Comparison of In-wheel Permanent Magnet Motors for Electric Traction

Transcription

1 Comparison of In-wheel Permanent Magnet Motors for Electric Traction M. E. Beniakar, P. E. Kakosimos, C. T. Krasopoulos, A. G. Sarigiannidis and A. G. Kladas Abstract -- This paper undertakes a comparative study between two different in-wheel Surface Mounted Permanent Magnet motors with Fractional Slot Concentrated Winding configurations designed for a light electric vehicle application. For the design of both motors two different approaches are followed, regarding the winding configuration and the relative dimensions of the motor, i.e. axial length and air-gap diameter, and additionally two alternative strategies are adopted concerning the selection of the reference operational point. The first motor comprises a double layer concentrated winding with all teeth wound while is slightly over-dimensioned increasing efficiency during over operation. A single layer concentrated winding with alternate teeth wound and unequal teeth distribution is adopted for the second motor dimensioned in terms of weight minimization considering the nominal operation. For the optimization of the first alternative, Taguchi s method is utilized, while for the latter one a Strength Pareto Evolutionary Algorithm variant is developed. Both performances are validated by examining manufactured prototypes under real conditions. Index Terms Electric traction, permanent magnet motors, fractional slot concentrated windings, unequal teeth distribution, Taguchi s method, strength Pareto evolutionary algorithm F t T m P t L R gap B n B t B E N ph f e k w P Φ A slot I N V P i J ff Q P ed I. NOMENCLATURE : tangential component of the magnetic force : mean electromagnetic torque : mean tangential pressure : active motor length : airgap radius : normal magnetic flux density component : tangential magnetic flux density component : mean magnetic flux density at the airgap : induced fundamental rms back Electromotive force : number of turns per phase : electric frequency : winding factor : number of poles : mean magnetic flux per pole : slot surface : nominal stator current : input stator rms voltage : input power : current density : fill factor : number of slots : total PM eddy-current losses The research leading to these results has received funding from the EU and General Secretariat of Research and Technology of Greece under SYN-- Grant. M. E. Beniakar, P. E. Kakosimos, C. T. Krasopoulos, A. G. Sarigiannidis, and A. G. Kladas are with the Laboratory of Electrical Machines and Power Electronics, Department of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece ( beniakar@central.ntua.gr, panoskak@gmail.com). p r θ r R s u v I u θ u K wsv K sov ω r p s ρ J m k mag W t L t T r P loss SS k un θ mag W t h mag w bs w br X G F i : number of rotor pole pairs : angular displacement in the rotor reference frame : stator inner radius : order of line current time harmonic : order of MMF space harmonic : amplitude of the u th current harmonic component : angle of the u th current harmonic component : winding factor for the v th space harmonic : slot opening factor for the v th space harmonic : rotor angular speed : equivalent stator pole pairs : permanent magnet resistivity : induced eddy current in a permanent current : magnet to pole ratio : stator tooth width : stator tooth length : electromagnetic torque ripple : total losses : sum of squares : unequality ratio : magnet angle : width of stator thicker tooth : magnet height : stator back iron thickness : rotor back iron thickness : design variables vector : i th objective function THD : total harmonic distortion II. INTRODUCTION ermanent magnet in-wheel motors have been widely P used in electric traction applications [, ] due to their inherent advantages of high performance and power density attracting an unprecedented interest within the research community especially for demanding applications [, ]. A favorable and competitive motor topology towards this direction is Surface Mounted Permanent Magnet (SMPM) motors [, ] combined with a Fractional Slot Concentrated Winding (FSCW) configuration offering beneficial characteristics [, ]. The nature of the application specifications, regarding both performance and efficiency, in conjunction with the needs for high power quality and reduced weight, have highlighted the necessity of the thorough investigation of their operational characteristics and behavior as well as their systematized optimization [- ]. In recent bibliography both approximate and systematized optimization techniques have been proposed for electric traction applications [-]. The Taguchi s method along with extended sensitivity analysis techniques have been reported to yield satisfactory results even in demanding aerospace applications [], in spite their simple nature. ----//$. IEEE

