Design and characterization of an induction motor for application in a commercial electric vehicle

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1 Design and characterization of an induction motor for application in a commercial electric vehicle Nuno Alexandre Barbas de Gomes Grilo Mestrado Integrado em Engenharia Electrotécnica e de Computadores Instituto Superior Técnico, Technical University of Lisbon, Portugal Supervisors: Duarte Mesquita e Sousa (Instituto Superior Técnico, Technical University of Lisbon, Portugal) Abstract Nowadays, electric vehicles are regarded as the future for a sustainable automobile industry. There are several electric motors designed for future integration in these vehicles, being the AC motors the most widely used nowadays. Among the AC motors group, the induction motors and the permanent magnet motors are the ones that have been most widely used. As a result, this thesis aims at performing the design and simulation of these motors, in order to allow their future integration in a commercial electric vehicle (FIAT Elletra Seicento). In order to perform the design of alternative electric motors, a basic computational tool was built using the Matlab software. This tool allows performing the design of three alternative motors (induction motor, axial flux permanent magnet brushless AC motor and permanent magnet cylindrical brushless AC motor), taking into account the inputs imposed by the user. After designing the motors, the simulation using the FEMM software was performed for two of the three motors which were previously designed: induction motor and permanent magnet cylindrical brushless AC motor. These simulations aimed at studying the distribution of the magnetic field lines across the motors for the working conditions imposed (nominal frequency of 50Hz and nominal current of 60A). After concluding the design and simulation process, it is possible to conclude that the axial flux permanent magnet brushless AC motor is the most attractive one for future application in electric vehicles, as it is characterised by a high torque, high efficiency and can be coupled to the rear wheels of the vehicles. Keywords Electric vehicles; induction motor; permanent magnets AC motor; design; simulation; computational tool; I. INTRODUCTION The first electric vehicle was built in 1830, but it was only by the end of the 19 th century that commercial electric vehicles were available (Larminie and Lowry, 2003). According to Jain et al. (2009) these vehicles are generally regarded as the future for a sustainable automobile industry. A wide variety of electric motors have been used for integration in electric vehicles. Historically, DC electric motors were the most widely used, since its torque/speed characteristic suit the traction requirement for being used in electric vehicles (Nanda and Kar, 2006). Nonetheless, recent advancements in technology have made AC electric motors much more preferable over the traditional DC motors (Nanda and Kar, 2006) AC electric motors are characterized by a much higher efficiency, greater reliability, more power density and less need of maintenance. Among the AC electric motors group, induction motor and permanent magnet brushless AC motor are the most widely used for integration in electric vehicles. This thesis aims at studying alternative motors that can be used for application in a commercial electric vehicle the Fiat Elletra Seicento vehicle. In particular, this study addresses the design and simulation of two main groups of electric motors: the induction motor and the permanent magnet brushless AC motor. The design of the induction motor and the permanent magnet brushless AC motor was performed using the Matlab software (MathWorks, 2010). Based on this software, we have built a computational tool that allows choosing the motor characteristics, giving the main dimensions of that motor as output. This tool represents an important advantage of this study, since it deals with the motor design in a simple and fast way. After concluding the design phase of the study, we have performed the simulation of the referred 1

