a pole pitch of 22.5° and the 12/20 MSRM has a pole pitch of 18°. The respective step angle, calculated using equation (24), p.33, was applied as the conduction angle during simulations. The phase winding of the 12/16 MSRM was excited every 31.5°, and the 12/20 MSRM was excited every 20°. (12/16) (12/20) Maximum inductance 0 10 20 30 40 50 60 70 Rotor angle (°) Figure 5-9: Idealistic inductance-rotor angle profile of a 12/16 and 12/20 MSRM The magnetic flux characteristics of the two MSRM configurations are shown in Figure 5-10. It is observed that both configurations have the same characteristic curve for the aligned position. However, at the unaligned position, the 12/16 MSRM has less flux linkage per current than the 12/20 MSRM. Therefore, from the literature (§2.3.3, p.31), the 12/16 MSRM should produce more torque than the 12/20 MSRM during steady-state operations. 101 Inductance (H) 0.25 0.2 Aligned position 0.15 0.1 Unaligned position 0.05 0 0 5 10 15 20 25 30 35 40 45 50 Current (A) Figure 5-10: Magnetic flux linkage characteristics of the 12/16 and 12/20 MSRM Steady-state transient solutions of 400 rpm, 550 rpm, and 750 rpm are provided in Table 5-4. Post-processed solution data from the MSRM operating at 550 rpm are shown in Figure 5-11. From Figure 5-11 it is observed that the torque waveform of the 12/20 MSRM takes longer to rise and does not stay at maximum torque as long. This was due to the phase current rising slower when operating using SPC, unlike the 12/16 MSRM operating for longer time using CCC. Note that the turn-on and turn-off angles do not occur at the same time. This is due to the different conduction angles used to operate the two configurations, as shown in the ideal inductance profile in Figure 5-9. (12/16) (12/20) 50 0 60 40 20 0 2 4 6 8 10 12 14 16 18 20 Time (ms) Figure 5-11: Simulated steady-state torque and phase current waveforms of the 12/16 and 12/20 MSRMs Observing the torque waveforms, it was visually represented that the 12/20 MSRM produces less torque than the 12/16 MSRM, provided the same geometry, magnetic material and winding turns were used. Therefore, as perceived from the magnetic flux linkage characteristics in Figure 5-10, 102 Flux linkage (Wb) Current (A) Torque (Nm) the 12/16 MSRM configuration will provide more torque at each set speed, as summarised in Table 5-4. Provided the same DC source voltage is used, as in these simulations, the torque- speed characteristic graph of the two motors will differ. Table 5-4: Dynamic performance of a 12/16 and 12/20 MSRM Pole configuration 12/16 12/20 12/16 12/20 12/16 12/20 Speed 400 400 550 550 750 750 RMS phase current 26.255 20.47 22.997 11.18 13.213 7.19 (A) Average torque (Nm) 34.83 24.30 29.47 10.59 13.02 4.83 Having more rotor poles in an SRM does not provide more torque as discussed in literature (§2.3.3, p.31). From the simulations, it was seen that torque decreases for a motor with more rotor poles, provided the geometry, material and windings are kept constant. However, conclusive assessments are recommended as a future study to verify the torque production of SRM pole configuration where every design aspect is kept constant. To improve the 12/20 MSRM and matching the torque-speed characteristics to the proposed MSRM, design iterations of the motor geometry, material, windings, and/ or motor control should be considered. These different design considerations constitute a new MSRM design from scratch, following the same design procedures shown in Figure 5-5. 5.2.1.3 Pole embrace The pole embrace, defined in §2.3.4, p.32, ensures the requirements of self-starting, high output torque, and low torque ripple in an SRM. Therefore, the stator and rotor pole arc angles must be defined. Pole pitch was defined from the chosen pole configuration. For the chosen 12/16 MSRM, the pole pitch of the stator and rotor is 30° and 22.5°. To ensure the three requirements of self- starting, high-output torque and low torque ripple were obtained for an SRM, a feasibility triangle was used to obtained the stator and rotor pole arc angles. The feasibility triangle, shown in Figure 5-12 was constructed using equations (24), (25) and (26). Refer to p.33 for the equations. The triangle formed from the three equations shows the possible stator and rotor pole arc angles, provided that the number of poles and phases is known. For the proposed MSRM, the pole arc angles were restricted to the overlapped feasibility triangles of a three-phase 12/16 and 12/20 SRM, as shown in Figure 5-12. 103 13 12 11 10 9 8 7 6 5 4 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Br Figure 5-12: Feasibility triangle of the proposed MSRM However, the feasible region was still quite large to decide on the correct choice of rotor pole arc and stator pole arc angles. R. Pohl suggested that the rotor arc angle should be approximately 40% of the rotor slot pitch to maximise the inductance difference between the unaligned and aligned positions [153]. For the 12/16 pole configuration, the rotor pole pitch is 22.5°, and for a 12/20 pole configuration, the rotor pole pitch is 18°. Calculating the rotor pole arc at 40% of the rotor slot pitch, the suggested pole arc angle of the respective pole configurations should be 9° and 7.2°. Using the overlapped feasible region, 9° was available for both a 12/16 and 12/20 three-phase SRM. Anas Labak suggests that pole arc angles should be made as large as possible to maximise aligned inductance [77]. However, a wide pole arc angle restricts the available coil space on the E-core stator cores. To obtain the same MMF, the axial length of the cores was increased to fit the same number of coil turns when the same conductor gauge was used. Therefore, to keep the axial length of the stator cores at a minimum, a 9° pole arc angle was chosen. Anas Labak states that an adequate choice of an SRM design is to have both the stator and the rotor pole arc angles equal [77]. Equal pole arc angles are an effective way to extend the positive torque zone and avoid zero torque zones at the aligned position [106]. The pole arc angle sets the pole width of the proposed MSRM, such that the respective pole height and the winding space conclude the geometry of the segmented E-core stator. Thus, for 104 Bs the proposed MSRM, a pole embrace of 0.4 and 0.5 was obtained for the respective 12/16 and 12/20 pole configurations. 5.2.1.4 Pole area The E-core consists of three poles. The pole width was already defined from the pole arc angle. Thus, the remaining parameter was the pole heights. The middle pole of the E-core is twice the height of the two outer poles as shown in Figure 2-20, p.46, keeping the magnetic flux density in each pole the same. Thus, the flux linkage in the middle pole is the sum of the flux linkages in the two outer poles. The purpose of the pole height was to obtain a pole area that operates at the required flux density. The flux density in the poles was defined as the knee point of the selected magnetic material. The required flux density in the core should be obtained at rated current. The pole heights were analysed using the magnetostatic solver. An excitation current, equal to the rated current, was applied to the windings, and the flux linkages in the core were graphically analysed. The analysis was conducted at the aligned position, as this is the position where the flux linkages in the core will be at the maximum. Note that during transient simulations, the flux linkage will be somewhat lower, as the excitation shall stop before reaching the aligned position. The graphical representation of the flux linkages in an E-core is shown in Figure 5-18. For the analysis of the pole heights, the winding turns and conductor gauge were kept constant. Thus, by increasing the pole height, the total length of the core increased, otherwise referred to as the axial length of the core. The pole heights were started at a value of which the total length of the core was equal to 100 mm. Pole heights were increased for each simulation, although they were restricted by the total length, as per §5.1. The pole height was chosen such that the flux linkage in the pole was equal to the knee point of the magnetic material while the winding was excited with the rated current. However, the pole height was chosen as the minimum while ensuring the required flux. This ensured that the total length of the core was such that the axial length of the motor was minimal. The minimal axial length of the motor was chosen purely to decrease motor volume and weight. It was uncertain whether an increased pole height operating at a lower flux density will provide an improved efficiency map for the proposed MSRM. Due to time constraints, a comparison between another motor with increased pole height was not accomplished in this study. Thus, analysis of pole height, with comparison to the efficiency map of the motor is recommended for future studies. 105 5.2.1.5 The proposed modular switched reluctance motor The proposed MSRM consists of twelve independent modular E-shaped stator cores and sixteen I-shaped rotor cores. A single E-shaped stator and an I-shaped rotor core are shown in Figure 5-13. Two coils are wound on to each stator and connected to six other coils, as observed in Figure 5-1. The physical parameters and characteristics of the stator and rotor are summarised in Table 5-5. Figure 5-13: Geometry parameters of the proposed MSRM The magnetic material of the stator and rotor is the non-oriented silicon steel M235-35A, as discussed in the next section. All the material characteristics used were provided by the material database of Ansys®. The magnetic material used to stack the stator and rotor cores is a 0.35 mm silicon steel lamination for the proposed MSRM. The ideal stacking factor of 95% is assumed and used for transient simulations based on literature (§2.3.8, p. 36). 106 Table 5-5: Geometry parameters of the proposed MSRM Geometry parameters of the SRM (unit: mm) Stator outer radius, 𝑟𝑠𝑜 160.25 Stator pole length, 𝑑𝑠 20 Rotor outer radius, 𝑟𝑟𝑜 177.5 Stator total length, 𝐿𝑠 110 Stator yoke width, 𝑦𝑠 15 Upper stator pole length, 𝐿𝑠1 12.45 Rotor yoke width, 𝑦𝑟 17 Middle stator pole length, 𝐿𝑠2 24.9 Stator pole arc, 𝛽𝑠 9˚ Lower stator pole length, 𝐿𝑠3 12.45 Rotor pole arc, 𝛽𝑟 9˚ Stator pole width, 𝜏𝑠 25.146 Air gap length, 𝑔 0.25 Rotor pole width, 𝜏𝑟 25.185 5.2.2 Magnetic material Both the stator and rotor cores consist of the same magnetic material. Magnetic material is an important decision for electrical machine design, as reviewed in §2.3.7, p.35. For an electrical motor, the material must exhibit low hysteresis losses and high magnetic polarization properties. The standard type of magnetic material used for SRMs includes non-oriented electrical steel, which is graded according to the European standard EN 1016 [70, 154]. The shortlisted materials for the proposed MSRM, along with their magnetic properties, are listed in Table 5-6. Table 5-6: Magnetic properties of the shortlisted magnetic material Thickness Max specific loss Hmin = Hmin = Grade (EN10106) (mm) (mW/kg) 1.5T 5000(AT/m) 10000(AT/m) M235-35A 0.35 2.35 1.6 1.7 M250-35A 0.35 2.50 1.6 1.7 M270-35A 0.35 2.70 1.6 1.7 M300-35A 0.35 3.00 1.6 1.7 M250-50A 0.5 2.50 1.6 1.7 M270-50A 0.5 2.70 1.6 1.7 M290-50A 0.5 3.00 1.6 1.7 The Powercore® and Hi-Lite range offered by ThyssenKrupp and Cogent Power (Grade EN 10303), only offer the significant benefit of lower losses around frequencies of 400 Hz. Because SRMs operate at frequencies about ten times lower than other motor types, these magnetic materials are not considered for shortlisting. 107 Calculating the phase switching frequency, it was noted that the frequency of 400 Hz was only exceeded at speeds of 1500 rpm and 1200 rpm, when considering a three-phase SRM of 16 or 20 rotor poles. The phase switching frequency was determined for the time it takes one rotor pole to move from one phase to an adjacent phase, provided as: 2𝜋 𝑇 = 𝑠 𝜔 𝑁 (46) 𝑏 𝑟𝑝 Considering the shortlisted magnetic materials, the material with minimum lamination thickness was considered, since thinner laminations reduce eddy current losses. The magnetic material, M235-35A is chosen for the proposed MSRM. The chosen magnetic material was one of four magnetic materials of the same lamination thickness. However, the magnetic material, M235- 35A, had the lowest specific loss out of the shortlisted materials, while still exhibiting properties of great tensile strength, as provided in [93, 155]. 5.2.2.1 M235-35A The magnetic material chosen for the proposed MSRM is the M235-35A of ThyssenKrupp. The B-H magnetisation curve of the magnetic material is shown in Figure 5-14. The magnetisation curve was obtained from the materials library of Ansys® Granta. 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 2000 4000 6000 8000 10000 12000 14000 H (A/m) Figure 5-14: B235-35A B-H characteristics The magnetisation curve was specifically used during the geometry design of an SRM. Motor performance depends on the maximum flux density at different parts of the motor i.e. stator and rotor yoke and poles. Note that when the flux density reaches a maximum and start to oversaturate the cores, a decrease in motor performance is expected [55]. Therefore, for an MSRM, the stator flux density, 𝐵𝑠 is assumed to be equal to the maximum flux density, 𝐵𝑚𝑎𝑥 and, therefore, operating at the knee value obtained from the B-H characteristics [53]. 108 B (Tesla) 5.2.3 Windings Conventional SRMs have concentrated windings around each stator pole, with each winding pair connected in series or parallel on diametrically opposite stator poles. However, as in the case of the E-core in chapter 4, the proposed MSRM has two cylindrical coils wound around a single E- core. The phase winding produces the required flux density in the air gap, owing to excitation current and result in output power of the motor. Thus, the objective of the coil design was to achieve the necessary flux density in the air gap region with minimal copper and iron losses. The parameters of the coil design were the winding slot space, the coil dimensions, the number of winding turns, the switching frequency, the maximum permissible current density, and the thermal effect of the winding [55]. 5.2.3.1 Slot space The winding space of a coil, also known as the slot area, was defined as the rectangular cross- sectional area between two poles, as shown in Figure 5-15, with the area defined as 𝑎 ∗ 𝑏. The cross-sectional area of the winding was determined to enclose an area of 512 mm2. Figure 5-15: Winding slot area for a single E-core The number of conductors that fit into the designated cross-sectional area of a winding was restricted by the fill factor (𝐹𝐹). For the proposed MSRM, round conductors are used instead of rectangular conductors, although more windings of rectangular conductors could fit in the given slot space. The simplest winding types are characterised by round conductors. Round conductors are also less expensive and easier to wind than rectangular conductors. Rectangular conductors 109 experience high mechanical stress when the conductor is bent around the corners of the stator cores. Therefore, rectangular conductors are seldom used in small or medium size SRMs. The 𝐹𝐹 of a round conductor was derived from the ratio of a circular area to the area of a square, where the square tangentially surrounds the circle. The theoretical fill factor, when calculated, is 78.54% for a round conductor and 100% for a rectangular conductor. However, the practical fill factor for hand-wound coils was found to be as high as 40% [77]. When using specialised winding machines to wind concentrated windings, the practical fill factor is 60% [55]. Even higher fill factors can be achieved when using a pressed coil [156, 157]. 5.2.3.2 Conductor gauge In parallel design, along with defining the slot area in the section above and fitting the required number of winding turns, the conductor size should be defined. According to the current density, an important parameter in an electric motor, the conductor size should be chosen. Current density is defined as the ratio of RMS current to the bare copper area, given as: 𝐼𝑅𝑀𝑆_𝑐𝑜𝑖𝑙 𝐼𝑅𝑀𝑆_𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 Current density: 𝐽 = = (47) 𝐴𝑠𝑠 ∗ 𝐹𝐹 𝐴𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 Where 𝐼𝑅𝑀𝑆_𝑐𝑜𝑖𝑙 is the RMS value of the current through the coil, and 𝐼𝑅𝑀𝑆_𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 is the current through a single conductor when stranded wire is used. 𝐴𝑠𝑠 is the winding space, or slot area as shown in Figure 5-15 and 𝐴𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 the cross-sectional area of a single conductor. The cross- sectional area of a single conductor constitutes a circular area, as per the AWG size. By design, it was chosen to accommodate the required conductors so that the current density through each coil does not exceed the maximum permissible value. Usually, a current density of 6 A/mm2 is specified for electric motors with natural cooling [55, 158]. This current density is usually the limit of PMSMs that have the risk of demagnetisation. Therefore, no permanent magnets are employed in an SRM. Thus, higher current densities can be tolerated and the motor is mainly dependent on the thermal limits of the winding insulation [55, 77]. If the specified current density is exceeded during the design stage, either the rated current has to be minimised or the conductor gauge has to be increased. 5.2.3.3 Winding turns The slot area, conductor gauge, and winding turns were an iterative process during the design of the proposed MSRM. Following the process, the coil was designed to obtain the rated torque at a fixed speed of 550 rpm operating under CCC. Multiple iterations were made to find the coil design that offered the required torque at a current density of 6 A/mm2. The current density of 6 110 A/mm2 was chosen as the limit of the overload torque-speed characteristics to keep copper losses at a minimum under overload conditions. Multiple 3D FEA models of different winding numbers were simulated. For these simulations, shown in Figure 5-16, the supply voltage, the core shapes, the slot area, and the current limit were kept constant. Note that, since the slot area was kept the same, the winding numbers changed the conductor sizes and the coil resistance. Therefore, in the case of the simulations shown in Figure 5-16, a larger conductor was used when the number of windings decreased. N=30 N=35 N=40 N=45 N=50 50 40 30 20 10 0 60 50 40 30 20 10 0 5 7 9 11 13 15 17 19 21 Time (ms) Figure 5-16: Torque and single-phase current waveforms when the number of winding turns is changed. The coil of 40 turns was chosen for the proposed MSRM, as the torque waveform was in between the stages of constant torque and constant power operation, as observed from the torque-speed profile in Figure 5-4. Thus, for speeds lower than 550 rpm, the torque will remain constant, and for speeds above 550 rpm, the torque will decrease with the increase of speed while maintaining constant power. For a coil of 40 turns, a 10-gauge conductor seemed to be an appropriate choice for the design. For up to 2600 Hz switching frequency, it can utilise 100% of the conductor area. However, a 10-gauge conductor can be difficult to wind by hand. Alternatively, five 17-gauge conductor strands were selected for the proposed MSRM. The five stranded conductors were equivalent to the 10-gauge conductor in terms of resistance, maximum allowable ampacity, and allowed for higher switching frequencies. The five stranded 17-gauge conductors will also be easier to wind around the stator cores. 