2 Additionally, several single and multi-objective optimization methodologies, employing genetic or evolutionary algorithms have been reported to approach the optimum solutions in a more systematized manner [,]. The advantages or disadvantages of the respective methods are considered application specific, as they benefit from their particular characteristics, regarding efficiency, computational cost and solution diversity. For the design of the two motors two different approaches are followed in this paper, regarding the winding configuration and the relative dimensions of axial length and air-gap diameter. Additionally, two alternative strategies concerning the optimization technique are developed involving the reference operational point. The first motor comprises a double layer concentrated winding with all teeth wound and is slightly over-dimensioned increasing efficiency during over operation. A single layer concentrated winding with alternate teeth wound and unequal teeth distribution is adopted for the second motor dimensioned in terms of weight minimization considering the nominal operation. Taguchi s method is employed for the optimization of the first alternative, while for the latter one a Strength Pareto Evolutionary Algorithm (SPEA) variant is developed. Finally, both prototypes are manufactured and their performance is validated by experiments. III. PRELIMINARY DESIGN The preliminary design procedure for the two inherently different SMPMs is based on the same classical machine design techniques and approximate analytical tools and was validated via Finite Element (FE) models. However, the initial design approaches were different regarding mainly the reference operating point. For the design process of the first motor the over condition was considered and consequently the motor was slightly overdimensioned and optimized for higher torque values. As a result, the first motor exhibits a higher torque capacity but a lower power density value and is bigger regarding both weight and size. The second motor was designed for the normal cruise operation, and the high torque operation was considered as over. The extreme over condition was accounted for in terms of the integration of specific constraints, regarding both thermal robustness and performance, in the optimization procedure. The motor was designed with an adequately high torque capacity to satisfy the over specifications, but optimized in terms of efficiency for the nominal operation. For this reason, it exhibits a high power density value and is very compact in size and weight, but requires higher currents to produce over torque values. Furthermore, the relative dimensions, i.e. the motor active length and the air-gap diameter are different. An increase in the air-gap diameter results in a much bigger increase in the output power than an equal increase in the axial length. However, the torque required and the operating speed must be considered. For very high torque requirements, a large diameter is recommended, as a particular amount of force developed in the air-gap would result in a larger amount of torque if the distance between it and the axis is increased. In addition, the short axial length causes high values of leakage flux at the air-gap. On the other hand, at higher speed operations, the common practice is to increase the axial length rather than the diameter if more power is needed. This is intended to retain the surface speed to a reasonable value and avoid high centrifugal forces and localized iron losses. Furthermore, a rotor of large axial length may experience mechanical oscillation and possible failure as the operating speed reaches very high levels. The first motor exhibits a low value of the L/ D g ratio in order to boost its torque capacity, given the relatively low operational speed values. The second motor has a slightly higher value of the L/ D g ratio, and smaller dimensions in general, presenting a more compact and balanced construction. A. Classical analytical machine design In a first step, classical analytical design methodologies are used, to determine the basic dimensions and operational characteristics of the two motors. It should be noted that such an analytical approach does not enable detailed design optimization, due to the approximate nature of the electromagnetic field representation, but provides a suboptimum set of design variables adequately close to the region of the global optimum. The initial design is focused on the satisfaction of the main operational specifications and some fundamental spatial limitations, mainly regarding the in-wheel nature of the motor configurations. For the needs of the preliminary analysis, on a first step, the basic dimensions and performance indexes of the motors are calculated. The produced electromagnetic torque can be calculated from the mean tangential pressure of the magnetic forces on the gap of the machine, which is expressed as follows: T R F T R L P () m gap t m gap t P B B dl () t n t Dg The back-electromotive Force (back-emf) of a SMPM, assuming a sinusoidal air-gap flux can be expressed as: E N f k () ph e w B LD g () P The back-emf level for the overing should be defined by the dc link voltage level of the inverter, assuming a maximum amplitude modulation ratio around one and a mean value around.. Therefore, the total number of turns per phase and the feasible combinations of L and D g, can be determined from (). The necessary slot surface can be computed by the following formula: A slot IN Nph J ff Q In a second step, the winding configuration and the combination of rotor poles and stator slots is determined in terms of winding factor maximization and selection of a favorable value for the electric frequency. In particular, a high frequency value should be avoided in order to enable the reduction of iron losses. However a very low frequency ()