2 motors using the Finite Element Method Magnetics (FEMM) software (Finite Element Method Magnetics, 2010). This simulation was performed imposing a Hz frequency and a A current, allowing to take some conclusions about the performance of the designed motors. This paper is organized as follows: in section II we present an overview of the electric motors most widely used for application in electric vehicles; in section III we describe the method used for the induction motor design, as well as for its simulation; in section IV is intended to present the design of two permanent magnet brushless AC motors (axial flux and cylindrical motor); in section V we present the simulation of a permanent magnet brushless AC motor, analysing the effect of imposing different positions for the permanent magnets in the rotor; and section VI presents the main conclusions of this study, as well as suggestions for further work in this area. II. OVERVIEW OF ELECTRIC MOTORS USED IN ELECTRIC VEHICLES There are a wide variety of motors that can be used for integration in electric vehicles: 1. Ehsani et al. (2003) propose the use of induction motors, permanent magnet brushless DC motors and switched reluctance motor; 2. Xue et al. (2008) present the same proposal than Ehsani et al. (2003), but they also advocate that brushed DC motors should be used; 3. Nanda and Kar (2006) highlight the relevance of permanent magnet brushless AC motors in such applications. Permanent magnet brushless DC motor As these motors are characterized by the absence of rotor windings and low rotor losses, their efficiency is higher than that of induction motors, conventional DC motors and switched reluctance motors (Ehsani et al., 2003; Xue et al., 2008). Furthermore, permanent magnet brushless DC motors efficiently dissipates the heat to the surroundings and the permanent magnets are not likely to suffer from any manufacturing defects or overheating. Regarding the drawbacks of this type of motor, it has a short constant power range due to its limited field weakening capability (consequence of the permanent magnet field presence) (Ehsani et al., 2003). In addition, the magnet is expensive and its mechanical strength makes it difficult to obtain a large torque into the motor (Xue et al., 2008). Brushed DC motor According to Xue et al. (2008), brushed DC motors show a high ability to achieve high torque at low speed. Nonetheless, these motors have a bulky construction, low efficiency, low reliability and higher need of maintenance. In addition, the friction between its brushes and commutator limits the maximum motor speed. Permanent magnet brushless AC motor According to Nanda and Kar (2006), permanent magnet brushless AC motors are the ones that give a direct competition to the induction motor drives, for use in electric vehicles. The main advantages of this type of motor are shared with the permanent magnet brushless DC motors (Nanda and Kar, 2006): (1) it has a high power density, due to the presence of high energy permanent magnets; (2) it is characterized by a high efficiency, due to the lower rotor losses; (3) the heat rises only in the stator; and (4) the permanent magnets are not likely to suffer from any manufacturing defects or overheating. On the other hand, the main disadvantage of these motors is associated with their complex construction. It is worth noting that the configuration of a permanent magnet brushless AC motor is very similar to that of permanent magnet brushless DC motor. Nonetheless, these motors are fed by a sinusoidal AC supply, rather than a rectangular one (Nanda and Kar, 2006). Induction motor According to Nanda and Kar (2006), at the present induction motors offer one of the most reliable and mature technologies for use in electrical vehicles. These motors are also characterized by a simple construction, reliability, low maintenance, low costs and ability to operate in hostile environments (Xue et al., 2008). In addition, these motors do not suffer from the speed limitations that can be found in brushed DC motors. Nonetheless, these also show an important disadvantage: they are characterised by a lower efficiency when compared to the permanent magnet motors, due to their rotor losses. Switched reluctance motor Switched reluctance motors have been gaining much interest as a candidate for applications in electric vehicles, because of its simple and rugged construction, simple control and ability of 2

3 extremely high speed operation (Ehsani et al., 2003). This type of motor is characterized by a high starting torque and its rotor structure is extremely simple (without any windings, magnets, commutators or brushes) (Xue et al., 2008). The main consequence of the absence of magnetic sources on the rotor (windings or permanent magnets) makes it easy to cool and insensitive to high temperatures. Nonetheless, these motors also show several disadvantages (Nanda and Kar, 2006): (1) it has certain noise problems; and (2) they are characterized by a lower efficiency when compared with permanent magnet motors. 