111 Current (A) Torque (Nm) 5.2.4 Thermal considerations Thermal management is a crucial aspect of electrical machine design, as high temperature inside the motor results in higher winding resistance, and hence higher copper losses in the winding. Thermal management is also the limiting factor of overload capability. As discussed in §5.1.2, SRMs offer better overload capability than permanent magnet motors, where the thermal limits of the permanent magnet are limited by the risk of demagnetisation. The thermal limits of an SRM are limited to the winding insulation, and therefore an overload capability of 5 to 10 times the rated torque of the motor can be achieved [159]. Thus, allowing greater operational freedom under transient operations. This section considered the thermal effects of the windings. The exact thermal behaviour of an electric motor is impossible to model due to the many variable factors of unknown loss components, airflow behaviour inside the machine and the operating cycle [160]. Various methods such as FEA and computational fluid dynamics (CFD) were proposed to model thermal behaviour. However, a certain degree of inaccuracy exists from the limitations, assumptions and boundary conditions of the modelling. Often, verification of thermal analysis by experimental testing is required to fully understand the thermal effect [160]. A thermal analysis simulation of the proposed MSRM is not within the scope of this study. Even though a complete thermal analysis was not part of the study, thermal simulations of the windings were done to ensure that the proposed MSRM operate within its temperature limits, as prescribed by the winding insulating material. These simulation results will help prove that the electromagnetic design of the MSRM can operate using the proposed conductors. The conductor considered for the proposed MSRM belongs to the thermal class of Class B, with a maximum temperature capability of 130˚C. Thermal analysis in an electrical motor is usually accomplished by applying the rated voltage under load to ensure rated current. This ensures that the rated losses occurre continuously inside the electrical motor, and once the steady-state temperature inside the motor is reached, the measured temperature can be documented. The temperature can be measured at different locations inside the motor, most typically against the windings [77]. For an MSRM, Anas Labak used a somewhat different approach, where a continuous DC current was applied to the winding [77]. The DC current through the winding was 25% higher than the rated current. This additional amount of current was deliberately passed continuously to justify the heat that would have been generated due to iron and stray losses under transient operations [77]. 112 A two-way steady-state thermal analysis using Ansys® Maxwell and Ansys® Fluent was used to simulate the temperature of the windings under excitation. The boundary conditions of natural convection were applied to the model with a convection film coefficient of 10 W/m2K. The value of the convection film coefficient was chosen from [161], where the thermal analysis of a transformer was evaluated. The steady-state thermal analysis of the winding temperature-current curve is shown in Figure 5-17. 22˚C Ambient 35˚C Ambient 130 110 90 70 50 30 10 0 10 20 30 40 50 60 Current (A) Figure 5-17: Steady-state thermal simulation From the temperature-current curve, it was observed that an ambient temperature of 22˚C was used. This is similar to the experimental ambient temperature of the thermal analysis of an MSRM by Anas Labak [77]. Since the Sasol Solar Challenge is held in September and South Africa is known for warm weather, the ambient temperature can be much higher than 22˚C. Therefore, three steady-state temperatures of the winding were assessed when an ambient temperature of 35˚C was assumed. It is seen that the temperature-current curve maintains the same shape, though only starting from the provided ambient temperature. Thus, the current limit can be adjusted based on the ambient temperature of the location. Assuming a winding hot spot of 20˚C higher than simulated on the outer surface of the coil, as done by Anas Labak, the maximum current at which the motor can operate safely without exceeding the thermal capacity of the winding insulation material was estimated at 55 A. Therefore, when an ambient temperature of 35˚C was expected, the motor could still operate safely at an excitation current of 45 A. 5.3 Finite element analysis Following the design process, shown in Figure 5-5, the proposed MSRM was designed to meet the specifications set out in §5.1, p.89. The design process went through a variety of iterations to obtain the proposed MSRM, with dimensions summarised in Table 5-5. During the process, the 113 Temperature (˚C) same numerical modelling methods, demonstrated in chapter 4 were used. This process involved the design and development of an MSRM and the analysis of its magnetostatic and transient characteristics. As mentioned previously, validating the design by experimental testing of a prototype will be the next step. However, due to the manufacturing & financial constraints (§1.5.3, p.10), the motor was only simulated using FEA. Therefore, this section analyses the proposed MSRM using the same boundary setup, mesh setup, excitation setup, solution, and analysis setup as described in chapter 4 to provide its magnetostatic and transient characteristics. These characteristics can eventually be used for validation when a prototype is manufactured in future studies. 5.3.1 Static analysis A 3D magnetic flux distribution of an E-core is shown in Figure 5-18a. The E-core shown is at an aligned position with an excitation of 24 A. Figure 5-18b shows an E-core at an aligned position with excitation of 40 A. It is observed that the maximum flux density at the stator poles is around 1.4 T and 1.8 T when excited. The flux at an excitation of 24 A is at the limit of the knee point value, as discussed in §5.2.2.1. An RMS current of around 23 A results in rated torque. Note that the flux density in the stator and rotor cores will not be obtained at the aligned positions during operation. This is because the conduction angle stops the excitation at an angle before the aligned position is reached. Therefore, designing the core to operate at a flux density equal to the knee point of the magnetic material under rated current is an extremity to ensure extreme saturation does not occur during operation. (b) (a) Figure 5-18: Flux distribution in an E-core at aligned position under excitation of (a) 23 A; (b) 40 A 114 The flux linkage curve of a phase winding is shown in Figure 5-19a. The flux linkage is shown for both the aligned and the unaligned positions with an excitation current ranging from 0 A to 50 A, in steps of 2.5 A. The static torque of the proposed MSRM is shown in Figure 5-19b. Static torque is simulated over half an electrical period under excitation current of 10 A to 60 A, in steps of 10 A. 0.25 0.2 Aligned position 0.15 0.1 Unaligned position 0.05 0 0 5 10 15 20 25 30 35 40 45 50 Current (A) (a) 14.0 12.0 60 A 10.0 8.0 6.0 4.0 10 A 2.0 0.0 0 2 4 6 8 10 12 Position (˚) (b) Figure 5-19: Magnetic characteristics of the proposed MSRM. (a) Flux linkage; (b) Static torque 5.3.2 Transient analysis As stated in §5.3.1, the same setup procedure discussed in §4.4, p.76 was followed. However, a difference in the setup was where the rotary region or ‘band’ as it is known was considered the outer region of the motor, instead of the inner region. The difference in the band setup was due to the proposed motor consisting of an outer rotor topology and not an inner rotor topology. The MSRM validated in chapter 4 consisted of an inner rotor topology. Additionally, only the Cylindrical Gap Mesh and Clone Mesh Density were disregarded by Ansys® Maxwell during the setup of an outer rotor motor even though the same mesh setup was used as discussed in §4.4.1.3, p.78. The mesh of the proposed MSRM is shown in Appendix C, Figure C-1, p176. 115 Torque (Nm) Flux linkage (Wb) The simulated steady-state torque and speed waveforms are shown in Figure 5-20. The steady- state operations shown are simulated at speeds of 400 rpm and 750 rpm. In these simulations, the DC-link voltage was 95 V and the turn-on and turn-off angles were 0° and 7.5°. Under low- speed operation, the current was restricted to 51 A, with a hysteresis band of 4 A, as shown in Figure 5-20a. 50 40 30 20 10 0 60 40 20 0 5 7 9 11 13 15 17 19 21 23 25 Time (ms) (a) 25 20 15 10 5 0 40 30 20 10 0 5 7 9 11 13 15 17 19 21 23 25 Time (ms) (b) Figure 5-20: Simulated steady-state torque and phase current waveforms: (a) Current chopping control operation at 400 rpm; (b) Single pulse control operation at 750 rpm The steady-state torque and current waveforms of 400 rpm and 750 rpm are shown, instead of the rated speed of 550 rpm. The speed of 400 rpm will be in the region of constant torque, and the 750 rpm simulation will be in the region of constant power. These speeds are chosen to 116 Current (A) Torque (Nm) Current (A) Torque (Nm) demonstrate the difference between torque and current waveforms when operating using CCC and SPC, as discussed in §2.1.3, p.22. When operating at 550 rpm, the torque and current waveform operate using both CCC and SPC. SPC will be used until the current reaches the current limit, and thereafter CCC will be used. 5.3.3 Conduction angles Analysing the steady-state performance of the 400 rpm and 750 rpm shown in Figure 5-20, the following was observed. At 400 rpm, a torque of 32 Nm was produced resulting in mechanical output power of 1.32 kW and at 750 rpm, a torque of 14.782 Nm was produced resulting in mechanical output power of 1.16 kW. Comparing the power-speed operating points with the rated power-speed profile, shown in Figure 5-4, it is observed that constant output power was not obtained at 750 rpm. Thus, a 160 W less than the expected constant power-speed operation was obtained. The difference in the power-speed operating point was due to the turn-on and turn-off angles as discussed in §2.1.3.2, p.23. The turn-on and turn-off angles can have a significant effect on the average torque output of an SRM, as shown in Figure 5-21. Demonstrating the effect of turn-on and turn-off angles. Two turn-on and turn-off angles were chosen to simulate. Thus, from the two turn-off angles and two turn-on angles, four conduction angles were possible, as was simulated. 0-7.5 0-8 -1-7.5 -1-8.5 40 30 20 10 0 50 40 30 20 10 0 1 3 5 7 9 11 13 Time (ms) Figure 5-21: Simulated steady-state torque and phase current waveforms when changing the conduction angles at 750 rpm 117 Current (A) Torque (Nm) Optimising the turn-on and turn-off angles form part of the motor controller. The design of the motor controller is not part of the scope of the study. Therefore, the turn-on and turn-off angles were kept constant during all steady-state simulations at all torque-speed operating points. Therefore, changing the conduction angles during the simulations shown in Figure 5-21 was merely to demonstrate the effects of the conduction angles on motor performance. The simulated data, for the possibilities of the conduction angles were summarised in Table 5-7. From the analysis, it was seen that the combination of the turn-on and turn-off angles of -1˚ and 7.5˚ was near the specified power of the motor. The conduction angle can be optimised to obtain the mechanical output power, as per design specification. However, to achieve the specified torque-speed profile, shown in Figure 5-4, the conduction angle should be analysed at each operating speed, as the conduction angles will differ at each torque-speed operating point. Table 5-7: Performance characteristics when changing the conduction angles at 750 rpm Turn-on; Turn- RMS phase Average torque Output power off angles current (A) (Nm) (W) 0˚; 7.5˚ 14.8 14.7 1151.5 0˚; 8.5˚ 16.5 16.9 1327.3 -1˚; 7.5˚ 21.0 23.8 1869.2 -1˚; 8.5˚ 23.2 26.6 2089.2 Note that the output power at the turn-on and turn-off angles of -1˚ and 8.5˚ produced higher output power. However, more RMS current was used for motor operation, and as a result the conduction angle combination was not necessarily more efficient. In [117], Seubsuang Kachapornkul et al. studied the performance improvements of a four-phase 8/6 SRM and a three phase 6/4 SRM by adjusting the turn-on and turn-off angles in search for the turn-on and turn-off angles that provide either optimal torque or efficiency. It was found that conduction angles optimised for efficiency provided an efficiency of around 5% difference at high speeds compared to the efficiency when the turn-on and turn-off angles were optimised for torque and an efficiency difference of 10% at low speeds compared to the efficiency when the turn-on and turn-off angles were optimised for torque. For the turn-on and turn-off angles optimised for torque, it was found that the output torque of the motor was higher than the output torque obtained from the turn-on and turn-off angles optimised for efficiency. It was noted that the operating comparisons were made at fixed motor speed, but not at the same torque. Thus, this will have an influence of the torque-speed characteristic graph, rated motor parameters and the efficiency map. Therefore, a motor controller should be designed for either efficiency or torque, based on 118 the application the motor will be used in [1]. It is recommended that future studies design a motor controller for the proposed MSRM to maximize efficiency for the full operating range. This motor design will indicate the efficiency improvement the conduction angles have on the motor performance when comparing the same operating point, i.e., equal speed and torque. 5.4 Performance characteristics Using the transient simulations, at different steady-state speeds, the performance characteristics of the proposed MSRM were obtained. The performance characteristics observed were the predicted torque-speed characteristics of the proposed MSRM and the efficiency map of the MSRM. The efficiency map provides efficiency at the full operating range of the motor. The efficiency map in this study was necessary to evaluate the proposed MSRM. The evaluation of the proposed MSRM is provided in §6.3.2, p.141. The proposed MSRM ratings were obtained by multiple 3D FEA simulations, summarised in Table 5-8. The resistance of a phase winding was calculated as the resistance depends on the conductor length and gauge. The predicted torque-speed characteristics of the proposed MSRM are provided in the following section. Table 5-8: Ratings of the proposed MSRM The calculated phase winding resistance (𝛀) 0.156288 DC-link voltage (V) 95 Rated current (A) ≈ 23.7 Rated torque (Nm) ≈ 32 Rated speed (rpm) ≈ 550 Rated power (kW) ≈1.84 From Table 5-8, it is seen that the specified power, summarised in Table 5-2, p95 was obtained for the proposed MSRM. However, this was only the rated torque-speed performance and not a full indication of the performance. Further performance evaluation is provided in the following sections. 119 5.4.1 Torque-speed characteristics Observing the torque-speed characteristics of the proposed MSRM, multiple simulations were run. Each simulation was a steady-state analysis, simulated at different speeds. Once completed, the data of each simulation were analysed and tabulated to construct the torque-speed profile. The torque-speed profile, constructed from multiple FEA simulations, is shown in Figure 5-22. The torque-speed curve of the FEA simulation was compared with the design-specified torque- speed characteristic profile. FEA Design Specification 35 30 25 20 15 10 5 0 200 300 400 500 600 700 800 900 Speed (rpm) Figure 5-22: Torque-speed characteristics of the proposed MSRM In Figure 5-22, it is observed that the torque drops rapidly beyond 550 rpm. As mentioned in §5.3.3, the simulations were conducted at constant conduction angles. Therefore, the constant power region was not obtained, but rather a falling power region, as reviewed in §2.1.3.1, p.22. For a constant power region beyond 550 rpm, the conduction angles should be suitably selected. For improved performance or efficiency, the conduction angles should be optimised. 