3 value could incur a very bad fault tolerance capability for the motors. SMPMs inherently exhibit small inductance values and an additional low operating frequency would result in reduced damping capability. Figure and illustrate the winding factor variation for the most commonly used feasible combinations of rotor poles and stator slots for all teeth wound and alternate teeth wound FSCW configurations respectively. Figure (c) illustrates the feasible combinations of L and D g for the given specifications and depicts the selected values for the two motors. Figure (d) shows the respective combinations of number of poles and electrical frequency and the selected values for the two motors. In a next step, a -D FE model is employed, in order to validate the analytical preliminary design process and to evaluate precisely the initial motor s topology performance, efficiency and power quality characteristics. The results of the model are used as feedback and specific dimensions and the electrical and/or the magnetic ing considered are adjusted, so that specifications are met. Number of rotor poles P Motor gap diameter D (mm) Winding factor variation for DL windings Number of stator slots Q L,D feasible combinations st motor.... nd motor Motor active length L (mm) Number of rotor poles P Winding factor variation for SL windings. Electrical frequency (Hz) Number of stator slots Q Poles Vs Frequency..... P= f= Hz P= f= Hz Number of poles P (c) (d) Fig.. Main results of classical analytical design. Winding factor variation for all teeth wound configurations, Winding factor variation for alternate teeth wound configurations, (c) Feasible combinations of motor axial length L and air-gap diameter D dictated by the torque and speed specifications, (d) Feasible number of poles and frequency values. B. Analytical prediction of PM eddy current losses In a third step, an analytical model is used to estimate the respective eddy-current losses on the PMs, considering the winding configuration, the basic motor dimensions and the calculated input current of the motors. In particular, a model that considers both space and time harmonics has been implemented based on [], however for the needs of the preliminary analysis, taking into account only the fundamental of the line current, as calculated from the FE model. As the inputs of the FE model are the three phase line currents and not the voltage waveforms, the resulting current time harmonics are difficult to be á priori determined. However, the model enables the á posteriori validation of the results, utilizing the measured current waveforms. The analytical model is based on the representation of the stator ampere-turns distribution by an equivalent current sheet of infinitesimal thickness disposed over the slot opening. For all teeth wound motor configurations the equivalent current density that accounts for the armature reaction is expressed in Fourier series as: NphIu Jsr, Rs, t KwvKsov u v R () s u sin upr vpsrt vpsr u Q while for alternate teeth motor configurations it is expressed as: NphIu Jsr, Rs, t KwvKsov u v R () s cos upr vpsrt vpsr u For an in-wheel motor, i.e. external rotor configuration, the resulting eddy-current losses in the surface mounted PMs are calculated using () r R r r ed r m r R m P p J rdrd dt Figure illustrates the winding configurations for the two motors and the respective qualitative electric ing distributions that account for the produced MMF waveforms and directly dictate the occurring eddy-current losses in the PMs. The first motor comprises a slot all teeth wound (double layer) FSCW and poles and the second motor comprises a stator slot alternate teeth wound (single layer) FSCW and poles. Fig.. Winding configurations and respective qualitative electric ing distributions, All teeth wound configuration and P/Q = /, Alternate teeth wound configuration and P/Q = /. For the purposes of the analysis two distinct operating conditions were analyzed, i.e. the normal cruise steady state operation and the extreme over operation, when a torque boost is required. The nominal speed is rpm, which corresponds to different respective nominal frequencies, given the different number of poles of the two motors. Additionally, different nominal current values, as computed by FE analysis, are used. Figure shows the variation of the PM eddy-losses with respect to the operating electrical frequency for the two motors, for both operating conditions. ()

4 PM eddy losses (W) Motor - Over Motor - Over Motor - Cruise Motor - Cruise Electrical frequency (Hz) Fig.. Permanent magnet eddy losses Vs frequency for the two motors. The analytical model also enables the investigation of the impact of several design parameters on the PM eddy-losses. The variation of the losses for the two motors as a function of the slot opening ratio and the magnet to pole ratio is shown in Fig. and Fig. for the respective nominal frequencies of Hz and Hz (The nominal rotational speed of rpm is considered). The second motor exhibits increased PM eddy losses, compared to the first. Slot opening ratio PM eddy losses Vs magnet to pole ratio and slot opening Hz All TW Magnet to pole ratio..... Slot opening ratio PM eddy losses Vs magnet to pole ratio and slot opening Hz Alter