1. The induction motor should be a highspeed motor; 2. The motor is composed by a squirrel cage rotor; 3. The stator and the rotor slots should have the geometry shown in figure 1 and 2, respectively; 4. Only 40% of the stator slots should be occupied by conductors (Gieras et al., 2004); 5. The number of rotor slots should be equal to the number of stator slots. III. DESIGN AND SIMULATION OF AN INDUCTION MOTOR In this section we present the method used for the design of an induction motor with a squirrel-cage rotor using the Matlab software (MathWorks, 2010), as well as its simulation using the Finite Element Method Magnetics (FEMM) software (version 4.2) (Finite Element Method Magnetics, 2010). The induction motor herein proposed is to be used coupled to the drive shaft of the electric vehicle. Design of an induction motor The method used for the induction motor design is based on the use of a set of equations (Kostenko and Piotrovski, 1979; Lipo, 1996; Toliyat and Kliman, 2004), whose application requires the prior choice of the inputs indicated below. These equations were used for building a basic computational tool using the Matlab software (Appendix), which allows the users to choose the inputs, giving the main dimensions of the motor as output. Inputs: Power of the induction motor Line voltage Current Number of pairs of poles Number of phases Speed Power factor Number of slots per pole per phase Airgap thickness Slip Mecanical losses In order to compute the main dimensions of the induction motor, we have imposed the following characteristics: Figure 1. Stator slot geometry (Kostenko and Piotrovski, 1979). Figure 2. Rotor slot geometry (Kostenko and Piotrovski, 1979). Based on the basic computational tool (built using the referred equations and conditions), it was possible to compute the main dimensions of a 15kW and high speed (2200 rpm) induction motor (table 1). Table 1. Results obtained for the main dimensions of the induction motor. Stator inner diameter, [m] 0,1 Stator outer diameter, [m] 0,2 Active length of the core, L [m] 0,3 Number of conductors per phase, 72 Number of stator slots, 36 Conductors per slot, 6 Conductors diameter, [mm] 2,3 Stator reactance, [ ] 2,3 Stator resistance, [ ] 0,01 Rotor reactance, [ ] 1,9 Rotor resistance, [ ] 0,1 Airgap reactance, [ ] 27,8 Maximum torque, [Nm] 46,4 Total losses, [W] 1826,6 Efficiency, [%] 89,2 3

4 Simulation of an induction motor In order to perform the simulation of the induction motor previously designed, we have used the FEMM software. FEMM is an open source finite element analysis software package for solving electromagnetic problems (Baltzis, 2008). Using this software, it is possible to address linear and nonlinear magnetostatic problems, linear and nonlinear time-harmonic magnetic problems, linear electrostatic problems and steady-state heat flow problems (Meker, 2008). In this section, we address a non-linear time-harmonic magnetic problem in such problems the magnetic field is time-varying and oscillates at one fixed frequency (which was chosen to be Hz). Firstly, a cross section of the induction motor previously designed was built (figure 3) the number of rotor and stator slots, the inner and outer diameters, the active length and the number of conductors per slot were extracted from the results obtained through the use of the computational tool. The materials chosen for this motor were the following: 1. M-19 Steel for the stator and rotor core (which is a laminated material characterized by a non-linear B-H curve); AWG Copper for the conductors; Aluminium for the squirrel-cage rotor bars. field lines are symmetrically distributed around each pole, as it would be expected. Figure 4. Magnetic field lines distribution in the middle cross section of the induction motor. Additionally to the magnetic field lines distribution, it is also important to analyse the distribution of the H field across the rotor and stator cores. Figure 5 shows this distribution across the stator core of the induction motor (the origin of the horizontal axis corresponds to the outer diameter of the stator). Figure 5. H field distribution across the stator of the induction motor (according to the red line shown in the figure). Figure 3. Middle cross section of the induction motor built using the FEMM software. Regarding the boundary conditions, and as the whole cross section of the motor was used, only the first order Dirichlet's was applied on the outer stator line and inner rotor line. Once built, and after imposing a frequency of Hz and nominal current of A, it was possible to analyse the distribution of the magnetic field lines through the entire cross section of the induction motor (figure 4). As it can be seen, the magnetic As it can be seen in the figure, the H field is always lower than A/m (H field for which the M-19 Steel saturates), which means that the material which composes the stator core does not saturate when the induction motor is working at a nominal frequency of Hz and a nominal current of A. Nonetheless, the higher H field is found near the stator slots where the current of the stator windings is flowing. Performing the same analysis in the rotor core allows concluding that the material which composes this core (M-19 Steel) does not saturate (for the same reasons described for the stator core). 4