5.4.2 Efficiency map The efficiency map of the proposed MSRM is shown in Figure 5-23. The efficiency map was constructed from various torque-speed profiled simulations (Appendix C.3, Figure C-4, p.179). The torque-speed profiles under the rated torque-speed characteristics were simulated by employing lower source voltages and current limits. Similarly, the overload region was simulated by employing higher source voltages and current limits. From each torque-speed profile, the output power is known at each operating point. For the same simulation, the phase voltage and phase current curves is provided by Ansys® Maxwell. Using 120 Torque (Nm) equation (56), p.140, the input power of each phase is calculated for each operating point that was simulated. When multiplying the input power of a single phase by three, the total input power of the motor is obtained. Thus, knowing the input power and output power at each torque-speed operating point of the simulation, an efficiency curve can be constructed. Between these efficiency curves, interpolation on the x-axis to the z-axis and on the y-axis to the z-axis was done to obtain data points in between the curves for construction of an efficiency map. The axis of the efficiency map is as follow: the x-axis represents the speed, the y-axis represents the torque, and the z-axis represents the efficiency. Using Matlab, the data of the x-axis, y-axis and z-axis are plotted using a contour plot in order visualise the 3D data using a 2D plot as shown in Figure 5-23. The efficiency map was provided to the extent of the overload torque-speed characteristics. The rated torque-speed characteristics were provided in the efficiency plot, shown by the black striped line and the operating points of the Mitsuba M2096-DII were plotted on the efficiency map, shown by the white dots. The expected contour line with the highest efficiency in the motor is provided by the yellow curved line. This contour line was drawn based on visual representation of the efficiency contours found for an SRM in literature (Figure 2-21, p.47). The contour lines for efficiency of the proposed MSRM differ from the yellow contour line. However, the difference may be the result of an efficiency map contour of an MSRM compared to an efficiency map contour of a conventional SRM. It is uncertain what efficiency map contour can be expected from an MSRM, as no efficiency maps for an MSRM was found in literature. Thus, further studies are proposed to analyse the difference of an efficiency map between a conventional SRM and MSRM. The construction of the efficiency map required the analysing of steady-state simulations, interpolating the data, and constructing an efficiency map as shown in Figure 5-23. However, Ansys® Maxwell offered a machine toolkit to automatically generate an efficiency map of the analysed motor. The machine toolkit will automatically simulate each operating point at the highest efficiency or torque operation, depending on how the machine toolkit is set up. Unfortunately, using the machine toolkit for SRMs was not yet functional with the release of Maxwell 2021R1 and Maxwell 2021R2. It was unknown when the machine toolkit of an SRM will be functional. The toolkit will provide an easy and time-saving method to construct an efficiency map. Note that the elapsed simulation time of each steady-state simulation took around 3 to 8 hours. Thus, constructing an efficiency map for the proposed MSRM took a considerable amount of time. When the functionality of the machine toolkit supports an SRM, it is proposed to construct an efficiency map of the proposed MSRM and compare the result with the efficiency map constructed, shown in Figure 5-23 and, if possible, an efficiency map constructed from experimental data. 121 Figure 5-23: The constructed efficiency map of the proposed MSRM To increase the motor efficiency of the proposed MSRM, a motor controller with optimised conduction angles for efficiency was proposed. However, a few mechanical design changes can also be considered. The first consideration is to design a 12/8 MSRM or 12/20 MSRM for the same torque-speed characteristics. Thereafter the efficiency map should be analysed to evaluate the effect of the pole configurations on the motor efficiency and operation. Other mechanical considerations are to optimise the pole embrace, pole area, and winding design. Optimising the pole area will influence the effect of flux density during operation, and altering the core to an extent could decrease flux leakage between the stator and rotor poles. Minimising flux leakage will provide higher torque for the same current excitation. The winding design is included as an optimisation parameter such that a parallel connection for a design could potentially offer increased efficiency. However, various winding designs, including conductor types, should be analysed in future studies. 5.5 Summary of the motor design A 12/16 E-core MSRM, rated at 1.84 kW was designed following the principles of Vanessa Siqueira De Castro Teixeira et al. [51], Nikunj R Patel et al. [75, 106, 74, 53], and Anas Labak [52, 57]. Power specifications were obtained by analysis of the Mitsuba M2096-DII evaluation results followed by the geometric design. The geometric design followed an iterative process, shown in Figure 5-5, p.96 to obtain the geometric parameters of an E-core with a corresponding winding design. The core, limited by geometric constraints, was designed to operate at the knee 122 point of the B-H characteristics of the chosen magnetic material. This was to ensure that the MSRM operates in a saturated region, although not oversaturated. The winding design ensured that the motor operated at the required current density. The selection of the conductor gauge was made in conjunction with the geometry design. This was because the winding space, winding turns, and fill factor were each a variable of the winding design. Although the winding was designed to operate at a specified current density under rated current, thermal analysis was provided to ensure the motor operate at respectable thermal conditions. Thermal analysis of a coil winding provided the maximum current that the coils can operate at while operating within the thermal limits of the magnetic material insulation. Operating within the thermal limits of the magnetic material ensured that the motor was not damaged while under strenuous operating conditions. After the core and winding design, the proposed MSRM was analysed. A range of transient simulation data was used to construct an efficiency map of the proposed MSRM. The constructed efficiency map was used to evaluate the proposed MSRM in a technique identical to the Mitsuba M2096-DII. Evaluation of the proposed MSRM is provided in chapter 6. When a prototype of the proposed MSRM is manufactured, the modular rotor segments, of rectangular shape, can be inserted into a cylinder of low magnetic permeability material. Similar materials can be used to house the stator cores in a single structure. However, the design of a motor housing would involve a comprehensive stress analysis and would most likely be coupled with a thermal and vibration analysis to ensure a complete design of the MSRM. During the electromagnetic design of an MSRM, many design aspects were ignored that include the assessment of acoustic noise levels, vibrations, bearing selections, housing design, and dynamic thermal analysis. These aspects were ignored as they extend the scope of the study, and require experience in different engineering field, i.e., aerodynamic flow analysis, thermal analysis, stress and vibration analysis, material selections and electronic design. All of these engineering fields need to be integrated to one motor design for complete finalisation. The aspects of acoustic noise levels, vibrations, bearing selections, housing design, and dynamic thermal analysis are proposed for future studies, and thereafter integrating the studies with one another to form a complete motor analysis that can be built. 123 CHAPTER 6 EVALUATION OF A TRACTION MOTOR In accordance with the objective of this study, this chapter focuses on the evaluation of a traction motor for solar vehicle application. This chapter discusses a simplified drive cycle where the efficiency map of a traction motor is used to analytically propel a solar vehicle through the drive cycle using only the energy extracted from the sun. When comparing the driving distance achieved by one traction motor with another, the most efficient motor is established, provided the same variable factors are used, i.e., the weather effects, time of year, route, and road surfaces. The chapter provides the evaluation of the Mitsuba M2096-DII, currently used as the traction motor in the solar vehicle of the NWU. The evaluation of the Mitsuba M2096-DII was used as a comparative baseline for the proposed MSRM and to stipulate the power specifications for the proposed MSRM (§5.1, p.89). Subsequently, the proposed MSRM was evaluated along the same drive cycle and input parameters as the Mitsuba M2096-DII. This chapter concludes the assessment of whether the proposed MSRM is a viable contender for solar vehicle applications. 6.1 Drive cycle as a method of evaluation The performance of a vehicle is evaluated by performing a dyno test for various driving cycles during its development phase. The drive cycle allows the development and comparison of fuel economy, emissions, and estimated driving ranges for ICE vehicles. Similarly, the expected driving distance and energy consumption of a traction motor can be evaluated. A driving cycle is classified as a model driving cycle or as a transient driving cycle [162, 163]. A model driving cycle consists of constant speed operation and does not represent an actual driving pattern. The model driving cycle is mainly used for specific applications, i.e., an emission test. The transient driving cycle represents an actual driving pattern that includes acceleration, deceleration, and constant speed operations. However, a significant difference between real- world applications and a transient driving cycle can still be expected. Different driving patterns can be used in a transient driving cycle. Driving patterns are based on both city and highway driving. Common driving cycles used by automotive manufacturers include the Federal Test Procedure-72 (FTP-72), the New European Driving Cycle (NEDC), the Highway Fuel Economy Test (HWFET) and the Indian Driving Cycle (IDC) [163, 164]. In this study, a numerically simulated drive cycle is used to evaluate a traction motor for solar vehicle application. This chapter compiles the drive cycle and evaluate both the Mitsuba M2096- DII BLDC motor and the proposed MSRM for comparison against each other. Comparing these 124 traction motors would support the justification that the solar vehicle could benefit from using an SRM as the traction motor. 6.1.1 Construction of a drive cycle The purpose of the Sasol Solar Challenge is to maximise the driving distance each day using only the energy extracted from the sun to charge the batteries. The team acquiring the furthest distance at the end of the 7 days is the winner of the Sasol Solar Challenge. Thus, having a traction motor that provides the best performance whilst using the least amount of energy would be beneficial for a team in these types of solar races. Evaluating a traction motor in a drive cycle that represents the Sasol Solar Challenge, should provide an expected driving distance and energy usage. This evaluation method would significantly support the decision on which traction motor to use in the Sasol Solar Challenge. Preferably, the numerical drive cycle simulation to evaluate a traction motor should include all vehicle dynamics, weather conditions, the solar position with respect to the vehicle location, and the precise energy usage of the traction motor. Incorporating all these factors into the evaluation would accurately predict the overall distance the traction motor could reach. However, it is difficult to include all these influencing factors, and thus a simplified approach has been proposed to evaluate a traction motor. When all influencing factors are held constant between the evaluation of the different traction motors, the best traction motor can be determined. In this section, the simplified approach of a drive cycle is constructed. The drive cycle is constructed in three sections and was interactively simulated to evaluate a traction motor for solar vehicle application. These sections consist of the following. 1. The output power required from the traction motor to propel the vehicle at a certain speed and road gradient. 2. The input power that is necessary to achieve the output power. This is the power used by the electric motor to achieve the mechanical output power. 3. The power availability during the drive cycle. This is the power extracted by the PV array. The three sections are used interactively to evaluate a traction motor. The procedure to evaluate a traction motor is described in §6.1.2, p134. 125 6.1.1.1 Output power The power used to propel the solar vehicle is known as the output power or often referred to as the mechanical output power of an electrical motor. The mechanical output power of an electric motor is the product of torque and rotational speed. In the construction of the drive cycle, the mechanical output power required from the traction motor was obtained from a route profile and vehicle dynamic equations. The pre-defined and simplified route profile is shown in Figure 6-1, along with the route gradient at route sections. The route chosen for the drive cycle is the R53, between Potchefstroom and Parys. The route is 47.5 km long and data at each 450 m route interval were obtained. The route data include the route altitude and the average route gradient of each section. The pre-defined route data provided in 450 m sections were obtained from plotaroute.com [165]. A simplified route of the drive cycle was created by placing the route sections in order of ascending road gradient. Thus, starting at the highest altitude of the pre-defined route, the lowest gradient is used to determine the altitude at the end of the first route section. Thereafter, the altitude for the next route section using the next road gradient is calculated and so forth.. The pre-defined route profile, simplified route profile and route gradients are shown in Figure 6-1. The route profiles show the route altitude (height above sea level). However, the altitude had no effect on the drive cycle and was only a representative of the route using the route gradient of each section. Pre-defined route Simplified route 1550 1500 1450 1400 1350 1300 3 2 1 0 -1 -2 -3 -4 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 Distance (km) Figure 6-1: The pre-defined and simplified route profile and route gradient 126 Gradient(˚) Altitude (m) The pre-defined route is typically used to evaluate a traction motor to evaluate the energy usage of the traction motor. However, the simplified route was used to demonstrate the use of a drive cycle when evaluating two or more traction motors. Even though an accurate travelling distance will not be obtained when comparing the travelling distance to experimental test data, the simplified route provides direct comparison between two traction motors. Therefore, to accurately determine the travelling distance a traction motor can propel the solar vehicle, which can also help to predict race strategies in solar races, a comprehensive drive cycle through the pre-defined route, including all external factors that have an effect on vehicle characteristics and power usage should be considered. Thus, a comprehensive drive cycle to predict race strategy for the solar vehicle is proposed as a future study. To demonstrate the drive cycle when comparing the proposed MSRM to the Mitsuba M2096-DII, the following assumptions are made for the simplified route.  The surface of the road is the same throughout the route. This means that water, gravel, potholes, or road friction do not play a role during the evaluation.  The route connected as a loop is considered an oval. The oval does not have excessive road curvatures that require deceleration and acceleration. Thus, the route is almost a straight path.  The use of momentum to climb a hill is excluded from the drive cycle.  By law, the maximum speed of the pre-defined route is 100 km/h. The Mitsuba M2096-DII can reach a top speed of 65 km/h on level road, thus the maximum speed allowed for the drive cycle is chosen as 75 km/h for downhill sections. Using vehicle dynamic equations, the mechanical output power required from the traction motor can be calculated at a specified velocity and route gradient. Vehicle dynamics is based on the direct application of Newton’s second law for longitudinal dynamics of a vehicle, as shown in Figure 6-2. Figure 6-2: Free body diagram of the longitudinal forces acting on the vehicle 127 The principle of the force balance is presented in equation (48). The traction force, 𝐹𝑇𝑟𝑎𝑐𝑡𝑖𝑜𝑛, generated by the traction motor must overcome the sum of all resistive forces acting on the vehicle: aerodynamic drag, 𝐹𝑑𝑟𝑎𝑔; slope force, 𝐹𝑠𝑙𝑜𝑝𝑒 (a component of the vehicle weight), and the friction force of the tyres, 𝐹𝑡𝑦𝑟𝑒 [166, 167]. Finally, the traction force can be represented by the torque production of the traction motor, 𝜏. Torque is the product of traction force and the radius of the wheel, provided in equation (52). Force balance: 𝐹𝑇𝑟𝑎𝑐𝑡𝑖𝑜𝑛 = 𝐹𝑑𝑟𝑎𝑔 + 𝐹𝑡𝑦𝑟𝑒 + 𝐹𝑠𝑙𝑜𝑝𝑒 (48) Aerodynamic drag 1 𝐹𝑑𝑟𝑎𝑔 = 𝐶𝑑𝜌𝐴𝑣 2 (49) force: 2 Where 𝐶𝑑 is the aerodynamic drag coefficient, 𝜌 is the density of air (𝑘𝑔/𝑚 3), 𝐴 is the frontal area of the vehicle (𝑚2) and 𝑣 is the speed of the vehicle (𝑚/𝑠). Slope force: 𝐹𝑠𝑙𝑜𝑝𝑒 = 𝑀𝑔𝑎 sin 𝜃𝑠 (50) Where 𝑀 is the mass of the vehicle including the driver (𝑘𝑔), 𝑔𝑎 is gravitational acceleration (𝑚/𝑠2) and 𝜃𝑠 is the angle of the driving surface (˚). 1 3.6𝑣 2 Tyre friction force: 𝐹𝑡𝑦𝑟𝑒 = 𝑀𝑔𝑎(0.005 + ( )(0.01 + 0.0095 ( ) ) (51) 𝑏 100 Where 𝑏 is the tyre pressure (𝑏𝑎𝑟), 𝑢 is the vehicle's speed (𝑘𝑚/ℎ). 𝜏 Traction force: 𝐹𝑇𝑟𝑎𝑐𝑡𝑖𝑜𝑛 = (52) 𝑟 Where 𝜏 is the motor torque (𝑁𝑚) and 𝑟 is the radius of the wheel (𝑚). The solar vehicle evaluated in the drive cycle was the 2020 solar vehicle of the NWU. The main parameters, obtained from the program manager of the NWU solar vehicle are summarised in Table 6-1. The vehicle and driver mass and tyre diameter was measured in the laboratory. The aerodynamic drag coefficient and vehicle frontal area was calculated by several lecturers and students using CFD. 128 Table 6-1: Solar vehicle characteristics Description Symbol Value A vehicle with driver mass (𝑘𝑔) 𝑀 245 Aerodynamic drag coefficient 𝐶𝑑 0.156 Air density (𝑘𝑔/𝑚3) 𝜌 1.225 Vehicle frontal area (𝑚2) 𝐴 1.2831 Tyre Pressure (𝑏𝑎𝑟) 𝑏 5 Tyre diameter (𝑚) 𝑟 0.505 When evaluating a traction motor using the drive cycle, the following assumptions are made for the vehicle dynamics:  External wind forces acting on the vehicle are excluded from the drive cycle. Wind from the front or rear of the car will affect the energy usage as the vehicle requires either more or less torque to maintain a similar speed.  The acceleration force, 𝐹𝑎 = 𝑀𝑎, where 𝑎 is the acceleration, is considered zero when calculating the force balance. For the drive cycle, a constant speed is assumed for each section of the route. 6.1.1.2 Input power Evaluating a traction motor’s energy usage in the drive cycle requires the input power to be known. The input power is defined by the summation of output power, friction and windage, copper and iron losses. However, achieving the same amount of output power by variation of speed and torque will not use the same amount of input power, thus losses is the difference between the input and output power at each operating point. The efficiency, 𝓃, of an electric motor is defined as the ratio between the output power, 𝑃𝑜𝑢𝑡, and the input power, 𝑃𝑖𝑛, with input power further divided into the sum of output power, friction and windage losses, 𝑃𝑓+𝑤, copper losses, 𝑃𝑐𝑢, and iron losses, 𝑃𝐹𝑒. 𝑃𝑜𝑢𝑡 𝑃𝑜𝑢𝑡 𝓃 = = Efficiency: (53) 𝑃𝑖𝑛 𝑃𝑜𝑢𝑡 + 𝑃𝑓+𝑤 + 𝑃𝑐𝑢 + 𝑃𝐹𝑒 Identifying the input power of each operating point requires an efficiency map. An efficiency map is a contour plot of motor efficiency that indicates motor efficiency in the operating range of speed and torque of the motor. Therefore, at the required output power of each route section at a set rotational speed, the efficiency map is used to obtain the input power [168]. The input power is 129 the amount of power used to propel the vehicle and, therefore, in the case of a solar vehicle, extracted from the batteries. The traction motor of the solar vehicles used in these solar races provides power in the range of 1 to 2 kW. To put this into perspective, it is almost the same amount of power as offered from by a hairdryer or kitchen kettle. Although these solar races provide a unique opportunity to showcase new technological ideas and creations, only two companies (Marand and Mitsuba) provide electric motors intended for solar racing events. Both these companies provide a BLDC motor for solar vehicles. 