TW.... Magnet to pole ratio Fig.. Permanent magnet eddy losses Vs slot opening ratio and magneto pole ratio for the two motors motor for nominal frequency Hz and motor for nominal frequency Hz. The initial analysis resulted in two first motor geometries that satisfy the dictated by the application specifications and dimensions. The main specifications and dimensions of the motors are tabulated in Table I. TABLE I MAIN SPECIFICATIONS AND DIMENSIONS Quantity Value Motor Motor Normal operation Torque. Nm.. Speed. rpm Over operation Torque. Nm.. Speed. rpm DC bus voltage (V) Number of conductors per phase Number of poles / slots/ phases // // Outer diameter (mm) Active motor length (mm) Air-gap length (mm).. IV. OPTIMIZATION METHODOLOGY As mentioned before, two different optimization strategies were employed for the determination of the final motor geometries, the first employing an approximate approach to the optimum solution and the other utilizing a multiobjective evolutionary methodology. A. Optimization of the first motor using Taguchi s method For the detailed optimization of the first motor, Taguchi s method was employed. In order to establish the prerequisite orthogonal arrays of the problem to be solved, Table II has to be filled with the chosen parameters for the machine optimization and their allowable values. The main stator parameters selected under this stage of optimization are the tooth width, W t, the magnet pitch to pole pitch ratio, k mag and the tooth length, L t, noted hereafter as A, B and C respectively. The initial values derived from the classical design are typed in bold font. Considering the fact that three parameters with three respective levels have been selected, a standard Taguchi s orthogonal array L- has to be adopted. Conducting the required computations, the average torque, T m, the torque ripple, T r, the power losses, P loss, and the THD of the back electromagnetic force are considered. The results derived from the computations employing Maxwell s stress tensor are tabulated in Table III. The average value of T m is. Nm, while the average ripple is calculated to be about % of the mean torque. Table III also depicts the average effect of the chosen parameters, illustrating the impact of the selected design variables. However, through the Analysis of Variance (ANOVA) the thorough evaluation of the effect of the various factors on the parameters of T m, T r, P loss and THD is feasible. The necessary calculation of the Sum of Squares (SS) can be computed by the following equation. i i SS m m Table IV summarizes the results of the ANOVA. The average and cogging torque considerably depend on the magnet pitch to pole pitch ratio, while the back-emf THD is equally affected almost by each parameter. The selection of the most suitable combination for this specific application is a result of a compromise due to the high degree of dependence. Regarding the aforementioned analysis, the combination A-B-C is chosen. Power losses remain almost unaffected by the selected variables variation, whereas the mean and cogging torque are significantly influenced. Considering the back-emf THD, the th combination presents the lowest value, however, the selected combination seems to be a more beneficial choice increasing mean torque by % and limiting cogging torque by %. TABLE II DESIGN VARIABLES AND LEVELS A (mm) B (%) C (mm)... TABLE III RESULTS FROM THE TAGUCHI S APPLICATIONS No A B C P loss (W) T m (Nm) T r (%) THD (%) ()

5 TABLE IV RESULTS OF THE ANALYSIS OF VARIANCE Factor A B C P loss (W) SS* -... %... T m (Nm) SS* -... %... T r (%) SS* -... %... THD (%) SS* -... %... The design parameters values for the selected optimal design for the first motor are tabulated in Table V. Electromagnetic field characteristics Design variables TABLE V DESIGN CHARACTERISTICS OF THE ST MOTOR Value (Normal / Over) Torque (Nm). /. Efficiency (%). /. Current RMS (A). /. Fundamental EMF (V). /. THD of EMF (%). /. Torque ripple (%) /. Magnet angle (%) Tooth width (mm). Back iron stator thickness (mm). Back iron rotor thickness (mm). Copper Fill factor. Total mass (kg). B. Optimization of the second motor using SPEA For the detailed optimization of the second motor a three objective optimization methodology is implemented, based on the SPEA technique. The concept of Pareto nondomination is utilized to produce an optimum solutions front [,]. The latter feeds an automated SMPM motor design script, generating a D Finite Element (FE) model corresponding to each optimization run, thus allowing for precise computation of the objective function values. The block diagram of the procedure is illustrated in Fig.. The selected design variable vector is: XG kun mag Lt Wt hmag wbs w () bi G where k un is the unequality ratio, θ mag is the magnet angle, L t is the stator tooth length, W t is the width of stator thicker tooth, h mag is the magnet height, w bs is the stator back iron thickness and w br is the rotor back iron thickness. The three objective functions F, F, F correspond to maximization of torque capability, minimization of total iron and copper losses and minimization of back-emf harmonic content and torque ripple, respectively. This objective profile accounts for performance, efficiency and power quality. The objective functions are expressed as follows: Fig.. Block