5 IV. DESIGN OF PERMANENT MAGNET BRUSHLESS AC MOTOR In this section we present the methods used for the design of two permanent magnet brushless AC motors (using the Matlab software) as well as its simulation (using the FEMM software). The first motor to be analysed is an axial flux permanent magnet brushless AC motor composed by two stators, which is to be used coupled to the rear wheels of the electric vehicle. The second one is the permanent magnet cylindrical brushless AC motor, which is to be used coupled to the drive shaft of the electric vehicle (in the same way described for the induction motor). The design of both motors was also performed using a set of equations which were used for building the referred basic computational tool (Appendix). Design of an axial flux permanent magnet brushless AC motor In the same way previously described, the method used for the design of the motor herein proposed is based on the use of a set of equations (Gieras et al., 2004). The application of these equations requires the choice of the same inputs referred for the induction motor, as well as the choice of an additional input that is described below. Additional input: Permanent magnet thickness The characteristics which were imposed for designing the axial flux permanent magnet brushless AC motor were the following: 1. The motor is composed by two stators; 2. The permanent magnets chosen for the motor design are trapezoidal magnets (figure 6); 3. The number of conductors per cable is set to one; 4. Only 40% of the stators slots should be occupied by conductors (Gieras et al., 2004); 5. The stators slots should have the geometry shown in figure 1. Figure 6. Rotor composed by Trapezoidal permanent magnets (Gieras et al., 2004). Based on the basic computational tool (built using the referred equations and conditions), it was possible to compute the main dimensions of a 7,5kW and low speed (700 rpm) axial flux permanent magnet brushless AC motor composed by two stators (table 2). As this motor is to be used coupled to the rear wheels of the electric vehicle, we need to design two motors with half of the power required for the vehicle as we want a 15kW total power, we have to design two motors of 7,5kW each. Table 2. Results obtained for the main dimensions of the axial flux permanent magnet brushless AC motor composed by two stators. Stators and rotor inner diameter, [m] 0,2 Stators and rotor outer diameter, [m] 0,3 Number of conductors per phase and per stator, 360 Number of stators slots, 36 Conductors per slot, 60 Conductors diameter, [mm] 1,6 Stator reactance, [ ] 9,1 Stator resistance, [ ] 1,4 Stator synchronous reactance, [ ] 11,2 Stator armature reactance, [ ] 2,1 Torque, [Nm] 98,7 Total losses, [W] 1097,1 Efficiency, [%] 86,8 Design of a permanent magnet cylindrical brushless AC motor In the same way described for the previous motors, the method used for the design of the motor herein proposed is based on the use of a set of equations (Kostenko and Piotrovski, 1979; Lipo, 1996; Gieras and Wing, 2002; Gieras et al., 2004; Toliyat and Kliman, 2004). The application of these equations requires the choice of the same inputs referred for the previous motor. The characteristics which were imposed for designing the permanent magnet cylindrical brushless AC motor were the following: 1. The permanent magnets chosen for the motor design are shown in figure The number of conductors per cable is set to one; 5

6 3. Only 40% of the stators slots should be occupied by conductors (Gieras et al., 2004); 4. The stators slots should have the geometry shown in figure 1. Figure 7. Rotor composed by external permanent magnets (Gieras and Wing, 2002). The main dimensions of a 15kW and high speed (2200 rpm) permanent magnet cylindrical brushless AC motor are presented in table 3 (obtained using the computational tool). Table 3. Results obtained for the main dimensions of the permanent magnet cylindrical brushless AC motor. Stator inner diameter, [m] 0,084 Stator outer diameter, [m] 0,120 Active length of the core, L [m] 0,263 Number of conductors per phase, 48 Number of stator slots, 36 Conductors per slot, 4 Conductors diameter, [mm] 3,175 Stator reactance, [ ] 0,398 Stator resistance, [ ] 0,014 Stator synchronous reactance (d component), [ ] 0,319 Stator synchronous reactance (q component), [ ] 0,239 Stator armature reactance (d component), [ ] 0,106 Stator armature reactance (q component), [ ] 0,026 Torque, [Nm] 68,349 Total losses, [W] 920,255 Efficiency, [%] 94,478 V. SIMULATION OF PERMANENT MAGNET CYLINDRICAL BRUSHLESS AC