6.1.1.3 Available power Per the definition of a solar vehicle, solar power is used to propel the vehicle. The energy extracted by the PV array during a solar race is stored in the batteries and the traction motor use the energy in the battery to propel the vehicle. The amount of solar power differs depending on the time of day, month, and latitudinal location. Solar energy is referred to as the available energy in the drive cycle. To save energy, solar racing teams attempt to drive ‘energy neutral’. The term ‘energy neutral’ is defined as using the same amount of energy to propel the vehicle as obtained from the PV array. Thus, no battery energy is used to propel the vehicle. For this drive cycle comparison, it is assumed that the vehicle starts with an empty battery, and the energy extracted from the sun is stored in the battery for use, respectively, by the traction motor. This is different from the driving principle used in solar races where a vehicle will typically start the race on a fully charged battery. When the drive cycle is started on a full battery, the driving distance can be improved as there is more available energy to use for the drive cycle. However, depending on the solar race, a team will drive conservative depending on the weather. The solar energy is extracted by the PV array obtained from the solar irradiance. Solar irradiance is based on the solar path observed throughout the year. In Figure 6-3, the solar path of Potchefstroom (lat. 26.7˚S, long. 27.1˚E, alt. 1351 m) is shown [169]. The two astronomical angles describe the solar position with respect to an observer. The solar altitude and solar azimuth are represented by circles and the cardinal directions. As observed in Figure 6-3, the solid yellow lines represent the June and December solstice. The red line represents the solar path on the 14th of September. The date is chosen as the Sasol Solar Challenge usually occurs within that period of the year. 130 Figure 6-3: Solar path and position at Potchefstroom [169] The extraction of solar energy is performed by a PV array on the solar vehicle. In the case of the NWU, the solar vehicle employs a single-axis rotating PV array. The rotation of the PV array allows for more energy extraction than a fixed PV array, due to the rotation improving the angle of the PV surface to the sun. The PV characteristics of the PV array used on the solar vehicle are listed in Table 6-2. Table 6-2: Solar vehicle PV array characteristics Description Value PV area (𝑚2) 4 PV cell efficiency (%) 24.3 131 To calculate the amount of energy extraction by the PV panels during the drive cycle, the following assumptions are made to simplify the setup and process:  Solar radiation is assumed for an ideal sunshine day. Thus, no weather effect or shadows influences the energy extraction of the PV array.  The angle of the PV surface to the sun is assumed to be a constant 80˚ during the drive cycle. Due to having only a single-axis tracking device, the PV cannot be maintained at a perpendicular angle to the sun. This is because the solar vehicle changes direction relative to the sun’s angle during travel, i.e. not travelling in a north-south direction. The World Solar Challenge in Adelaide is a perfect example of how a single-axis tracking device on a vehicle can be fully exploited. This is because the solar vehicles travel in an almost constant north-to-south direction.  The irradiance graph of a single location is assumed usable for the drive cycle as a minimal longitudinal difference between Potchefstroom and Parys exists. This allows the drive cycle over time to only consider one irradiance graph when calculating the available energy from the sun at each time period. If a longer route is chosen, different solar irradiance graphs at each time period should be used to achieve a representable drive cycle. The energy extracted from the PV array is calculated using the solar radiance and a solar tracking PV array at the location of Potchefstroom. The tracking device is similar to a single-axis rotating PV array. Thus, a perpendicular angle between the surface of the PV array and solar irradiance could be maintained, which is known as direct radiation. As mentioned in the assumptions above, the PV array surface to the solar irradiance angle will be constant at 80˚. However, an hour before the drive cycle starts, a perpendicular angle is maintained to extract energy from the sun. This is done to have energy available at the start of the drive cycle. A perpendicular angle is used for that hour, since the vehicle can be placed at an optimum angle to accumulate solar energy an hour before the start of each day’s drive in the Sasol Solar Challenge. Then the drive begins. Therefore, the simulated drive cycle is operational from 08H00 to 16H00. Figure 6-4 shows the available solar radiation on a PV array with a 1 m2 (red line) and 4 m2 (blue line) area where direct radiation is maintained. The purple line indicates the extractable energy on a 4 m2 PV array when the PV efficiency of 24.3% is included. Thus, the less than the available radiation from the sun on a 1 m2 PV array is extracted from a 4 m2 PV array. The extracted soar energy from radiation on the PV array of the vehicle is shown by the green line, where the maximum radiation is maintained for the charging time and thereafter the PV array is extracting energy from the sun at an 80˚ angle between the PV surface and the sun. 132 4 3.5 3 2.5 2 1.5 1 0.5 0 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 Time of day Direct radiation of 1 square meter Direct radiation of 4 square meter Energy extracted by PV array with 80 degree surface angle during drive cycle Charge start before vehicle drive Start of vehicle drive End of vehicle drive Energy extractable by PV array from direct radiation Figure 6-4: Radiation over time on the 14th September at Potchefstroom It should be known that solar radiance is only power, as in the case of input and output power. In the drive cycle, the energy usage should be known. Energy is merely the product of power and time, as provided in equation (54). The solar energy extracted by the PV array of the solar vehicle is shown in Figure 6-5. The energy accumulation curve includes both the accumulation curve of a PV array with direct radiation at all times and a PV array perpendicular at an 80° surface to solar radiation angle. Energy: 𝐸 = 𝑃𝑡 (54) Where 𝐸 is energy (𝑊ℎ), 𝑃 the power (𝑊) and 𝑡 is time (ℎ). 133 Radiation (kW/m2) 8 7 6 5 4 3 2 1 0 6 8 10 12 14 16 Time of day Energy extracted by PV array from direct radiation Energy extracted by PV array with 80 degree surface angle during drive cycle Charge start Start of drive End of drive Figure 6-5: Energy accumulation throughout the day It can be observed that around 1 kWh of energy is additionally extracted from a PV array of a perpendicular angle at all times. Thus, a solar vehicle with a rotating PV array can benefit in a solar race. 6.1.2 Drive cycle procedure Using the simplified approach, a traction motor is evaluated when the solar vehicle is propelled through the drive cycle. The drive cycle starts at 08H00 after the initial solar energy is extracted by the PV array between 07H00 and 08H00. The available energy amounts to 582.1 Wh, at which the drive cycle begins. In this evaluation, an energy-neutral operation is used. This means that no energy is extracted from the battery, and only the energy acquired from the sun is used to propel the vehicle. During the drive cycle, a positive energy balance (equation (55)) must be obtained at all times in order for the evaluation to adhere to an energy neutral operation. 𝐸𝑀𝑒𝑐ℎ Energy balance: 𝐸𝑏𝑎𝑙𝑎𝑛𝑐𝑒 = 𝐸𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 − 𝐸𝑢𝑠𝑒𝑑 = 𝐸𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 − (55) 𝜂 Here, 𝐸𝑏𝑎𝑙𝑎𝑛𝑐𝑒 is the energy balance, 𝐸𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 the available energy, 𝐸𝑢𝑠𝑒𝑑 the used energy for propulsion and 𝐸𝑀𝑒𝑐ℎ the mechanical output energy for propulsion. 134 Energy accumulation (kWh) The procedure of the drive cycle is as follows:  Run the traction motor through the simplified route under the operating conditions of: o The most efficient operating points of the traction motor per road section. The most efficient operating point at each road section was determined by calculating the mechanical output required to propel the vehicle at speeds of 5 km/h to 75 km/h in intervals off 5 km/h. Thus, the required output torque was calculated to achieve the desired speed. Thereafter the efficiency at the operating point was obtained using the efficiency map. o The operating point using the least amount of energy for the route section. Because the required output torque is a factor of vehicle speed, the torque requirement is not linear with speed. Therefore, the vehicle is propelled using less energy through the route section than operating at speeds of maximum efficiency. However, it takes longer to propel the vehicle through the route section. o some operating points use less power at lower speed than the most efficient operating point requiring higher speeds. o The maximum operating speed at the given road gradient; and o Constant speed conditions of 10 to 70 km/h in a 10 km/h interval.  Integrate the input power, output power and available power and simulate the drive cycle between the hours of 08H00 and 16H00; using a variety of operating conditions to obtain the maximum driving distance while keeping the energy balance above zero. It is realised that the 47 km pre-defined route could easily be driven within an hour. Therefore, the proposed drive cycle runs as a loop connecting the start and end point of the route. Employing a loop is similar to the Sasol Solar Challenge where loops are used along the main route to increase the driving distance during the race. 6.2 The Mitsuba M2096-DII The Mitsuba M2096-DII is preferred by many solar racing teams, including the NWU. The Mitsuba M2096-DII is a BLDC motor consisting of 32 poles and 36 slots. The expected nominal power is 2 kW at 810 rpm, with a rated efficiency of 95%. By examination of the motor, it was seen that the stator poles are wound using the whole coil type, such that the three-phase circuit of the motor consists of four Wye circuit configurations, connected in parallel with one another. Mitsuba offers several modification options for their motors. These modifications are made to improve the characteristics according to their user requirements. The modifications include a change in permanent magnets, magnetic materials, and coil configurations. These modifications 135 are expensive and additional to the cost of the base motor. The modifications are not a viable solution for many teams when aiming to improve the operating capability of their motor. To improve the Mitsuba M2096-DII of the NWU, the coil configurations were changed to improve the characteristics to the requirements of the solar vehicle. Thus, in this study, the changed configuration is evaluated using the drive cycle. 6.2.1 Characteristics The Mitsuba M2096-DII characteristic graph (Appendix D, p.181) was replicated experimentally in the laboratory. The experimental procedure followed is described in Appendix A, §A.1, p.168. Figure 6-6 and Figure 6-7 show the characteristic graphs of the Mitsuba M2096-DII. The speed and efficiency characteristics of the motor are shown as the load torque increases. Both the datasheet and experimentally obtained data are shown in the torque, speed and efficiency versus DC current curves in Figure 6-6. Speed (Datasheet) Speed (Test data) Torque (Test data) Torque (Datasheet) Efficiency (Test data) Efficiency (Datasheet) 1200 100 1000 80 800 60 600 40 400 200 20 0 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 DC Current (A) Figure 6-6: Mitsuba M2096-DII characteristics from datasheet and experimental tests In Figure 6-6 it is observed that the motor speed is around 17% higher than expected from the datasheet, the motor efficiency is around 10% lower and efficiency starts to increase at a higher load torque than the data provided from the datasheet. This comparison concluded that the traction motor uses a lot more energy than anticipated from the datasheet. The motor was not operating at the best torque-speed characteristic requirements of the NWU solar vehicle, and therefore the coil configuration was modified in the laboratory. The coil configuration was changed from four Wye circuit configurations, connected in parallel to four Delta circuit configurations, connected in parallel. The comparison between the two coil configurations is shown in Figure 6-7. 136 Speed (rpm) Torque (Nm) Efficiency (%) Speed (Wye) Speed (Delta) Torque (Wye) Efficiency (Wye) Torque (Delta) Efficiency (Delta) 1200 100 1000 80 800 60 600 40 400 200 20 0 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 DC Current (A) Figure 6-7: Mitsuba M2096-DII characteristics from Wye and Delta circuit configurations In Figure 6-7 it is observed that the motor rotate at a lower speed and allows an increase in the load torque given the same amount of input current. The delta coil configuration provided a slight efficiency increase when compared to the wye coil configuration. However, it provided a better efficiency range for the required speed of the NWU solar vehicle. These characteristic graphs provide information about the Mitsuba M2096-DII, but it quickly became apparent that the graphs do not contribute useful information about the efficiency of various operating conditions. Efficiency under various operating conditions was necessary to understand the operating capability of a traction motor. This requires an efficiency map, as mentioned in §6.1.1.2. An efficiency map of the Mitsuba M2096-DII connected in a parallel Delta circuit configuration is shown in Figure 6-8. The efficiency map is presented by a colour contour. The efficiency value presented by colour is indicated in the legend, which ranges from a dark blue indicating 0% efficiency to a dark red indicating the maximum of 90% efficiency. The efficiency map is constructed from experimental data, using a similar method to the procedure discussed in Appendix A, §A.1, p168. Using the experimental data, various torque-speed and efficiency graphs were constructed. Interpolating between the efficiency graphs was performed to construct the efficiency map. The difference in the procedure is that a range of speeds is run at a set load torque that is documented and repeated at a different load torque. 137 Speed (rpm) Torque (Nm) Efficiency (%) Figure 6-8: Mitsuba M2096-DII efficiency map 6.2.2 Evaluation results Integrating the available power of solar energy, the output power from the vehicle dynamics, and the input power from the efficiency map, the Mitsuba M2096-DII was run through the drive cycle. The energy evaluation is shown in Figure 6-9. The energy evaluation includes the total accumulation of solar energy, the energy used for propulsion, and the energy balance. Observing the used energy and energy balance waveforms, it is seen that the waveforms tend to have a couple of arc shaped curvatures. These waveforms are due to the simplified route used in the drive cycle. The simplified route, shown in Figure 6-1, has a shallow slope that increases as the road gradient increases. Due to the steep gradient, energy should be stored before the slope can be driven. Energy storage assists in maintaining the energy balance at a positive value. In the circumstance of using an integration method through the pre-defined route and not the simplified route, the energy waveforms will be a linearized waveform. 138 Energy balance Energy output Energy Input 6000 5000 4000 3000 2000 1000 0 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 Time of day (HH:MM) Figure 6-9: The Mitsuba M2096-DII energy usage through the drive cycle The travelling distance and speed when using the Mitsuba M2096-DII as a traction motor are shown in Figure 6-10. Due to the assumption of average speed for each route section, acceleration and deceleration were excluded from the drive cycle. Therefore, starting each loop in the drive cycle assumed the least amount of power usage i.e., the vehicle propels using gravity. Thus, the average speed through each route section does not show a linearized or smooth waveform, as one would expect. This is because the simplified route was used instead of the pre- defined route, and the average speed chosen during the section differed from one another as acceleration, deceleration and average speed changes was not included into the simplified drive cycle. The total distance obtained by the traction motor is 398.25 km with an average speed of 52.145 km/h during the evaluation of an eight-hour drive cycle. Vehicle velocity Distance traveled 90 400 375 350 75 325 300 60 275 250 225 45 200 175 150 30 125 100 15 75 50 25 0 0 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 Time of day (HH:MM) Figure 6-10: The Mitsuba M2096-DII drive distance and speed through the drive cycle 139 Velocity (km/h) Energy (kWh) Distance (km) 6.2.3 Summary of the Mitsuba M2096-DII The Mitsuba M2096-DII was evaluated as a traction motor using the drive cycle. Running the vehicle through the simplified route, a travelling distance of 395.25 km was obtained within the operating time of eight-hours. During that time, the total energy usage of the motor was calculated to be 6.06 kWh. The evaluation provided a baseline for the evaluation of an SRM. Thus, the baseline provided a reference on whether an SRM could be considered a viable contender for solar vehicle application. 6.3 The proposed modular switched reluctance motor The proposed MSRM, designed in chapter 5, consists of a three-phase 12/16 pole configuration. The rated power is 1.84 kW at 550 rpm. The MSRM has 24 coils, with each phase winding connected in series. Chapter 5 provided a comprehensive overview of the proposed MSRM. 6.3.1 Characteristics Multiple torque-speed characteristic curves were simulated to obtain information over the whole operating range so that an efficiency map could be constructed. The multiple torque-speed characteristics that were simulated are shown in Appendix C.3, Figure C-4, p.179. The simulations for the operating range lower than the rated torque-speed characteristics were performed using lower source voltages and current limits. The overload torque-speed characteristics were simulated using higher source voltages and current limits. For each of these torque-speed characteristics graphs, an efficiency curve was obtained. The efficiency of each steady-state simulation was calculated by dividing the output power with the input power. Input power is defined as the product of voltage and current. However, the input power equation of an SRM differs from that of AC motors. The input power of an SRM is calculated from the input current and input voltage waveforms during a period (𝑇𝑠) using equation (56). 𝑞 𝑃 = ∑ 𝑉𝐼 ∆𝑡 Input Power: 𝑖𝑛 𝑇 (56) 𝑠 Interpolating between each efficiency curve of the respected torque-speed graph, shown in Appendix C.3, Figure C-4, p.179 was performed to construct an efficiency map. The efficiency map, shown in Figure 6-11 is presented by a colour contour. The efficiency value presented by colour is indicated in the legend, which ranges from a dark blue indicating 0% efficiency to a dark red indicating the maximum efficiency of 80%. 