diagram of the implemented optimization methodology, utilizing the SPEA algorithm. SPEA is an evolutionary algorithm with great application in engineering, since it has no prerequisites for the objective function and exhibits good solution diversity on both the objective and search space and stable convergence. The algorithm negotiates a fixed size of Pareto front members and when the front isn t fully refined, dominated solutions with the best fitness values are additionally obtained in the final solution set. In any case, the designer must select the final topology-solution, known as the best compromise solution. The constraints handling strategy is the death penalty. For every trial vector generated in each generation, constraint functions are evaluated and the potential population member is immediately rejected if at least a single constraint is violated. If none constraint is violated, the objective functions for the vector are evaluated and the solution enters the mating pool so that mutation, recombination and tournament selection are performed. The trial vector is compared in terms of non-domination during the tournament selection and if it enters the current generation population, it competes with all the current Pareto front members, and the front is updated. It should be noted that a new generation member can dominate multiple members of the Pareto, which are eliminated from the front. The resulting Pareto front in the D objective function space is presented in Fig.. Figure also depicts the three projections of the Pareto front on the respective objective function surfaces. The position of the initial design in the objective function D space is also indicated. The conflicting nature of the objective functions is evident from the final shape of the front. The design parameters values for the selected optimal design for the second motor are tabulated in Table VI. F F F F T P THD T.. T P THD T m, loss EMF r m loss, EMF r, () where the index refers to the electromagnetic characteristics of the initial design. Fig.. Resulting Pareto front and its projections on the respective objective function surfaces. The position of the initial design in the objective function space is indicated.

6 Electromagnetic field characteristics Design variables TABLE VI DESIGN CHARACTERISTICS OF THE ND MOTOR Value (Normal / Over) Torque (Nm). /. Efficiency (%). /. Current RMS (A). /. Fundamental EMF (V). /. THD of EMF (%). /. Torque ripple (%). /. Magnet angle (%) Tooth width (mm). Back iron stator thickness (mm). Back iron rotor thickness (mm). Unequality ratio (%). Copper Fill factor. Total mass (kg). capacity and exhibits higher efficiency at torque boost operating regions. The optimized motor topologies have been validated by measurements on two manufactured prototypes. The two motors are shown in Fig.. Figure shows the experimental results, regarding the produced electromagnetic torque, obtained for the two motors under real operating conditions. The experimental results are in good agreement with the simulation ones. Furthermore, the differences regarding the operational characteristics of the two motors that stem from their respective design and optimization approaches are highlighted. Phase A EMF (V) V. RESULTS AND DISCUSSION The simulation results for the two motors are illustrated in Fig.. The magnetic flux density distribution for the over operation and the back-emf and instantaneous torque waveforms for both the nominal and over operations are depicted for both motors. - - Phase A EMF waveform Over - Torque (Nm) Instantaneous torque (Nm) Over Phase A EMF (V) Torque (Nm) Phase A EMF waveform Over - Instantaneous torque (Nm) Over Fig.. Main simulation results for the two motor configurations. Magnetic flux distribution at over, back-emf and electromagnetic torque waveforms for the first and the second motor. From Fig. it is obvious that the second motor exhibits superior operational behavior for the specific application, in terms of efficiency and torque and back-emf waveform quality. However, the first motor has a higher torque Fig.. The two manufactured prototypes, mounted in a light electric vehicle s wheel. Output torque (Nm) motor measured motor fit motor measured motor fit Input current rms (A) Fig.. Experimental results for the two motors: electromagnetic torque Vs line current rms. VI. CONCLUSION In this paper two in-wheel Surface Mounted Permanent Magnet motors with Fractional Slot Concentrated Winding configurations designed for a light electric vehicle application are presented. Two different winding configurations and relative dimensions of axial length and air-gap diameter are utilized in order to highlight the advantages for this specific application. Additionally, two alternative strategies concerning the optimization technique are developed involving the reference operational point. The first motor, optimized by applying Taguchi s method, presents higher torque capacity while the other topology, derived from a SPEA routine benefits from its specific geometrical characteristics, exhibiting an overall improved operational profile. Consequently, through the analysis developed in the paper validated by experimental results, both configurations present complementary advantages, concerning efficiency under low ing and overtorque capacity respectively.