MOTORS In this section, and in the same way described for the induction motor, we address two non-linear time-harmonic magnetic problems using the FEMM software: 1. Simulation at a 50Hz frequency and 60A current of a permanent magnet cylindrical brushless AC motor composed by external magnets; 2. Simulation at a 50Hz frequency and 60A current of a permanent magnet cylindrical brushless AC motor composed by internal magnets. Simulation of a permanent magnet cylindrical brushless AC motor composed by external magnets In the same way described for the simulation of the induction motor, a cross section of the permanent magnet cylindrical brushless AC motor composed by external magnets was designed (figure 8) - the number of stator slots, the inner and outer diameters, the active length and the number of conductors per slot were extracted from the results obtained through the use of the computational tool. The materials chosen for this motor were the following: 1. M-19 Steel for the stator and rotor core; AWG Copper for the conductors; 3. Alnico 5 for the permanent magnets. We have decided to use Alnico 5, because this is the material most widely used in the permanent magnets applied in electric vehicles (Gieras and Wing, 2002). The main advantage of this material is related with its high flux density (thus producing high output torques) (Meker, 2008). Figure 8. Cross section of the permanent magnet cylindrical brushless AC motor composed by external magnets built using the FEMM software. For this analysis, the boundary conditions were the same as those described for the induction motor. After processing the simulation of the motor (imposing a frequency of Hz and nominal current of A), it was possible to analyse the results obtained for the distribution of the magnetic field lines on the entire cross section of the motor. The results are shown in figure 9. 6

7 Figure 9. Magnetic field lines distribution in the middle cross section of the permanent magnet cylindrical brushless AC motor composed by external magnets. Analysing the results shown in figure 9, it is possible to notice that the magnetic field lines (in the same way described for the induction motor) are symmetrically distributed around each pole, as it would be expected. Regarding the distribution of the H field across the rotor and stator cores, we have verified that the H field is always lower than A/m in both structures (H field for which the M-19 Steel saturates). As a result, we can conclude that the stator and rotor cores are not saturated when the motor is working at a nominal frequency of Hz and a nominal current of A. Simulation of a permanent magnet cylindrical brushless AC motor composed by internal magnets The simulation of the permanent magnet cylindrical brushless AC motor composed by internal magnets is very similar to the simulation performed for the previous motor. Firstly, we have designed the middle cross section of the motor, according to figure 10 (using the results obtained through the use of the computational tool). The materials used for this design were the same than those described for the permanent magnet cylindrical brushless AC motor composed by external magnets. The main difference here is associated with the permanent magnet position in the rotor. Figure 10. Cross section of the permanent magnet cylindrical brushless AC motor composed by internal magnets built using the FEMM software. The boundary conditions, working frequency and current imposed were the same used for the previous motor. The simulation results obtained for these conditions are shown in figure 11. Figure 11. Magnetic field lines distribution in the middle cross section of the permanent magnet cylindrical brushless AC motor composed by internal magnets. Analysing Figure 11, we can conclude that the magnetic field distribution, like for the previous two motors, are symmetrically distributed around each pole, as it would be expected. Analysing the distribution of the H field across the rotor and stator cores allowed concluding that the stator and rotor cores are not saturated when the motor is working at a nominal frequency of Hz and a nominal current of A (since the H field is always lower than A/m in both structures). Nonetheless, the H field distribution on the permanent magnets shows values higher than the saturation threshold which characterizes its material (Alnico 5 is characterized by a saturation threshold of 5000 A/m) (figure 12) as a result, the material which composes the permanent magnets 7