140 Figure 6-11: Proposed MSRM efficiency map The efficiency map was constructed from simulated data. Therefore, it should be noted that friction and windage losses were excluded from the efficiency map. Due to manufacturing and financial constraints (§1.5.3, p.10), it is recommended to experimentally evaluate the proposed MSRM, after a comprehensive bearing selection process is finalised and a prototype is manufactured. 6.3.2 Evaluation results Similar to the Mitsuba M2096-DII (§6.2.2), the proposed MSRM was run through the drive cycle. The energy evaluation of the proposed MSRM, together with the Mitsuba M2096-DII is shown in Figure 6-12. For the evaluation of the proposed MSRM, the following factors have an effect on the results:  The efficiency map of the proposed MSRM did not account for friction and windage losses. Therefore, the amount of energy used to propel the vehicle in each route section will be higher. Constructing an efficiency map of experimental testing after a prototype is built is recommended.  The turn-on and turn-off angles (§5.3.3, p.117) were kept constant. Optimising these angles can significantly affect motor performance and efficiency [55]. Thus, using an optimised motor controller will greatly affect the efficiency map and, therefore, driving distance when the MSRM is evaluated.  The weight difference of the proposed MSRM was not considered in the drive cycle. In the study, the weight of the vehicle was assumed to be the total weight of the vehicle, driver, 141 and traction motor. However, the difference in weight will affect the torque requirements, as seen by vehicle dynamics (§6.1.1.1, p.126).  The proposed MSRM was not an optimised design, but was simply an XDM to evaluate future development justifications (§1.5.3, p.10). Therefore, optimising the motor design for efficiency will improve the driving distance when evaluated. Energy balance (MSRM) Energy output (MSRM) Energy Input (MSRM) Energy Balance (BLDC) Energy output (BLDC) Energy Input (BLDC) 6000 5000 4000 3000 2000 1000 0 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 Time of day (HH:MM) Figure 6-12: The proposed MSRM energy usage through the drive cycle compared to the Mitsuba M2096-DII BLDC Observing the energy waveforms, the same phenomena occurred as with the evaluation of the Mitsuba M2096-DII (§6.2.2, p.138). Comparing the energy balance in Figure 6-12, it is observed that the energy balance of the proposed MSRM from 12H00 onwards is shaped out of sequence with the Mitsuba M2096-DII. This was due to the propelled speed of the motor not being the same during the two evaluations but merely keeping the energy balance at a positive value while trying to maximise the travelling distance. To maximise the travelling distance, the speed should be maximised. However, the speed was regulated by the usable energy (equations (52), (53) and (55)). Figure 6-13 shows the travelling distance and speed of the proposed MSRM as the traction motor compared to the Mitsuba M2096-DII BLDC. The total distance obtained was 375.975 km with an average speed of 50.036 km/h during the evaluation of the eight-hour drive cycle. 142 Energy (kWh) Vehicle velocity (MSRM) Vehicle Velocity (BLDC) Distance traveled (MSRM) Distance travelled (BLDC) 100 400 375 350 80 325 300 275 60 250225 200 40 175150 125 100 20 75 50 25 0 0 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 Time of day (HH:MM) Figure 6-13: The proposed MSRM drive distance and speed through the drive cycle compared to the Mitsuba M2096-DII BLDC 6.3.3 Summary of the proposed modular switched reluctance motor The proposed MSRM was evaluated as a traction motor using the drive cycle. Running the vehicle through the simplified route, a travelling distance of 375.975 km was obtained within the eight- hour operating time. During that time, the total energy usage of the motor was calculated to be 6.083 kWh. This evaluation provided a good baseline for future design assessments of an SRM. 6.4 Evaluation of the two traction motors Both Mitsuba M2096-DII and the proposed MSRM were evaluated using the drive cycle, constructed in §6.1.1. The operating torque-speed characteristic points of each motor to propel the vehicle through the drive cycle are shown in Figure 6-14. Figure 6-14 shows the speed-torque characteristic points of each drive cycle evaluation. Also shown was the torque-speed characteristic graph of the proposed MSRM as specified in Table 5-2, p.95 and obtained through the simulation data (§5.4.2, p.120). For an alternative XDM, it was proposed to change the specified torque-speed characteristics of the proposed MSRM, such that the rated torque is higher and the rated speed is lower. The proposal to change the torque-speed characteristics was to move the highest efficiency region, as shown in Figure 5-23, p122, to the left of the operating points. Moving the highest efficiency contour region to the left would allow more operating points of the proposed MSRM, as shown in the figure below, to operate using lower input power. Thus, higher efficiency is achieved at the operating point, and therefore the driving distance of the proposed MSRM could be extended. 143 Velocity (km/h) Distance (km) BLDC Specified torque-speed characteristics MSRM Simulated torque-speed characteristics 45 40 35 30 25 20 15 10 5 0 -5200 300 400 500 600 700 800 900 -10 -15 -20 Speed (rpm) Figure 6-14: Operating torque-speed characteristics through the drive cycle A new design is needed when changing the torque-speed characteristics. Additionally, changing the torque-speed characteristics for an alternative design will not necessarily provide an improved efficiency map. Therefore, an iterative design process of various MSRMs is required to obtain the most efficient MSRM. Note that an iterative design for optimised motor performance requires ample time, computing power, and simulation accuracy. 6.5 Summary of the traction motor evaluations The objective of this chapter was to evaluate a traction motor for solar vehicle application. More specifically, to evaluate an SRM for solar vehicle application. To evaluate an SRM, a drive cycle was constructed such that a traction motor has to propel the solar vehicle of the NWU through a pre-defined route using only the energy of the sun. The travelling distance depends on motor performance and energy usage. Thus, by evaluating different motors, the best performing traction motor could be selected from the drive cycle. Both the proposed MSRM and Mitsuba M2096-DII were evaluated using the drive cycle. The Mitsuba M2096-DII was evaluated to use as a comparative baseline to obtain the motor specifications used to design the proposed MSRM. After the design of the proposed MSRM (chapter 5), the proposed MSRM was evaluated. The driving distance and average speed of the two traction motors are summarised in Table 6-3. Compared to the Mitsuba M2096-DII, the proposed MSRM travelled 23 km less than the Mitsuba M2096-DII within the same operating time of eight hours. This is a 5.59% difference in driving distances. 144 Torque (Nm) Table 6-3: Drive cycle comparison Mitsuba M2096-DII Proposed MSRM Difference (%) Distance (km) 398.25 375.975 5.59 Average speed (km/h) 52.145 50.036 4.04 After evaluating both traction motors, it was concluded that the proposed MSRM consumed more energy to propel the vehicle. The proposed MSRM consumed more energy, and therefore less travelling distance was achieved by the proposed MSRM. However, it should be noted that the proposed MSRM was not designed for optimal performance and neither was the motor controller. The motor controller used to operate the proposed MSRM in the simulations used constant conduction angles instead of the optimised conduction angles used to improve motor efficiency. If a motor controller was used to operate the proposed MSRM at the most efficient conduction angles for the required torque and speed, the motor would have extended the total travelling distance. However, the detailed effect the conduction angles have on the efficiency map of the proposed MRM is unknown. Thus, a motor controller operating the motor at the conduction angles of optimised efficiency should be used to construct an efficiency map to evaluate the proposed MSRM. Thereafter, a better understanding will be obtained if the change of conduction angles truly have an effect on the motor efficiency. When an efficiency map is constructed of an optimised MSRM design, a comprehensive selection of bearings, a housing design and friction and windage losses should be included. The friction and windage losses will provide additional losses and therefore decrease the evaluated driving distance. Note that the drive cycle used evaluates the performance of the motors, and does not include the mechanical or structural affects it may have on the evaluated outcomes. A complete mechanical and structural design of the proposed MSRM is recommended as a future study for a complete evaluation of the proposed MSRM. Nevertheless, the proposed MSRM, designed and evaluated as an un-optimised XDM, justify future development of an SRM for solar vehicle application. 145 CHAPTER 7 CONCLUSION Since no SRM has been adequately evaluated against a permanent magnet motor, i.e., a BLDC or PMSM in solar vehicle applications, the objective of this study was to evaluate an SRM for solar vehicle application. The process followed in the study is listed below: 1. Literature review. 2. Validating the electromagnetic simulation methods. 3. Design of the proposed modular switched reluctance motor (MSRM). 4. Constructing a drive cycle. 5. Testing and evaluating the Mitsuba M2096-DII BLDC. 6. Evaluating the proposed MSRM for solar vehicle application. 7.1 Literature review A literature review of the principles and design considerations of an SRM was discussed in chapter 2. From literature it was obtained that an SRM is designed for the specified torque-speed characteristics by considering the aspects of the geometric dimensions, pole configurations, magnetic material properties and winding parameters. Some geometrical variations can be made to improve the efficiency and performance of an SRM. These geometrical variations include the modular, multilayer, hybrid, and transverse constructions of an SRM. It was concluded that an MSRM offered the best efficiency and performance improvement. MSRMs were found to have many advantages, such as independent flux paths, no flux reversals, larger slot spaces for windings, lower rotor inertia, better heat dissipation, and easy manufacturing. The modular construction of an SRM was found to increase efficiency when an MSRM was compared to conventional SRMs. Thus, an MSRM was an appropriate selection for the design of an SRM. 7.2 Validation of the electromagnetic simulation methods A literature review of electromagnetic modelling methods was provided in chapter 3. It was found that finite element analysis (FEA) is the most popular method for solving an electromagnetic problem. The FEA software, Ansys® Maxwell, was used in many of the studies found in the literature and was available for use in this study. 146 The validation of the electromagnetic modelling method was provided in chapter 4. Both the magnetostatic and transient solvers of Ansys® Maxwell were used to create a simulation model of an MSRM. A simulation model of the MSRM designed by Wen Ding et al. in [96, 110, 109, 97, 107, 111] was created to compare the simulation results against the simulated results and experimental data of Wen Ding et al. The magnetostatic solver was used to obtain the magnetostatic characteristics, i.e., flux linkage and static torque of the MSRM. A 5% to 13% deviation occurred between the simulated data and experimental data provided by Wen Ding et al. Because of the effect the geometric parameters and the magnetic material had on the simulations the modelling method deemed acceptable for the magnetostatic simulations. The transient solver was used to simulate the steady-state behaviour of the MSRM. The steady- state simulations of the MSRM was performed using a setup that provided the best accuracy for the amount of computing power and time. The simulation data deviated between 13.11% and 12.884% compared to the simulated and experimental data provided by Wen Ding et al. For these simulation setups, both the stacking factor and coil resistances were unknown. The validation of the electromagnetic simulation methods was concluded that the simulations were set up and followed correctly to obtain adequate results compared to the data of Wen Ding et al. Thus, it was concluded that the same methods and procedures to set up and analyse an MSRM, designed in chapter 5 could be used. 7.3 Design of the proposed modular switched reluctance motor An un-optimised exploratory development model of an MSRM, proposed in §2.6, p.45 was designed in chapter 5. The proposed MSRM consists of a radial flux, outer rotor MSRM. The modular structure as the diameter of the motor can be increased for increased torque operations without increasing the losses in the magnetic material. Thus, the modular structure increases efficiency and performance. An iterative process, involving the geometry design, winding design, flux density observation and the required torque-speed characteristics was followed to design the proposed 12/16 E-core MSRM. . In conclusion, the proposed MSRM specified to a 355 mm diameter, 100 mm axial length, three- phase, 24 coil motor rated at 1.84 kW, at a speed of 550 rpm. A 3D simulation model in the transient solver was used to simulate the proposed motor at a variety of speeds. Simulations 147 provided the output torque and input power. Using a set of these simulation results, the torque- speed characteristic graph of the proposed MSRM was constructed. The efficiency map was constructed from the speed-torque characteristic graphs simulated using different source voltages and current limits. The efficiency map was then used to evaluate the proposed MSRM through the drive cycle. 7.4 Construction of a drive cycle A method to evaluate a traction motor for solar vehicle applications was necessary. To evaluate the proposed MSRM, it was chosen to construct a drive cycle to simulate the propulsion of the NWU solar vehicle through a route using only the extracted energy of the sun to power the traction motor. For the vehicle to operate at a certain speed, a certain amount of torque was required from the traction motor. The torque was a function of speed, the vehicle drag coefficient and vehicle mass. Therefore, using an efficiency map of a traction motor, the input power for the calculated output power was determined. In conclusion, using the drive cycle, the travel distance of each traction motor was determined. 7.5 Testing and evaluation of the Mitsuba M2096-DII The Mitsuba M2096-DII BLDC was tested in the laboratory on a motor test bench. The Mitsuba M2096-DII was tested using the method provided in Appendix A, p.168. The test data was used to construct an efficiency map of the Mitsuba M2096-DII. The efficiency map was then used to evaluate the Mitsuba M2096-DII through the drive cycle. To propel the vehicle through the drive cycle using the Mitsuba M2096-DII as the traction motor, a total travelling distance of 395.5 km was obtained, with a total energy usage of 6.06 kWh. This evaluation set a reference point of what is expected from the proposed MSRM. 7.6 Evaluation of the modular switched reluctance motor for solar vehicle application Evaluation of the proposed MSRM for solar vehicle application was presented in chapter 6. The efficiency map constructed of the proposed MSRM was used to evaluate the proposed MSRM through the drive cycle. The proposed MSRM was used to propel the solar vehicle of the NWU through the drive cycle, similar to the evaluation of the Mitsuba M2096-DII. A total travelling distance of 375.975 km was obtained using the proposed MSRM as the traction motor. For the drive cycle, the total energy consumption was 6.083 kWh. When comparing the 148 proposed MSRM to the Mitsuba M2096-DII, it is seen that the proposed MSRM obtained a travelling distance of 23 km less than the Mitsuba M2096-DII for roughly the same amount of energy usage. Thus, it was concluded that the proposed MSRM used more energy to drive when considering the average energy used per distance travelled. Even though the proposed MSRM did not travel further or equal distance compared to the Mitsuba M2096-DII, the proposed MSRM shows some promise as a traction motor in solar vehicle application. Considering that the proposed MSRM is an un-optimised XDM, the proposed MSRM achieved a travelling distance of only 5.59% less than the Mitsuba M2096-DII. If the design of the proposed MSRM and/ or motor controller is optimised for efficiency, the expectation of extended or equal travelling distance is expected. Future development and optimisation of the proposed MSRM will help to improve motor performance and efficiency and therefore the travelling distance when using the proposed MSRM as a traction motor in the solar vehicle of the NWU. In conclusion, this study evaluated a switched reluctance motor for solar vehicle application, by adequately evaluating a XDM of the proposed MSRM against a permanent magnet motor, generally used for solar vehicles. The use of an SRM for solar vehicle applications is justified for future development studies to obtain an optimised SRM as a traction motor in a solar vehicle. 7.7 Recommendations for future studies Additional work or considerations are revealed throughout the study, either due to limitations, literature, or the work performed. This section proposes the recommended studies to further investigate or improve related research. These studies include: 7.7.1 Numerical methods Ansys® Maxwell was used as the numerical simulation software. Many of the studies discussed in the literature used Ansys® Maxwell to design an SRM. Although Ansys® Maxwell was used in many studies, it is proposed to replicate the design using different numerical simulation software, i.e., JMAG or Altair Flux as listed in §3.1.2, p.49. Using a different software will provide additional validation of the electromagnetic simulation methods. 7.7.2 Alternative motor design considerations In this study an un-optimised XDM of an MSRM was designed. According to the definition of an XDM, the proposed MSRM designed in chapter 5 has the risk of performing less than optimal. For future design of an MSRM, the following design considerations are recommended. 149 7.7.2.1 Core shape In this study, an E-core was chosen for the design based mainly on Xinglong Li [115]. The research question was formed that a core with more poles whilst keeping the axial length and winding turns constant will be more efficient given that flux paths in the core are minimised. A research question formulated in §2.6, p.45 was briefly analysed in §5.2.1.1, p.97. It was found that the core shapes were not directly comparable. Therefore, a future study is proposed to fully evaluate the research question of the efficiency effect when using different core shapes. For an alternative design of an MSRM, it is proposed to design a C-core and IIII-core with the same torque-speed characteristics, listed in Table 5-2, p.95. Thereafter, the designs can be compared to each other and each motor can be evaluated using the drive cycle to find the most efficient MSRM design. 7.7.2.2 Pole configuration When comparing a 12/16 MSRM with a 12/20 MSRM, it was found that the 12/16 MSRM produced higher torque. This is contradictory to the literature discussed in §2.3.3, p.31. However, the comparative designs in the literature changed the pole area, embrace, and winding turns, unlike the comparative designs of the 12/16 and 12/20 MSRM in §5.2.1.2, p.101. The 12/20 MSRM is still an alternative option. However, it is necessary to alter the winding and pole geometry to achieve the same torque-speed characteristics as the 12/16 MSRM. The motor can then be evaluated by comparing the efficiency maps and the drive cycle evaluations. By redesigning the windings and pole geometry, the 12/20 MSRM should produce more torque as more torque is expected based on the conclusive results found in literature (§2.3.3). 7.7.2.3 Pole geometry The pole geometry of the E-core was arbitrarily chosen for this study, based on the core dimensions found in literature. The pole area and pole embrace were analysed during the design process to find the parameters that produced the most torque within the geometry constraints (Table 5-1, p.90). It is proposed to optimise the pole and core geometry by changing the pole embrace, pole area, and yoke area. However, optimizing the geometry based on these parameters is an extensive process. 7.7.2.4 Winding design For a three-phase BLDC, the windings can be Wye or series connected. However, this is not the case for an SRM when using an asymmetric half-bridge converter as the motor controller. All the 150 phase coils of the proposed MSRM are connected in series. It is proposed to connect the coils in a parallel combination and evaluate the performance effects. Another winding alteration to consider is to use square-shaped conductors. This will improve the fill factor and result in more winding turns around the core. Thus, the same output torque will be produced using less current. 7.7.3 Thermal assessment Thermal considerations on the coils were provided in §5.2.4, p.112. Predicting coil temperature was done by coupling a magnetostatic simulation to a steady-state thermal analysis. The coils were excited with constant DC while the motor was stationary. Thus, the simulation provided the coil temperatures to ensure that the thermal limitations of the coil insulation were not exceeded. A comprehensive understanding of thermal behaviour of the proposed MSRM is still required. The use of FEA and CFD are proposed to model the thermal behaviour. Thereafter, experimental testing is proposed to verify the thermal behaviour. 7.7.4 Design optimisation The design of the proposed MSRM was an un-optimised XDM. As the proposed MSRM is justified, an optimised MSRM is desired. Therefore, it is proposed to optimise the proposed MSRM for efficiency. Optimising the proposed MSRM can be achieved by either the geometrical, material, and winding design or by optimising the conduction angles. 7.7.5 Motor controller design The design of a motor controller, nor the conduction angles, were included in the scope of this study. However, conduction angles are part of the motor controller and are an important aspect to operate the motor. The design a motor controller to operate at the optimal conduction angles of the proposed MSRM. Using a motor controller that operate the motor at its most efficient torque-speed characteristics will improve the energy usage of the traction motor. Note that optimising of conduction angles requires some level of sophistication to predict the conduction angles at each torque-speed operating point. 7.7.6 Creating an efficiency map The efficiency map of the proposed MSRM was constructed using multiple torque-speed characteristic graphs. Each torque-speed characteristic graph was analysed and the efficiency at 151 the operating points was calculated. After all torque-speed characteristic points were analysed, an efficiency map was constructed. This was a time-consuming process; as multiple simulations had to be run for a single torque-speed characteristic graph, i.e. speeds at 100 rpm to 1000 rpm in steps of 50 rpm. Ansys® Maxwell offers a unique toolkit in the software that can construct an efficiency map. The toolkit uses the designed motor and the parameters set within the toolkit to construct the efficiency map. Unfortunately, the toolkit is not functional for an SRM with the release of Maxwell 2021R1. A functional toolkit will provide an easy method to construct an efficiency map. Thus, allowing additional motor designs to be evaluated in less time using the drive cycle. It is proposed to construct an efficiency map of the proposed MSRM and evaluate the proposed MSRM. Evaluation of the MSRM is proposed as the toolkit offers the functionality to construct an efficiency map for the most efficient operating conditions. Thus, evaluation of an efficient motor operation is less time-consuming, as the toolkit automatically sets the conduction angles. Therefore, a study to optimise conduction angles for efficiency is not necessary when the toolkit is used. However, the toolkit must be functional for SRMs. 7.7.7 Prototype manufacturing and experimental testing Due to financial constraints (§1.5.3, p.10), the proposed MSRM was not manufactured in this study. Therefore, validation of the proposed MSRM using experimental tests was not possible. Manufacturing the proposed MSRM will allow experimental tests of static, dynamic, and thermal characteristics to be performed. It is proposed to compare the experimental test data with the simulated data to fully validate the efficiency map of the proposed MSRM. This will provide a comparison for the similarity of an efficiency map of a conventional SRM and the proposed MSRM. Before a prototype of the MSRM is manufactured, additional design aspects should be considered. These additional designs include the motor housing design, bearing selections, and the motor controller. Preferably, the optimised design should be constructed to minimise the financial implications. 7.7.8 Drive cycles for solar races Chapter 6 presented an analytical evaluation of a traction motor. A traction motor was evaluated using the constructed drive cycle. However, the drive cycle is simplified and uses a lot of assumptions. When two traction motors are compared against each other, these simplifications 152 and assumptions have little effect on the results when the better traction motor should be selected. However, using the simplified route cannot determine the expected driving distance for a route. It is proposed to include all variable factors of the road, weather, and vehicles in the drive cycle to allow use of the drive cycle as a prediction tool for solar racing teams. The drive cycle will not only predict the driving distance, but also provide information on the most efficient driving patterns. The driving pattern can then be used to instruct the driver on how to drive and consequently increasing the driving distance. 7.8 Final thoughts The opinion of Nir Vaks and Nvah Zarate is that an SRM is a potential candidate for the next generation traction motor in EVs. After combining the opinion of Nir Vaks and Nvah Zarate with the use of an electric motor in solar races, the research topic was formulated. The research topic was to evaluate an SRM for solar vehicle application. This study evaluated an MSRM using a simplified drive cycle. An un-optimised XDM MSRM was designed and evaluated using the drive cycle. Due to financial constraints, no prototype of the proposed MSRM was manufactured. Therefore, a numerical simulation of the proposed MSRM was analysed to construct an efficiency map. The proposed MSRM was evaluated and is concluded to be justified for future development even though it was concluded that the proposed MSRM was less efficient than the Mitsuba M2096-DII. 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Thus, testing an electrical motor is often done as preventative maintenance to ensure that issues are well known before any visual damage occurs. Visual damage to an electric motor can often be irreversible. In this study, the Mitsuba M2096-DII was tested to verify its motor characteristics and to construct an efficiency map. The methodology to test the motor is described in this section. A.1 Methodology of motor testing The Mitsuba M2096-DII are tested in the laboratory to verify motor characteristics and construct its efficiency map. The method to characterise the electric motor by experimental testing is done as follows. The electric motor is run at full speed under no-load conditions. Once the maximum speed is obtained, the load is gradually increased, effectively increasing the output torque. However, decreasing motor speed is shown in Figure 6-6 and Figure 6-7. Theoretically, the motor would not draw current from the power supply under no-load conditions. As the load increases, the speed of the motor will decrease and the current drawn by the power supply will increase until the motor stalls or the maximum current is drawn [170]. The construction of an efficiency map follows the same procedure as that of a characteristic graph. However, an efficiency map is constructed from various characteristic graphs starting at the no-load speed, and each characteristic graph thereafter starting at a speed lower than the no- load speed. The methodology followed to experimentally test and characterise the Mitsuba M2096-DII is performed using the prescribed laboratory setup. A.1.1 Laboratory setup A diagram of the laboratory setup is shown in Figure A-1, with the laboratory setup consisting of the following equipment:  A battery used as the power supply  The Mitsuba M2096C motor controller  The Mitsuba M2096-DII BLDC motor  The T40-S2TOS6 torque transducer 168  A hydraulic braking system  The G070 torque-rpm transducer  The GEN3t portable data recorder  A personal computer, and  The Perception software used to control the data recorder and record measurement data Figure A-1: Motor testing setup in the laboratory Power measurements consisting of current were obtained using the Chauvin Arnoux E3N clamp meters. The voltages were obtained using test leads. The mechanical torque and speed of the motor were obtained by the torque transducer, while the hydraulic braking system was used to control the load. All the measured signals are transmitted through the data controller to the PC and shown using the required software. Using the software, the measurement data is viewed and recorded after validating that the measured data are correct. A.1.2 Reliability and validity of the experimental data Validation of the measurement equipment is necessary to ensure that reliable data is shown and recorded when using the data recorder and the required software. Measurement equipment is validated against other measuring equipment as follows.  Current and voltage are measured using the Fluke 374 FC digital multimeter. 169  Motor speed is measured using a tachometer, and  Motor torque is validated with a calculation performed by hand. The shaft is locked and a weight is added to a known distance. Thus, the torque is known and compared to the value shown using the software. Comparing the data obtained by the data recorder with other measuring equipment proved that the data are reliable and sufficient to be recorded for analysis. A.1.3 Experimental data and analysis The experimental data are obtained by the portable data recorder and stored on the computer when recorded. Analysis of the measurements shows that the battery voltage decreases as the load is applied to the motor, exceeding the maximum current limits. However, this does not affect motor performance since the input voltage of the motor controller can operate within the range of 45-160V. Analysis of motor torque shows some torque ripple. Torque ripple is a known phenomenon in electric motors [171, 172]. However, torque ripple measurements are probably exaggerated with the vibration of the test bench under operation. Also, the shaft is not correctly aligned between the electric motor, torque transducer, and braking system. The alignment of the shaft was made by human eye, and the electric motor was run between adjustments until the least amount of torque ripple could be noticed. Another factor that contributes to shaft misalignment and torque ripple is the rubber coupling between the shaft of the torque transducer and the braking system. Ideally, there would be a single shaft between all connected equipment. Ultimately, experimental data of the Mitsuba M2096-DII are obtained and analysed using the Perception software. When adjusting the load, the speed and torque measurements were taken after stabilisation. The analysed data are exported to Microsoft Excel for the construction of the characteristic graphs. A.2 Summary of motor tests The characteristics of the Mitsuba M2096-DII were desirable to validate the motor datasheet (Figure D-1, p.181). Constructing an efficiency map was necessary to evaluate the motor in §6.2.1, p.136 and §6.3.1, p.140. The efficiency map was also important for the NWU when planning drive operations in a solar race. Thus, motor testing holds valuable information about an electric motor and is not only used for preventative maintenance. Following the prescribed methodology, any electric motor intended as a traction motor can be tested for characterisation and construction of an efficiency map when required to evaluate the electric motor. 170 APPENDIX B VALIDATION OF A MODULAR SWITCHED RELUCTANCE MOTOR B.1 Two-dimensional validation Modelling an electric motor in 2D requires an additional amount of input to obtain a model that predicts the characteristics and performance of an actual electric motor. Different correction methodologies compensate for the effects of 2D models. These methodologies allow an accurate representation of an electric motor. However, these methodologies only account for certain electric motors. Thus, in the case of new motor design concepts, a considerable need to accurately predict the electric motor is expected. This is the case of the MSRM, as mentioned in §3.1, p.48. This section validates the MSRM of Wen Ding et al., found in articles [96, 110, 109, 97, 107, 111]. Validation of a 2D model is compared to 2D FEA data obtained in [110]. Figure B-1: Flux distribution at an aligned position for a 2D model in Ansys® Maxwell 171 Figure B-1 shows the magnetic flux paths of the E-core MSRM in a 2D plane. For this validation, both the magnetic characteristics of flux linkage and inductance are validated. The magnetic characteristics are validated using Ansys® Maxwell and FEMM, as shown in Figure B-2. FEMM Ansys Article 0.14 0.12 0.1 Aligned position 0.08 0.06 0.04 Unaligned position 0.02 0 0 0.5 1 1.5 2 2.5 3 3.5 4 Current (A) (a) 0.08 0.06 Aligned position 0.04 0.02 Unaligned position 0 0.5 1 1.5 2 2.5 3 3.5 4 Current (A) (b) Figure B-2: Magnetic characteristics of the 2D MSRM model. (a) Flux linkage; (b) Inductance In Figure B-2 it is observed that the simulated data using both software is fairly far from the FEA data provided by the article. The geometric setup for 2D is not the same as for a 3D model, as only one plane is used as the simulating field plane. Note from the geometry shown in Figure B-1, that a 2D geometry includes a side view of the stator cores, but a top view of the rotor cores. It could well be that the geometry was incorrect from the article, thus the reason for obtaining the difference in simulation data. Otherwise, it was most likely because no correction factor was included in the simulations. Nevertheless, no further analysis is necessary for the difference in 2D MSRM simulations. 172 Inductance (H) Flux linkage (Wb) B.2 Three-dimensional validation The magnetic characteristics by variation of the coil shape and variation of the coil fillet mentioned in §4.4.3, p.81 are included in this section. Following the procedure in §4.4.2, the magnetic characteristics graphs are constructed and compared with the FEA data and the experimental data. The magnetic characteristics by variation of the coil shape are compared in Figure B-3. The shape of the coil is altered from a square to a rectangular shape. A rectangular shape is obtained by minimising opposing coil cross-sectional areas. Analysing the flux linkage, minimal deviation occurs between the simulated, experimental, and FEA data. Observing the static torque graph, it is seen that there is no difference in torque variation, except when compared to the FEA data. Thus, the variation in coil shape does not affect the magnetostatic characteristics of the MSRM. 7mm 11mm 15mm 0.12 0.1 Aligned position 0.08 0.06 0.04 Unaligned position 0.02 0 0 0.5 1 1.5 2 2.5 3 3.5 Current (A) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 20 25 30 35 40 45 Position (˚) Figure B-3: Magnetic characteristics by variation of the coil shape: (a) Flux linkage; (b) Static torque. The magnetic characteristics by variation of the coil fillet are compared in Figure B-4. The radius of the coil fillet is increased during simulations. Note that all four phase coils are changed to the same coil fillet value. Analysing the flux linkage, minimal deviation occurs between the simulated, experimental, and FEA data. Observing the static torque graph, it is seen that there is no 173 Flux linkage(Wb) Torque (Nm) difference in torque variation, except when compared to the FEA data. Thus, the variation of coil fillets does not affect the magnetostatic characteristics of the MSRM. 4mm 8mm 12mm 0.12 0.1 Aligned position 0.08 0.06 Unaligned position 0.04 0.02 0 0 0.5 1 1.5 2 2.5 3 3.5 Current (A) 1 0.9 3 A 0.8 0.7 0.6 0.5 0.4 0 A 0.3 0.2 0.1 0 0 5 10 15 20 25 30 35 40 45 Position (˚) Figure B-4: Magnetic characteristics by variation of the coil fillet: (a) Flux linkage; (b) Static torque. B.3 Summary of the validation A 2D model of the MSRM used to validate the numerical methods in chapter 4 was constructed using both FEMM and Maxwell 2D. It was observed that a large difference between the simulation data and the comparative FEA data obtained from article [110] occured. This is likely due to incorrect material, boundary, and geometry settings compared to the simulation data provided by Wen Ding et al. in the respective article. Supplementary analysis of a 2D model was not provided, and a transient 2D simulation would not be possible for an MSRM. This is because the magnetic flux is 3D and not 2D as expected for a conventional SRM. The magnetostatic characteristics, analysed by a parametric sweep of the geometric parameters, were provided in §4.3.3, p.71. In this appendix, the magnetostatic characteristics that do not influence the magnetostatic characteristics were included. These geometric parameters included the coil shape, as the coil was changed from a square to a more rectangular shape, and the coil fillet by increasing the radius of the fillet on the edges of the coil. 174 Flux linkage (Wb) Torque (Nm) APPENDIX C DESIGN OF A MODULAR SWITCHED RELUCTANCE MOTOR During the analysis of the proposed MSRM, the same numerical modelling methods, demonstrated in chapter 4 was used. This process involved the design and development of an MSRM and analysing its magnetostatic and transient characteristics. This appendix contains the mesh model of the proposed MSRM for transient solutions. Furthermore, the steady-state thermal validation and solution setup are explained, so that the coil temperature during excitation could be obtained, as discussed in §5.2.4, p.112. C.1 Modular switched reluctance motor transient mesh A quarter view of the mesh generated by Ansys® Maxwell is shown in Figure C-1. The mesh setup used to simulate the transient solutions of the proposed MSRM in §5.3.2, p.115 consisted of the following mesh selection for each geometric aspect. Refer to §5.2.4, p.112 as a minor difference in the mesh setup occur, compared to the setup used for validation in §4.4.1.3, p.78.  