8 saturates when the motor is working at a nominal frequency of Hz and a nominal current of A. Figure 12. H field distribution across the permanent magnet of the rotor (the origin of the horizontal axis corresponds to the inner diameter of the rotor). VI. CONCLUSIONS AND FURTHER RESEARCH This section presents the main conclusions that can be drawn from this study, as well as suggestions for further research in this area. Conclusions The first stage of this thesis was intended to study alternative motors for future application in electric vehicles. There are several options, so there is need to analyse the advantages and disadvantages associated with the use of each type of electric motor. After studying the main characteristics of the motors in use for applications in electric vehicles, we have analysed in more detail the following two types of electric motors: induction motor and permanent magnet AC brushless motor. These two motors are the most widely used nowadays. This type of analysis is of great importance, since it will represent the basis for the future development of new motors for a commercial electric vehicle (FIAT Elletra Seicento). In order to complete this analysis, our study was divided into two phases: (1) design; and (2) simulation phases. For the design phase of this thesis, we have built a computational tool using the Matlab software. Using this tool, we have performed the design of three different motors: induction motor, axial flux permanent magnet AC brushless motor and permanent magnet cylindrical brushless AC motor. After concluding this design, it is possible to conclude that the most attractive one for a future application in electric vehicles will be the axial flux permanent magnet brushless AC motor. There are several reasons that justify this choice: 1. It as the higher torque ( ); 2. It as a high efficiency ( ); 3. It can be used coupled to the vehicle wheels this type of drive system does not have a gear system and, as a consequence, does not show the associated mechanical losses. It is worth noting that the permanent magnet cylindrical brushless AC motor is the one with the higher efficiency. Nonetheless, as it has a lower torque, high speed and high dimensions, it cannot be coupled to the vehicle wheels. Comparing the results obtained from the design of the three motors it is possible to take several additional conclusions: 1. Taking the efficiency as the criterion, the permanent magnet cylindrical brushless AC motor is the most attractive one. This behaviour is in accordance to Gieras and Wing (2002), Nanda and Kar (2006) and Xue et al. (2008), since they advocate that the efficiency of such a motor is expected to be the higher due to the presence of the permanent magnets in the rotor; 2. Taking the torque as the criterion, the axial flux permanent magnet AC brushless motor is the preferred one. Regarding the tool developed using the Matlab software, it represents an important advantage of this study. This tool allows the design of alternative motors for future integration in electric vehicles. Given the simplicity of this tool, any person will be able to use it, provided that he has all the inputs asked. Nonetheless, the tool was developed based on certain conditions that must be taken into account by the users before using it: 1. The motors designed using the tool must be air cooled; 2. The motors should work at a 50/60Hz of nominal frequency; 3. The power of the motor should be lower than 100kW (Gieras et al., 2004). Once the design phase is concluded, we have performed the simulation of the following motors: induction motor, permanent magnet cylindrical brushless AC motor with external rotor magnets and permanent magnet cylindrical brushless AC motor with internal rotor magnets. These simulations are of great importance, since they allow evaluating the performance of the previously designed motors after imposing different working conditions. Regarding the results of these simulations, it is possible to take several conclusions: 8

9 1. The magnetic field lines shown for all the three motors are symmetrically distributed around each pole, as it would be expected. Nonetheless, there are some deviations from the typical behaviour, which is related with the method used by the FEMM software to compute the results; 2. The material which has been chosen for the stator and rotor core (M-19 Steel) represent a good choice, since it does not saturate when the motors (all the three motors which have been simulated) are working at a 50Hz frequency and with a 60A current; 3. The results obtained for the magnetic field across the motors are in accordance with the literature. After performing all the designs and simulation analysis, it is possible to conclude that the FEMM software represents an useful tool that should be used to complement the design phase. The reason that justifies this complementarity is related with the possibility to verify the motor performance when different working conditions for the designed motors are