Band o Inside selection length-based mesh of 5 mm  Rotor core segments o Inside selection length-based mesh of 5 mm  Stator core segment o Inside selection mesh of 5 mm  Coils o Inside selection length-based mesh of 4 mm 175 Figure C-1: 3D FEA mesh model of the proposed MSRM C.2 Thermal validation and analysis The thermal analysis of the coil windings ensures that an electric machine operates within respectable temperature limits. As discussed in §5.2.4, p.112, the insulation of the coil and magnetic material sets the temperature limit of the proposed motor. To ensure an electric motor operates within its thermal limits is a very complex simulation process. A steady-state thermal analysis of the coil windings was obtained to predict the maximum allowable excitation current. To ensure that the proper temperature of a coil during simulation was obtained, the validation of a C-core is performed. The C-core was part of an MSRM, designed by Anas Labak, who provided an experimental test point for thermal analysis in [52]. The validation of the coil was compared to the experimental data, which were obtained by keeping the C-core motor stationary and applying a constant DC excitation while measuring the coil temperature. Steady-state coil temperature was reached when the temperature settled on a value. C.2.1 Thermal validation The objective of validating thermal analysis on a coil was to ensure that the temperature obtained from the solution was accurate. An accurate temperature solution acknowledged that the correct 176 simulation setup was followed. For steady-state thermal analysis, a two-way simulation was set up using both Ansys® Maxwell and Ansys® Steady-State Thermal. Both simulations were linked with each other, so that the thermal analysis was conducted from the results of the magnetostatic analysis. The following setup and process were followed to obtain a steady-state thermal solution. Note that the setup for Ansys® Maxwell is not discussed, as it follows the same setup and procedure discussed in §4.3.1, p.66. C.2.1.1 Excitation setup The excitation of the coil is set up in the same way as the magnetostatic simulation setup in Ansys® Maxwell. A single coil wound around the C-core consists of 65 turns. A current excitation of 40 A is applied to the coil. C.2.1.2 Boundary setup The boundary setup in Ansys® Maxwell is the same as the magnetostatic simulation setup. However, for Ansys® Steady-State Thermal, the following boundary setup is performed as follows:  Import the heat-generated load from Ansys® Maxwell.  Apply a convection film coefficient of 10 W/m2K to all surfaces. The film coefficient is assumed from the thermal study of an air-cooled transformer [161].  Set the initial temperature, otherwise known as the ambient temperature, at 22˚C. C.2.1.3 Solution and analysis setup The solution and analysis setup in Ansys® Maxwell is the same as the magnetostatic simulation setup. The solution and analysis setup in Ansys® Steady-State Thermal is set to analyse the temperature on the surfaces of the coil. When the solution setup is applied, the temperature distribution on the coil surfaces will be shown. C.2.2 Thermal procedure To obtain the temperature distribution of a coil, the following sequence is followed between the simulations. 1. Solve the magnetostatic simulation of the coil and core segment in Ansys® Maxwell. 2. Link the magnetostatic solution to Ansys® Steady-State Thermal setup in Ansys® Workbench. This allows for interaction between the two simulation environments. 3. Set up and solve the thermal analysis of the coil as discussed above. 177 C.2.3 Thermal analysis results A series of thermal simulations were completed to obtain a temperature-current graph, shown in Figure 5-17, p113. The graph shows the steady-state temperature of the coil when an excitation current was applied. Following the procedures, the steady-state coil temperature was obtained for both the validated model and the proposed MSRM model. C.2.4 Thermal distribution of the validated model The thermal distribution of the coil for the C-core designed by Anas Labak is shown in Figure C-2. The coil was excited with constant current excitation of 40 A. When comparing the coil surface temperature to the experimentally measured temperature in [77], a 10.13% difference was obtained. Thermal analysis of the electric motor was not part of the study, but was simply used as an indication to ensure that the proposed MSRM, designed in chapter 5 operates within respectable temperature limits as described in §5.2.4, p.112. Figure C-2: Temperature distribution of a C-core coil under 40 A excitation C.2.5 Thermal distribution of the proposed modular switched reluctance motor The thermal distribution of the coils for the E-core in the proposed MSRM is shown in Figure C-3. The coils were excited with a constant 25 A. The surface temperature obtained by the two-way coupled simulation was around 40˚C. From the temperature distribution on the coil surface, it is observed that the temperature difference was only 0.3˚C. Therefore, the temperature difference shown on the coils was negligible. 178 Figure C-3: Temperature distribution of the proposed E-core coils under 20 A excitation C.3 Torque-speed characteristics To construct an efficiency map of the proposed MSRM, enough operating points must be simulated. The efficiency map was constructed by interpolating between the efficiency curves obtained from the torque-speed characteristics. Seven torque-speed characteristic graphs were constructed from the simulations, as shown in Figure C-4. Note that the simulations were done only between the speed region of 250 rpm to 850 rpm. Simulations were limited to the region to save simulation time, since the study was limited to computer resources. Furthermore, the expected operating range was expected to occur in that region, based on the operating points of the Mitsuba M2096-DII when operated through the drive cycle (§6.2, p.135). 115V-70A 105V-60A 95V-50A 85V-40A 75V-30A 65V-20A 55V-10A 50 45 40 35 30 25 20 15 10 5 0 200 300 400 500 600 700 800 900 Speed (rpm) Figure C-4: Torque-speed characteristics of the proposed MSRM 179 Torque (Nm) C.4 Summary of the modular switched reluctance motor design Transient simulations were a vital part of the study. Transient simulations were used to construct torque-speed characteristics of the proposed MSRM, shown in Figure C-4. These torque-speed characteristics were then used to construct efficiency graphs from which the efficiency map was constructed. Thus, the setup of the transient model is significant. The mesh setup of the proposed MSRM is shown in Figure C-1. Note that a quarter of the model was used to minimise computational time and resources. This is possible due to symmetry planes, as discussed in §4.4.1.2, p.78. Before finalising the design and after the winding design, a thermal analysis of the coils was required. Thermal analysis was required to evaluate the maximum excitation current under the maximum allowable temperature specified by the class of conductor insulation. Refer to §5.2.4, p.112. The validation of a steady-state thermal simulation of a C-core MSRM was provided in §C.2.3. The validation setup and method were used to analyse the coil temperature of the proposed MSRM using a two-way solver coupling between Ansys® Maxwell and Ansys® Steady- State Thermal. The predicted temperature-current graph of the coils is shown in Figure 5-17, p.113. 180 APPENDIX D EVALUATION D.1 The Mitsuba M2096-DII Figure D-1: Mitsuba M2096-DII motor characteristics as from the datasheet 181 Table D-1: Analytical evaluation of the Mitsuba M2096-DII through the drive cycle Energy used Energy of Distance Speed time taken Time of day Energy by motor the sun as (km) (km/h) (H) (HH:MM) balance (W) (W) input (W) 0 0 0 7:00 1.6 1.6 1.6 0 0 0 7:03 29.03945 27.43945 29.03945 0 0 0 7:06 56.6566 27.61715 56.6566 0 0 0 7:09 84.44965 27.79305 84.44965 0 0 0 7:12 112.4168 27.96715 112.4168 0 0 0 7:15 140.5563 28.13945 140.5563 0 0 0 7:18 168.8662 28.30995 168.8662 0 0 0 7:21 197.3449 28.47865 197.3449 0 0 0 7:24 225.9904 28.64555 225.9904 0 0 0 7:27 254.8011 28.81065 254.8011 0 0 0 7:30 283.775 28.97395 283.775 0 0 0 7:33 312.9105 29.13545 312.9105 0 0 0 7:36 342.2056 29.29515 342.2056 0 0 0 7:39 371.6587 29.45305 371.6587 0 0 0 7:42 401.2678 29.60915 401.2678 0 0 0 7:45 431.0313 29.76345 431.0313 0 0 0 7:48 460.9472 29.91595 460.9472 0 0 0 7:51 491.0139 30.06665 491.0139 0 0 0 7:54 521.2294 30.21555 521.2294 0 0 0 7:57 551.5921 30.36265 551.5921 0 0 0 8:00 582.1 30.50795 582.1 0.9 75 0.012 8:00 589.4433 7.343329 589.4433 1.8 75 0.012 8:01 596.7949 7.351569 596.7949 2.7 70 0.012857 8:02 604.6807 7.885798 604.6807 3.6 70 0.012857 8:02 612.5759 7.895199 612.5759 4.5 70 0.012857 8:03 620.4805 7.904569 620.4805 6.75 70 0.032143 8:05 640.2827 19.80222 632.2233 7.2 70 0.006429 8:06 644.2501 3.967406 634.1317 8.1 70 0.012857 8:06 652.1918 7.941744 637.0775 9.9 70 0.025714 8:08 668.1029 15.91111 640.5675 11.25 70 0.019286 8:09 680.0603 11.95738 641.8565 12.15 70 0.012857 8:10 688.0433 7.98298 640.1089 14.85 65 0.041538 8:12 713.8964 25.85306 638.6504 15.3 65 0.006923 8:13 718.2143 4.317985 637.8923 16.2 65 0.013846 8:14 726.8581 8.643763 634.9366 17.1 65 0.013846 8:14 735.5122 8.654121 630.1792 20.25 65 0.048462 8:17 765.8827 30.37044 608.442 22.05 60 0.03 8:19 784.7461 18.86338 598.6341 23.4 60 0.0225 8:20 798.9247 14.17868 588.9322 25.2 60 0.03 8:22 817.8709 18.94613 573.9486 182 27.45 60 0.0375 8:24 841.6192 23.74836 550.0936 31.5 60 0.0675 8:29 884.5479 42.92869 502.7337 34.2 60 0.045 8:31 913.295 28.74705 466.7513 36 60 0.03 8:33 932.5158 19.22079 440.8398 38.25 55 0.040909 8:36 958.7974 26.28167 407.9501 39.6 55 0.024545 8:37 974.6057 15.80824 386.6513 40.5 55 0.016364 8:38 985.1607 10.55504 370.862 41.4 55 0.016364 8:39 995.7286 10.56794 354.1197 41.85 55 0.008182 8:39 1001.017 5.288787 345.181 43.2 55 0.024545 8:41 1016.903 15.88554 314.8189 43.65 55 0.008182 8:41 1022.205 5.301544 303.8193 45 55 0.024545 8:43 1038.128 15.92362 269.0544 45.9 50 0.018 8:44 1049.823 11.69533 243.0015 46.35 50 0.009 8:44 1055.677 5.853347 228.4884 46.8 50 0.009 8:45 1061.534 5.857122 213.307 47.25 50 0.009 8:46 1067.395 5.860886 196.85 48.15 75 0.012 8:46 1075.215 7.820353 204.6704 49.05 75 0.012 8:47 1083.042 7.827002 212.4974 49.95 70 0.012857 8:48 1091.436 8.393424 220.8908 50.85 70 0.012857 8:49 1099.837 8.400997 229.2918 51.75 70 0.012857 8:49 1108.245 8.40854 237.7003 54 60 0.0375 8:52 1132.813 24.56771 262.268 54.45 60 0.0075 8:52 1137.734 4.921143 267.1892 55.35 55 0.016364 8:53 1148.48 10.74578 277.935 57.15 50 0.036 8:55 1172.162 23.68263 301.6176 58.5 45 0.03 8:57 1191.942 19.77915 321.3967 59.4 40 0.0225 8:58 1206.802 14.86014 336.2569 62.1 30 0.09 9:04 1266.46 59.65808 395.915 62.55 25 0.018 9:05 1278.433 11.97277 407.8877 63.45 65 0.013846 9:06 1287.652 9.219026 405.5074 64.35 65 0.013846 9:06 1296.879 9.226988 401.3228 67.5 65 0.048462 9:09 1329.235 32.35661 381.5717 69.3 60 0.03 9:11 1349.313 20.07821 372.9787 70.65 60 0.0225 9:13 1364.396 15.08243 364.1805 72.45 60 0.03 9:14 1384.537 20.14128 350.3921 74.7 60 0.0375 9:17 1409.764 25.22648 328.0152 78.75 60 0.0675 9:21 1455.309 45.54503 283.2717 81.45 60 0.045 9:23 1485.768 30.45965 249.0018 83.25 50 0.036 9:25 1510.19 24.42215 232.0941 85.5 50 0.045 9:28 1540.785 30.59462 206.8551 86.85 50 0.027 9:30 1559.177 18.39196 189.5445 87.75 50 0.018 9:31 1571.453 12.2758 176.7193 88.65 50 0.018 9:32 1583.74 12.28729 162.7987 89.1 50 0.009 9:32 1589.888 6.14793 155.0153 90.45 50 0.027 9:34 1608.349 18.4608 129.1583 183 90.9 50 0.009 9:35 1614.508 6.159234 119.6914 92.25 50 0.027 9:36 1633.002 18.49446 89.17164 93.15 50 0.018 9:37 1645.346 12.3435 63.76695 93.6 50 0.009 9:38 1651.522 6.175876 49.57638 94.05 50 0.009 9:38 1657.7 6.178613 34.71642 94.5 50 0.009 9:39 1663.882 6.181339 18.5799 95.4 75 0.012 9:40 1672.128 8.246008 26.82591 96.3 75 0.012 9:40 1680.379 8.250812 35.07672 97.2 70 0.012857 9:41 1689.224 8.845457 43.92218 98.1 70 0.012857 9:42 1698.075 8.850912 52.77309 99 70 0.012857 9:43 1706.931 8.856336 61.62943 101.25 70 0.032143 9:45 1729.096 22.16437 75.73444 101.7 65 0.006923 9:45 1733.874 4.778231 79.02759 102.6 60 0.015 9:46 1744.232 10.3581 87.18323 104.4 55 0.032727 9:48 1766.856 22.6243 105.3573 105.75 50 0.027 9:50 1785.547 18.69037 122.2125 106.65 45 0.02 9:51 1799.406 13.8593 132.7466 109.35 35 0.077143 9:55 1852.977 53.5713 183.5638 109.8 30 0.015 9:56 1863.415 10.4373 192.0756 110.7 35 0.025714 9:58 1881.322 17.90786 204.7576 111.6 30 0.03 10:00 1902.239 20.91672 219.3662 114.75 25 0.126 10:07 1990.366 88.12652 280.7877 116.55 35 0.051429 10:10 2026.459 36.09372 298.3312 117.9 40 0.03 10:12 2047.546 21.08658 301.3566 119.7 40 0.04 10:14 2075.697 28.15119 303.3557 121.95 40 0.05 10:17 2110.942 35.24515 300.3447 126 40 0.09 10:23 2174.535 63.59308 290.1555 128.7 40 0.06 10:26 2217.035 42.4995 278.6128 130.5 40 0.04 10:29 2245.412 28.37745 268.8376 132.75 40 0.05 10:32 2280.933 35.5202 251.6173 134.1 40 0.03 10:34 2302.27 21.33724 239.8108 135 40 0.02 10:35 2316.505 14.23505 230.4385 135.9 40 0.02 10:36 2330.748 14.24309 220.0417 136.35 40 0.01 10:37 2337.872 7.124528 214.0418 137.7 40 0.03 10:38 2359.258 21.38534 193.3656 138.15 40 0.01 10:39 2366.39 7.132315 185.5859 139.5 40 0.03 10:41 2387.798 21.40835 160.4508 140.4 40 0.02 10:42 2402.08 14.28159 138.1264 140.85 40 0.01 10:43 2409.224 7.143562 125.6983 141.3 40 0.01 10:43 2416.369 7.145386 112.2745 141.75 40 0.01 10:44 2423.516 7.147196 97.85549 142.65 75 0.012 10:45 2432.095 8.579003 106.4345 143.55 75 0.012 10:45 2440.677 8.581564 115.0161 144.45 70 0.012857 10:46 2449.874 9.197346 124.2134 145.35 70 0.012857 10:47 2459.074 9.200226 133.4136 184 146.25 70 0.012857 10:48 2468.277 9.203075 142.6167 148.5 70 0.032143 10:50 2491.297 23.01995 157.5773 148.95 65 0.006923 10:50 2496.258 4.960404 161.0526 149.85 60 0.015 10:51 2507.008 10.75025 169.6004 151.65 55 0.032727 10:53 2530.476 23.46773 188.6179 153 50 0.027 10:54 2549.849 19.37364 206.1564 153.9 45 0.02 10:56 2564.207 14.3581 217.1893 156.6 35 0.077143 11:00 2619.644 55.4369 269.872 157.05 30 0.015 11:01 2630.434 10.78929 278.7359 157.95 35 0.025714 11:03 2648.937 18.50312 292.0132 158.85 30 0.03 11:05 2670.535 21.59818 307.3032 162 25 0.126 11:12 2761.371 90.83555 371.4337 163.8 35 0.051429 11:15 2798.499 37.12839 390.0119 165.15 40 0.03 11:17 2820.17 21.67111 393.6218 166.95 40 0.04 11:19 2849.079 28.90875 396.3785 169.2 40 0.05 11:22 2885.236 36.15706 394.2794 173.25 40 0.09 11:28 2950.372 65.13639 385.6335 175.95 40 0.06 11:31 2993.831 43.45829 375.0496 177.75 40 0.04 11:34 3022.816 28.98549 365.8824 180 40 0.05 11:37 3059.061 36.24521 349.3871 181.35 40 0.03 11:39 3080.815 21.75355 337.997 182.25 40 0.02 11:40 3095.32 14.5048 328.8944 183.15 40 0.02 11:41 3109.826 14.50662 318.7611 183.6 40 0.01 11:42 3117.08 7.253953 312.8906 184.95 40 0.03 11:43 3138.844 21.76427 292.5934 185.4 40 0.01 11:44 3146.1 7.255509 284.9369 186.75 40 0.03 11:46 3167.868 21.76859 260.1621 187.65 40 0.02 11:47 3182.382 14.51396 238.07 188.1 40 0.01 11:48 3189.64 7.257411 225.7557 188.55 40 0.01 11:48 3196.898 7.257678 212.4442 189 40 0.01 11:49 3204.155 7.25793 198.136 189.9 60 0.015 11:50 3215.043 10.88734 209.0233 190.8 60 0.015 11:51 3225.931 10.88782 219.9111 191.7 60 0.015 11:51 3236.819 10.88826 230.7994 192.6 60 0.015 11:52 3247.708 10.88865 241.688 193.5 60 0.015 11:53 3258.597 10.88899 252.577 195.75 60 0.0375 11:56 3285.82 27.22365 279.8007 196.2 60 0.0075 11:56 3291.265 5.444881 285.2455 197.1 60 0.015 11:57 3302.155 10.88987 293.9329 198.9 60 0.03 11:59 3323.935 21.77998 307.8081 200.25 60 0.0225 12:00 3340.27 16.335 316.2391 201.15 60 0.015 12:01 3351.16 10.88992 320.4056 203.85 60 0.045 12:04 3383.829 32.66885 328.8747 204.3 60 0.0075 12:04 3389.273 5.44461 329.8058 205.2 60 0.015 12:05 3400.162 10.88899 330.5059 185 206.1 60 0.015 12:06 3411.051 10.88865 329.6098 209.25 60 0.0525 12:09 3449.158 38.10691 321.2869 211.05 60 0.03 12:11 3470.93 21.77244 314.3881 212.4 60 0.0225 12:12 3487.258 16.32763 306.8351 214.2 60 0.03 12:14 3509.026 21.7676 294.673 216.45 60 0.0375 12:16 3536.23 27.2048 274.2744 220.5 60 0.0675 12:20 3585.184 48.95322 232.9391 223.2 60 0.045 12:23 3617.806 32.62263 200.8322 225 60 0.03 12:25 3639.548 21.74194 177.4419 227.25 55 0.040909 12:27 3669.187 29.63895 147.9095 228.6 55 0.024545 12:29 3686.965 17.77793 128.5804 229.5 35 0.025714 12:30 3705.585 18.61984 124.8659 230.4 35 0.025714 12:32 3724.2 18.61483 120.2066 230.85 35 0.012857 12:33 3733.505 9.305458 117.1382 232.2 35 0.038571 12:35 3761.413 27.90819 105.4662 232.65 35 0.012857 12:36 3770.713 9.299899 100.6308 234 35 0.038571 12:38 3798.604 27.89077 84.20768 234.9 35 0.025714 12:39 3817.19 18.58611 67.40528 235.35 35 0.012857 12:40 3826.481 9.290641 57.63389 235.8 35 0.012857 12:41 3835.77 9.288991 46.74254 236.25 35 0.012857 12:42 3845.057 9.28731 34.77099 237.15 75 0.012 12:43 3853.724 8.666612 43.4376 238.05 75 0.012 12:43 3862.389 8.665097 52.1027 238.95 70 0.012857 12:44 3871.671 9.282322 61.38502 239.85 70 0.012857 12:45 3880.952 9.280523 70.66555 240.75 70 0.012857 12:46 3890.23 9.278694 79.94424 243 60 0.0375 12:48 3917.282 27.05212 106.9964 243.45 60 0.0075 12:48 3922.691 5.408458 112.4048 244.35 55 0.016364 12:49 3934.489 11.79794 124.2028 246.15 50 0.036 12:51 3960.433 25.94394 150.1467 247.5 45 0.03 12:53 3982.04 21.60745 171.7541 248.4 40 0.0225 12:55 3998.238 16.19788 187.952 251.1 30 0.09 13:00 4062.96 64.72198 252.674 251.55 25 0.018 13:01 4075.89 12.93044 265.6044 252.45 50 0.018 13:02 4088.816 12.92559 270.9813 253.35 50 0.018 13:03 4101.737 12.92065 274.3718 256.5 50 0.063 13:07 4146.919 45.18223 282.15 258.3 50 0.036 13:09 4172.708 25.78943 284.0403 259.65 50 0.027 13:11 4192.036 19.32773 283.9101 261.45 50 0.036 13:13 4217.787 25.75064 280.772 263.7 50 0.045 13:16 4249.942 32.15575 272.27 267.75 50 0.081 13:20 4307.728 57.78524 249.5209 270.45 50 0.054 13:24 