imposed. Further research Regarding further research, this thesis is intended to be used for a future construction of the designed motors, in order to be integrated in a specific commercial electric vehicle FIAT Elletra Seicento. As we have developed a basic tool that allows the design of three alternative electric motors, it might be useful to improve it for example improve its graphical interface. After performing the simulation of the permanent magnet brushless AC motor at a 50Hz frequency and 60A current, it was possible to conclude that the material chosen for the permanent magnets was saturated (Alnico 5). As a result, it might be interesting to impose the use of different materials for these magnets, analysing the effect of these new materials on the performance of the motors. VII. APPENDIX: COMPUTATIONAL TOOL A basic computational tool was developed using the Matlab software. This tool allows performing the design of alternative motors for future application in electric vehicles: induction motor, axial flux permanent magnet AC brushless motor and permanent magnet cylindrical brushless AC motor. The first step required for using this tool is related with the choice of the motor the user wants to design (figure 13). After choosing the motor to be designed, the user is asked to provide the inputs he wants to impose for the motor: figure 14 shows the inputs window for the design of the induction motor; the input windows for the remaining two motors are very similar, but with an additional input (permanent magnet thickness). After introducing the inputs, the results obtained for the main dimensions of the motor to be designed are provided by the tool according to figure 15 (the results obtained for the remaining two motors are shown through a very similar window). Figure 13. Window used for the selection of the motor to be designed. 9

10 Figure 14. Inputs window for the design of an induction motor. Figure 15. Outputs window with the main dimensions obtained for an induction motor. VIII. REFERENCES [1] Baltzis KB. The finite element method magnetic (FEMM) freeware package: May it serve as an educational tool in teaching electromagnetics?. Education and Information Technologies, 2008; 5(1): [2] Boldea I, Nasar SA. The Induction Machine Handbook. ISBN: , CRC Press, [3] Ehsani M, Gao Y, Gay S. Characterization of Electric Motor Drives for Traction Applications. Industrial Electronic Society 2003; 1: [4] Finite Element Method Magnetics. Available through the internet via www. URL: Consulted between March and October [5] Fitzgerald AE, Kingsley C, Umans SD. Máquinas Eléctricas. Porto Alegre: Bookman, [6] Gieras JF, Wang RJ, Kamper MJ. Axial Flux Permanent Magnet Brushless Machines. USA: Kluwer Academic Publishers, [7] Gieras JF, Wing M. Permanent Magnet Motor Technology Design and Applications. New York: Marcel Dekker, Second Edition, [8] Jain M, Sheldon S, Williamson. Suitability Analysis of In-Wheel Motor Direct Drives for Electric and Hybrid Electric Vehicles. Concordia University, Canada, [9] Juliani ADP, Gonzaga DP, Monteiro JRBA. Magnetic Field Analysis of a Brushless DC Motor. International Conference on Electrical Machines, [10] Kolondzovski Z, Petkovska L. Determination of a Synchronous Generator Characteristics via Finite Element Analysis. Serbian Journal of Electrical Engineering, 2005; 2(2): [11] Kostenko M, Piotrovski L. Máquinas Eléctricas Máquinas AC. Volume II, Edições Lopes da Silva, Larminie J, Lowry J. Electric Vehicle Technology Explained. England: John Wiley & Sons, [12] Lipo AT. Introduction to AC Machine Design. Volume I, University of Wisconsin, Madison Wisconsin, USA, [13] MathWorks. Available through the internet via www. URL: Consulted between March and October [14] Meeker D. Finite Element Method Magnetics, Version 4.2, User s Manual [15] Nanda G, Kar NC. A survey and comparison of characteristics of motor drives used in electric vehicles. Canadian Conference on Electrical and Computer Engineering, 2006; [16] Ombach G, Junak J. Comparative study of IPM motors with different air gap flux distribution. J. 4 th IET Conference on Power Electronics, Machines and Drives, 2008; [17] Toliyat HA, Kliman GB. Handbook of Electric Motors Second Edition, Revised and Expanded. ISBN: , Marcel Dekker Inc, United States of America, [18] West JGW. DC, induction, reluctante and PM motors for electric vehicles. Power Engineering Journal 1994; 8(2): [19] Xue X, Cheng K, Cheung N. Selection of Electric Motor Drives for Electric Vehicles. Australian Universities Power Engineering Conference [20] Yang T, Zhou L, Li L. Parameters and Performance Calculation of Induction Motor by Nonlinear Circuit- Coupled Finite Element Analysis. International Conference on Power Electronics and Drive Systems, 2009;