4346.18 38.4524 230.9921 272.25 50 0.036 13:26 4371.782 25.60201 215.2643 274.5 50 0.045 13:29 4403.746 31.96429 191.3949 186 275.85 50 0.027 13:30 4422.904 19.15769 174.85 276.75 50 0.018 13:31 4435.667 12.76291 162.5119 277.65 50 0.018 13:32 4448.423 12.75571 149.0598 278.1 50 0.009 13:33 4454.798 6.37513 141.5036 279.45 50 0.027 13:35 4473.912 19.11436 116.3002 279.9 50 0.009 13:35 4480.28 6.367741 107.0417 281.25 50 0.027 13:37 4499.372 19.09194 77.11949 282.15 50 0.018 13:38 4512.09 12.71845 52.08975 282.6 50 0.009 13:38 4518.447 6.356341 38.07964 283.05 50 0.009 13:39 4524.801 6.354405 23.39548 283.5 50 0.009 13:39 4531.154 6.352457 7.430074 284.4 75 0.012 13:40 4539.62 8.466896 15.89697 285.3 75 0.012 13:41 4548.084 8.463391 24.36036 286.2 70 0.012857 13:42 4557.148 9.064001 33.42436 287.1 70 0.012857 13:42 4566.208 9.059918 42.48428 288 70 0.012857 13:43 4575.264 9.055805 51.54009 290.25 60 0.0375 13:45 4601.653 26.38898 77.92907 290.7 60 0.0075 13:46 4606.926 5.273499 83.20257 291.6 55 0.016364 13:47 4618.427 11.50079 94.70335 293.4 50 0.036 13:49 4643.704 25.27718 119.9805 294.75 45 0.03 13:51 4664.742 21.03814 141.0187 295.65 40 0.0225 13:52 4680.505 15.76274 156.7814 298.35 30 0.09 13:58 4743.416 62.91146 219.6929 298.8 25 0.018 13:59 4755.971 12.5549 232.2478 299.7 50 0.018 14:00 4768.517 12.54558 237.2446 300.6 50 0.018 14:01 4781.053 12.53617 240.2507 303.75 50 0.063 14:05 4824.854 43.80128 246.6479 305.55 50 0.036 14:07 4849.83 24.9757 247.7245 306.9 50 0.027 14:08 4868.536 18.70568 246.9722 308.7 50 0.036 14:10 4893.441 24.90557 242.989 310.95 50 0.045 14:13 4924.515 31.07424 233.4056 315 50 0.081 14:18 4980.283 55.76801 208.6392 317.7 50 0.054 14:21 5017.341 37.05723 188.7153 319.5 50 0.036 14:23 5041.99 24.64951 172.0349 321.75 50 0.045 14:26 5072.739 30.74849 146.9497 323.1 50 0.027 14:28 5091.154 18.41478 129.662 324 35 0.025714 14:29 5108.667 17.51364 124.8413 324.9 35 0.025714 14:31 5126.157 17.48973 119.0569 325.35 35 0.012857 14:32 5134.893 8.735826 115.4188 326.7 35 0.038571 14:34 5161.064 26.17095 102.0096 327.15 35 0.012857 14:35 5169.775 8.711371 96.58562 328.5 35 0.038571 14:37 5195.872 26.09685 78.36861 329.4 35 0.025714 14:39 5213.238 17.36654 60.34665 329.85 35 0.012857 14:39 5221.912 8.673771 49.95839 330.3 35 0.012857 14:40 5230.58 8.667397 38.44544 187 330.75 35 0.012857 14:41 5239.241 8.660992 25.84757 331.65 75 0.012 14:42 5247.318 8.077787 33.92536 332.55 75 0.012 14:42 5255.391 8.072157 41.99752 333.45 70 0.012857 14:43 5264.033 8.642463 50.63998 334.35 70 0.012857 14:44 5272.669 8.63594 59.27592 335.25 70 0.012857 14:45 5281.298 8.629387 67.90531 337.5 60 0.0375 14:47 5306.43 25.13133 93.03663 337.95 60 0.0075 14:47 5311.449 5.019477 98.05611 338.85 55 0.016364 14:48 5322.393 10.94368 108.9998 340.65 50 0.036 14:50 5346.43 24.03762 133.0374 342 45 0.03 14:52 5366.421 19.99056 153.028 342.9 40 0.0225 14:54 5381.389 14.96834 167.9963 345.6 30 0.09 14:59 5441.048 59.65914 227.6554 346.05 25 0.018 15:00 5452.939 11.89009 239.5455 346.95 50 0.018 15:01 5464.815 11.87598 243.8728 347.85 50 0.018 15:02 5476.676 11.86179 246.2045 351 50 0.063 15:06 5518.08 41.4033 250.2037 352.8 50 0.036 15:08 5541.659 23.57913 249.8837 354.15 50 0.027 15:10 5559.304 17.6457 248.0715 355.95 50 0.036 15:12 5582.78 23.47552 242.6582 358.2 50 0.045 15:15 5612.04 29.25977 231.2603 362.25 50 0.081 15:20 5664.466 52.42665 203.1526 364.95 50 0.054 15:23 5699.242 34.77586 180.9473 366.75 50 0.036 15:25 5722.347 23.10469 162.7221 369 50 0.045 15:28 5751.137 28.79056 135.679 370.35 50 0.027 15:29 5768.363 17.22567 117.2021 371.25 35 0.025714 15:31 5784.734 16.37115 111.2389 372.15 35 0.025714 15:32 5801.072 16.33749 104.3023 372.6 35 0.012857 15:33 5809.228 8.156043 100.0844 373.95 35 0.038571 15:35 5833.645 24.41696 84.92126 374.4 35 0.012857 15:36 5841.767 8.121829 78.90772 375.75 35 0.038571 15:39 5866.08 24.31358 58.90744 376.65 35 0.025714 15:40 5882.246 16.1655 39.68443 377.1 35 0.012857 15:41 5890.315 8.069589 28.69199 377.55 35 0.012857 15:42 5898.376 8.060775 16.57242 378 35 0.012857 15:42 5906.428 8.05193 3.365494 378.9 70 0.012857 15:43 5914.471 8.043055 11.40855 379.8 70 0.012857 15:44 5922.505 8.03415 19.4427 380.7 70 0.012857 15:45 5930.53 8.025213 27.46791 381.6 70 0.012857 15:45 5938.547 8.016247 35.48416 382.5 70 0.012857 15:46 5946.554 8.007249 43.49141 384.75 70 0.032143 15:48 5966.532 19.97856 55.41061 385.2 70 0.006429 15:49 5970.521 3.988899 57.34043 386.1 70 0.012857 15:49 5978.492 7.970953 60.31553 387.9 70 0.025714 15:51 5994.407 15.91442 63.80878 188 389.25 70 0.019286 15:52 6006.318 11.91165 65.05211 390.15 70 0.012857 15:53 6014.248 7.929535 63.25108 392.85 65 0.041538 15:55 6039.803 25.55486 61.49429 393.3 65 0.006923 15:56 6044.052 4.249646 60.66784 394.2 65 0.013846 15:57 6052.544 8.491108 57.55956 395.1 65 0.013846 15:57 6061.024 8.480164 52.62815 398.25 65 0.048462 16:00 6090.618 29.59384 30.11435 D.2 The proposed modular switched reluctance motor Table D-2: Analytical evaluation of the proposed MSRM through the drive cycle Energy used Energy gain Distance Speed time taken Time of day Energy by motor by the sun (km) (km/h) (H) (HH:MM) balance (W) (W) as input (W) 0 0 0 7:00 0 1.6 1.6 0 0 0 7:03 0 27.43945 29.03945 0 0 0 7:06 0 27.61715 56.6566 0 0 0 7:09 0 27.79305 84.44965 0 0 0 7:12 0 27.96715 112.4168 0 0 0 7:15 0 28.13945 140.5563 0 0 0 7:18 0 28.30995 168.8662 0 0 0 7:21 0 28.47865 197.3449 0 0 0 7:24 0 28.64555 225.9904 0 0 0 7:27 0 28.81065 254.8011 0 0 0 7:30 0 28.97395 283.775 0 0 0 7:33 0 29.13545 312.9105 0 0 0 7:36 0 29.29515 342.2056 0 0 0 7:39 0 29.45305 371.6587 0 0 0 7:42 0 29.60915 401.2678 0 0 0 7:45 0 29.76345 431.0313 0 0 0 7:48 0 29.91595 460.9472 0 0 0 7:51 0 30.06665 491.0139 0 0 0 7:54 0 30.21555 521.2294 0 0 0 7:57 0 30.36265 551.5921 0 0 0 8:00 0 30.50795 582.1 0.9 75 0.012 8:00 0 7.343329 589.4433 1.8 60 0.015 8:01 0 9.190746 598.6341 2.7 60 0.015 8:02 0 9.203574 607.8376 3.6 60 0.015 8:03 0 9.216353 617.054 4.5 60 0.015 8:04 0 9.229083 626.2831 6.75 60 0.0375 8:06 0 23.12808 649.4112 7.2 60 0.0075 8:07 0 4.635061 654.0462 8.1 60 0.015 8:07 3.393159 9.279518 659.9326 189 9.9 60 0.03 8:09 9.814659 18.59645 672.1075 11.25 60 0.0225 8:11 15.47666 13.97988 680.4254 12.15 60 0.015 8:11 21.42343 9.335329 683.814 14.85 60 0.045 8:14 43.3587 28.0794 689.9581 15.3 60 0.0075 8:15 47.69932 4.690543 690.308 16.2 60 0.015 8:16 57.78328 9.390155 689.6142 17.1 60 0.015 8:16 70.02634 9.402205 686.7734 20.25 60 0.0525 8:20 117.9828 33.00191 671.8188 22.05 60 0.03 8:21 148.3219 18.92344 660.4032 23.4 60 0.0225 8:23 173.2883 14.2234 649.6601 25.2 60 0.03 8:25 209.552 19.00532 632.4018 27.45 60 0.0375 8:27 260.5411 23.82165 605.2343 31.5 60 0.0675 8:31 359.1743 43.05868 549.6598 34.2 60 0.045 8:34 429.4745 28.83233 508.192 36 60 0.03 8:35 479.4323 19.27702 477.5111 38.25 60 0.0375 8:38 547.7702 24.158 433.3313 39.6 60 0.0225 8:39 591.2336 14.52743 404.3954 40.5 60 0.015 8:40 621.7876 9.698444 383.5397 41.4 60 0.015 8:41 654.008 9.709182 361.0286 41.85 60 0.0075 8:41 670.9148 4.858602 348.9803 43.2 60 0.0225 8:43 725.406 14.59178 309.0809 43.65 60 0.0075 8:43 744.4059 4.869231 294.9502 45 60 0.0225 8:44 804.0641 14.62352 249.9156 45.9 55 0.016364 8:45 848.2877 10.65013 216.3421 46.35 55 0.008182 8:46 872.2151 5.329728 197.7444 46.8 55 0.008182 8:46 896.9909 5.332826 178.3014 47.25 50 0.009 8:47 922.4708 5.869679 158.6912 48.15 50 0.018 8:48 922.4708 11.75053 170.4418 49.05 50 0.018 8:49 922.4708 11.76537 182.2072 49.95 50 0.018 8:50 922.4708 11.78012 193.9873 50.85 50 0.018 8:51 922.4708 11.79478 205.7821 51.75 50 0.018 8:52 922.4708 11.80937 217.5914 54 50 0.045 8:55 922.4708 29.58666 247.1781 54.45 50 0.009 8:55 922.4708 5.92809 253.1062 55.35 50 0.018 8:57 922.4708 11.86685 264.973 57.15 50 0.036 8:59 922.4708 23.77611 288.7491 58.5 50 0.027 9:00 925.9753 17.86885 303.1135 59.4 50 0.018 9:01 929.5168 11.92992 311.5019 62.1 50 0.054 9:05 942.5723 35.87213 334.3185 62.55 50 0.009 9:05 945.4894 5.99059 337.392 63.45 50 0.018 9:06 952.7729 11.99129 342.0998 64.35 50 0.018 9:07 962.1709 12.00469 344.7065 67.5 50 0.063 9:11 999.9905 42.12079 349.0077 69.3 50 0.036 9:13 1024.459 24.14091 348.6802 70.65 50 0.027 9:15 1045.043 18.13947 346.236 190 72.45 50 0.036 9:17 1075.451 24.23049 340.0583 74.7 50 0.045 9:20 1119.019 30.35871 326.8486 78.75 50 0.081 9:25 1204.09 54.83942 296.6173 81.45 50 0.054 9:28 1265.279 36.69484 272.1233 83.25 50 0.036 9:30 1309.172 24.522 252.752 85.5 50 0.045 9:33 1369.829 30.71744 222.8124 86.85 50 0.027 9:34 1408.7 18.46459 202.4055 87.75 50 0.018 9:35 1436.196 12.32377 187.2343 88.65 50 0.018 9:37 1465.319 12.33491 170.4454 89.1 50 0.009 9:37 1480.683 6.171607 161.2529 90.45 50 0.027 9:39 1530.494 18.5313 129.9734 90.9 50 0.009 9:39 1547.915 6.182556 118.7354 92.25 50 0.027 9:41 1602.723 18.56389 82.49061 93.15 50 0.018 9:42 1645.401 12.38935 52.20266 93.6 50 0.009 9:42 1668.556 6.198666 35.24628 94.05 45 0.01 9:43 1692.216 6.890512 18.47627 94.5 45 0.01 9:44 1717.299 6.893767 0.287544 95.4 75 0.012 9:44 1717.299 8.276796 8.56434 96.3 75 0.012 9:45 1717.299 8.281438 16.84578 97.2 75 0.012 9:46 1717.299 8.286055 25.13183 98.1 75 0.012 9:47 1717.299 8.290646 33.42248 99 70 0.012857 9:47 1717.299 8.887903 42.31038 101.25 65 0.034615 9:49 1717.299 23.95479 66.26517 101.7 60 0.0075 9:50 1717.299 5.195125 71.4603 102.6 55 0.016364 9:51 1717.299 11.34085 82.80114 104.4 50 0.036 9:53 1717.299 24.9787 107.7798 105.75 45 0.03 9:55 1717.299 20.84548 128.6253 106.65 40 0.0225 9:56 1717.299 15.65169 144.277 109.35 40 0.0675 10:00 1728.459 47.04377 180.1604 109.8 40 0.01125 10:01 1730.187 7.853346 186.2861 110.7 40 0.0225 10:02 1735.043 15.71741 197.147 111.6 40 0.0225 10:04 1742.137 15.73156 205.7848 114.75 40 0.07875 10:08 1772.236 55.16954 230.8557 116.55 40 0.045 10:11 1792.379 31.59968 242.3119 117.9 40 0.03375 10:13 1809.686 23.73418 248.7394 119.7 40 0.045 10:16 1835.91 31.69042 254.2057 121.95 40 0.05625 10:19 1874.494 39.68325 255.3051 126 40 0.10125 10:25 1951.165 71.61873 250.2525 128.7 40 0.0675 10:29 2006.832 47.87458 242.4602 130.5 40 0.045 10:32 2047.161 31.97102 234.1019 132.75 40 0.05625 10:35 2103.377 40.02293 217.9096 134.1 40 0.03375 10:37 2139.512 24.04432 205.8186 135 40 0.0225 10:39 2165.307 16.04194 196.066 135.9 40 0.0225 10:40 2192.766 16.05166 184.6585 136.35 40 0.01125 10:41 2207.305 8.029427 178.1482 191 137.7 40 0.03375 10:43 2254.665 24.10242 154.8914 138.15 40 0.01125 10:43 2271.367 8.038782 146.2274 139.5 40 0.03375 10:45 2323.886 24.12999 117.8386 140.4 40 0.0225 10:47 2365.445 16.09782 92.37783 140.85 40 0.01125 10:47 2388.057 8.052198 77.81786 141.3 40 0.01125 10:48 2411.549 8.054363 62.38056 141.75 40 0.01125 10:49 2436.6 8.056506 45.38586 142.65 75 0.012 10:49 2436.6 8.595947 53.98181 143.55 75 0.012 10:50 2436.6 8.598338 62.58015 144.45 75 0.012 10:51 2436.6 8.600704 71.18085 145.35 75 0.012 10:52 2436.6 8.603045 79.78389 146.25 70 0.012857 10:52 2436.6 9.220118 89.00401 148.5 50 0.045 10:55 2436.6 32.29091 121.2949 148.95 50 0.009 10:56 2436.6 6.46193 127.7569 149.85 50 0.018 10:57 2436.6 12.92753 140.6844 151.65 50 0.036 10:59 2436.6 25.86941 166.5538 153 50 0.027 11:01 2440.104 19.4143 182.4636 153.9 50 0.018 11:02 2443.646 12.94853 191.8706 156.6 50 0.054 11:05 2456.701 38.8719 217.687 157.05 50 0.009 11:05 2459.618 6.482373 221.2522 157.95 50 0.018 11:06 2466.902 12.96784 226.9366 158.85 50 0.018 11:08 2476.3 12.9719 230.5106 162 50 0.063 11:11 2514.12 45.43242 238.1234 163.8 50 0.036 11:13 2538.588 25.98187 239.6368 165.15 50 0.027 11:15 2559.172 19.49566 238.5489 166.95 50 0.036 11:17 2589.58 26.00602 234.1467 169.2 50 0.045 11:20 2633.148 32.52557 223.1038 173.25 40 0.10125 11:26 2709.82 73.24931 219.6817 175.95 40 0.0675 11:30 2765.486 48.87841 212.8932 177.75 40 0.045 11:33 2805.816 32.60324 205.1672 180 40 0.05625 11:36 2862.031 40.77159 189.7236 181.35 40 0.03375 11:38 2898.166 24.47133 178.0596 182.25 40 0.0225 11:40 2923.961 16.31736 168.5824 183.15 40 0.0225 11:41 2951.42 16.31969 157.4429 183.6 40 0.01125 11:42 2965.96 8.160664 151.0638 184.95 40 0.03375 11:44 3013.319 24.48503 128.1896 185.4 40 0.01125 11:44 3030.022 8.16262 119.6495 186.75 40 0.03375 11:46 3082.541 24.49041 91.62107 187.65 40 0.0225 11:48 3124.099 16.32885 66.39137 188.1 40 0.01125 11:48 3146.711 8.164939 51.94413 188.55 40 0.01125 11:49 3170.203 8.165254 36.61773 189 40 0.01125 11:50 3195.254 8.165548 19.73207 189.9 75 0.012 11:50 3195.254 8.710219 28.44229 190.8 75 0.012 11:51 3195.254 8.710506 37.15279 191.7 75 0.012 11:52 3195.254 8.710768 45.86356 192 192.6 75 0.012 11:53 3195.254 8.711004 54.57456 193.5 70 0.012857 11:53 3195.254 9.333453 63.90802 195.75 65 0.034615 11:55 3195.254 25.1295 89.03752 196.2 60 0.0075 11:56 3195.254 5.44487 94.48239 197.1 55 0.016364 11:57 3195.254 11.87984 106.3622 198.9 50 0.036 11:59 3195.254 26.13598 132.4982 200.25 45 0.03 12:01 3195.254 21.77994 154.2781 201.15 40 0.0225 12:02 3195.254 16.33468 170.6128 203.85 40 0.0675 12:06 3206.415 49.00085 208.4533 204.3 40 0.01125 12:07 3208.142 8.16613 214.8918 205.2 40 0.0225 12:08 3212.999 16.33149 226.3668 206.1 40 0.0225 12:10 3220.092 16.33033 235.6034 209.25 40 0.07875 12:14 3250.191 57.14468 262.6493 211.05 40 0.045 12:17 3270.335 32.64412 275.15 212.4 40 0.03375 12:19 3287.641 24.47733 282.3207 214.2 40 0.045 12:22 3313.865 32.62769 288.7243 216.45 40 0.05625 12:25 3352.449 40.76872 290.9091 220.5 40 0.10125 12:31 3429.121 73.33143 287.5692 223.2 40 0.0675 12:35 3484.788 48.84414 280.7464 225 40 0.045 12:38 3525.117 32.54084 272.958 227.25 40 0.05625 12:41 3581.332 40.64908 257.3918 228.6 40 0.03375 12:43 3617.467 24.37408 245.6306 229.5 40 0.0225 12:45 3643.262 16.24264 236.0787 230.4 40 0.0225 12:46 3670.721 16.23706 224.8566 230.85 40 0.01125 12:47 3685.261 8.116382 218.4332 232.2 40 0.03375 12:49 3732.62 24.34032 195.4143 232.65 40 0.01125 12:49 3749.323 8.110426 186.822 234 40 0.03375 12:51 3801.842 24.32196 158.6251 234.9 40 0.0225 12:53 3843.4 16.20666 133.2732 235.35 40 0.01125 12:53 3866.012 8.100877 118.7619 235.8 40 0.01125 12:54 3889.504 8.099214 103.3695 236.25 40 0.01125 12:55 3914.555 8.09753 86.4158 237.15 75 0.012 12:56 3914.555 8.635486 95.05129 238.05 75 0.012 12:56 3914.555 8.633522 103.6848 238.95 75 0.012 12:57 3914.555 8.631534 112.3163 239.85 75 0.012 12:58 3914.555 8.62952 120.9459 240.75 75 0.012 12:58 3917.863 8.627481 126.2657 243 70 0.032143 13:00 3926.49 23.09909 140.7375 243.45 65 0.006923 13:01 3927.978 4.973204 144.2231 244.35 65 0.013846 13:02 3931.317 9.944263 150.828 246.15 55 0.032727 13:04 3935.714 23.49305 169.9242 247.5 50 0.027 13:05 3939.218 19.36924 185.7889 248.4 50 0.018 13:06 3942.76 12.90638 195.1538 251.1 50 0.054 13:09 3955.815 38.6873 220.7856 251.55 50 0.009 13:10 3958.733 6.443128 224.3116 193 252.45 50 0.018 13:11 3966.016 12.88209 229.9102 253.35 50 0.018 13:12 3975.414 12.87646 233.3887 256.5 50 0.063 13:16 4013.234 45.02204 240.5911 258.3 50 0.036 13:18 4037.702 25.69407 241.8168 259.65 50 0.027 13:20 4058.286 19.25437 240.4875 261.45 50 0.036 13:22 4088.694 25.65039 235.7297 263.7 50 0.045 13:25 4132.262 32.02652 224.1878 267.75 50 0.081 13:29 4217.333 57.54164 196.6587 270.45 40 0.0675 13:33 4273 47.84251 188.8343 272.25 40 0.045 13:36 4313.329 31.83768 180.3427 274.5 40 0.05625 13:40 4369.544 39.7303 163.8578 275.85 40 0.03375 13:42 4405.68 23.80157 151.524 276.75 40 0.0225 13:43 4431.474 15.85211 141.5816 277.65 40 0.0225 13:44 4458.934 15.83945 129.9619 278.1 40 0.01125 13:45 4473.473 7.914921 123.337 279.45 35 0.038571 13:47 4520.621 27.11224 103.3017 279.9 35 0.012857 13:48 4537.204 9.028835 95.74749 281.25 35 0.038571 13:50 4589.641 27.06035 70.37057 282.15 40 0.0225 13:52 4631.2 15.76684 44.57885 282.6 35 0.012857 13:52 4653.865 9.003466 30.91748 283.05 35 0.012857 13:53 4677.521 8.99895 16.25949 283.5 35 0.012857 13:54 4702.66 8.994404 0.115587 284.4 75 0.012 13:55 4702.66 8.390649 8.506236 285.3 75 0.012 13:55 4702.66 8.386637 16.89287 286.2 70 0.012857 13:56 4702.66 8.981203 25.87408 287.1 70 0.012857 13:57 4702.66 8.976539 34.85061 288 70 0.012857 13:58 4702.66 8.971844 43.82246 290.25 65 0.034615 14:00 4702.66 24.13139 67.95385 290.7 60 0.0075 14:00 4702.66 5.223895 73.17774 291.6 55 0.016364 14:01 4702.66 11.39188 84.56962 293.4 50 0.036 14:03 4702.66 25.03431 109.6039 294.75 45 0.03 14:05 4702.66 20.83231 130.4362 295.65 40 0.0225 14:07 4702.66 15.60631 146.0425 298.35 40 0.0675 14:11 4713.82 46.72501 181.6072 298.8 40 0.01125 14:11 4715.548 7.77359 187.6531 299.7 40 0.0225 14:13 4720.404 15.53507 198.3317 300.6 40 0.0225 14:14 4727.498 15.51879 206.7568 303.75 40 0.07875 14:19 4757.597 54.18518 230.8432 305.55 40 0.045 14:21 4777.74 30.8698 241.5695 306.9 40 0.03375 14:23 4795.047 23.10689 247.3698 308.7 40 0.045 14:26 4821.271 30.74751 251.8932 310.95 40 0.05625 14:30 4859.855 38.33342 251.6428 315 40 0.10125 14:36 4936.526 68.70971 243.6811 317.7 40 0.0675 14:40 4992.193 45.59286 233.607 319.5 40 0.045 14:42 5032.522 30.2977 223.5755 194 321.75 40 0.05625 14:46 5088.738 37.76009 205.1203 323.1 40 0.03375 14:48 5124.873 22.59532 191.5803 324 40 0.0225 14:49 5150.668 15.0379 180.8237 324.9 40 0.0225 14:50 5178.127 15.01719 168.3817 325.35 40 0.01125 14:51 5192.666 7.500776 161.3427 326.7 40 0.03375 14:53 5240.026 22.47081 136.4543 327.15 40 0.01125 14:54 5256.728 7.479697 127.2312 328.5 40 0.03375 14:56 5309.247 22.40708 97.11951 329.4 40 0.0225 14:57 5350.806 14.91118 70.47213 329.85 40 0.01125 14:58 5373.418 7.447463 55.30742 330.3 40 0.01125 14:59 5396.91 7.442019 39.25778 330.75 40 0.01125 14:59 5421.961 7.436554 21.64313 331.65 70 0.012857 15:00 5421.961 8.492201 30.13533 332.55 70 0.012857 15:01 5421.961 8.485006 38.62034 333.45 70 0.012857 15:02 5421.961 8.477781 47.09812 334.35 70 0.012857 15:02 5421.961 8.470525 55.56864 335.25 70 0.012857 15:03 5421.961 8.463238 64.03188 337.5 65 0.034615 15:05 5421.961 22.74919 86.78107 337.95 60 0.0075 15:06 5421.961 4.921941 91.70301 338.85 55 0.016364 15:07 5421.961 10.73001 102.433 340.65 50 0.036 15:09 5421.961 23.56342 125.9964 342 45 0.03 15:11 5421.961 19.59104 145.5875 342.9 40 0.0225 15:12 5421.961 14.6661 160.2536 345.6 25 0.108 15:18 5421.961 70.06755 230.3211 346.05 25 0.018 15:19 5421.961 11.62405 241.9452 346.95 10 0.09 15:25 5421.961 57.88436 299.8296 347.85 45 0.02 15:26 5430.201 12.80912 304.3985 351 50 0.063 15:30 5468.021 40.21804 306.7969 352.8 50 0.036 15:32 5492.489 22.89164 305.2202 354.15 50 0.027 15:34 5513.073 17.12522 301.7618 355.95 50 0.036 15:36 5543.481 22.77507 294.1286 358.2 50 0.045 15:39 5587.049 28.37378 278.934 362.25 50 0.081 15:43 5672.12 50.80269 244.6659 364.95 50 0.054 15:47 5733.309 33.67237 217.1495 366.75 50 0.036 15:49 5777.202 22.35977 195.6159 369 50 0.045 15:51 5837.859 27.84898 162.8079 370.35 50 0.027 15:53 5876.731 16.65517 140.5916 371.25 50 0.018 15:54 5904.226 11.08068 124.1772 372.15 50 0.018 15:55 5933.349 11.06237 106.1158 372.6 50 0.009 15:56 5948.714 5.52429 96.27599 373.95 50 0.027 15:57 5998.524 16.54517 63.01039 374.4 50 0.009 15:58 6015.945 5.505788 51.09565 375.75 55 0.024545 15:59 6072.892 14.99211 9.141073 375.975 50 16:00 6083.561 2.744785 1.216534 16:00 195 This page intentionally left blank 196