7 Powered by TCPDF ( VII. REFERENCES [] P. Seibold, M. Gartner, F. Schuller, and N. Parspour, Design of a transverse flux permanent magnet excited machine as a near-wheel motor for the use in electric vehicles, in th International Conference onelectrical Machines,, pp.. [] A. Tessarolo, M. Mezzarobba, and R. Menis, A novel interior permanent magnet motor design with a self-activated flux-weakening device for automotive applications, in th International Conference onelectrical Machines,, pp.. [] P. E. Kakosimos, A. G. Sarigiannidis, M. E. Beniakar, A.G. Kladas, and C. Gerada, Induction Motors versus Permanent Magnet Actuators for Aerospace Applications, IEEE Trans. Ind. Electron., in Press, DOI./TIE... [] G.-A. Capolino and A. Cavagnino, New Trends in Electrical Machines Technology Part I, IEEE Trans. Ind. Electron., vol., no., pp., Aug.. [] P. E. Kakosimos and A. G. Kladas, Modeling of interior permanent magnet machine using combined field-circuit analysis, in th IEEE International Conference on Electrical Machines,, pp.. [] G. Pellegrino, A. Vagati, P. Guglielmi, and B. Boazzo, Performance Comparison Between Surface-Mounted and Interior PM Motor Drives for Electric Vehicle Application, IEEE Trans. Ind. Electron., vol., no., pp., Feb.. [] M.E. Beniakar, A.G. Sarigiannidis, P.E. Kakosimos and A.G. Kladas, Multi-objective Evolutionary Optimization of a Surface Mounted PM Actuator with Fractional Slot Winding for Aerospace Applications, IEEE Trans. Magn., in Press, DOI./TMAG... [] E. M. Tsampouris, M. E. Beniakar, and A. G. Kladas, Geometry Optimization of PMSMs Comparing Full and Fractional Pitch Winding Configurations for Aerospace Actuation Applications, IEEE Trans. Magn., vol., no., pp., Feb.. [] J. Junak and G. Ombach, Performance optimisation of the brushless motor with IPM rotor for automotive applications, in th International Conference onelectrical Machines,, pp.. [] J. S. Choi, K. Izui, S. Nishiwaki, A. Kawamoto, and T. Nomura, Topology Optimization of the Stator for Minimizing Cogging Torque of IPM Motors, IEEE Trans. Magn., vol., no., pp.,. [] X. Meng, S. Wang, J. Qiu, J. G. Zhu, Y. Wang, Y. Guo, D. Liu, and W. Xu, Dynamic Multilevel Optimization of Machine Design and Control Parameters Based on Correlation Analysis, IEEE Trans. Magn., vol., no., pp.,. [] A. Mahmoudi, S. Kahourzade, N. A. Rahim, and W. P. Hew, Design, Analysis, and Prototyping of an Axial-Flux Permanent Magnet Motor Based on Genetic Algorithm and Finite-Element Analysis, IEEE Trans. Magn., vol., no., pp.,. [] S. Lim, S. Min, and J.-P. Hong, Level-Set-Based Optimal Stator Design of Interior Permanent-Magnet Motor for Torque Ripple Reduction Using Phase-Field Model, IEEE Trans. Magn., vol., no., pp.,. [] F. Parasiliti, M. Villani, S. Lucidi, and F. Rinaldi, Finite-Element- Based Multiobjective Design Optimization Procedure of Interior Permanent Magnet Synchronous Motors for Wide Constant-Power Region Operation, IEEE Trans. Ind. Electron., vol., no., pp., Jun.. [] L. Chen, J. Wang, P. Lombard, P. Lazari, and V. Leconte, Design optimisation of permanent magnet assisted synchronous reluctance machines for electric vehicle applications, in th International Conference onelectrical Machines,, pp.. [] P. Lazari, J. Wang, and L. Chen, A computationally efficient design technique for electric vehicle traction machines, in th International Conference onelectrical Machines,, pp.. [] L. dos Santos Coelho, L. Z. Barbosa, and L. Lebensztajn, Multiobjective Particle Swarm Approach for the Design of a Brushless DC Wheel Motor, IEEE Trans. Magn., vol., no., pp.,. [] N. Takorabet, J. P. Martin, F. Meibody-Tabar, F. Sharif, and P. Fontaine, Design and optimization of a permanent magnet axial flux wheel motors for electric vehicle, in th International Conference on Electrical Machines,, pp.. [] X.-D. Xue, K. W. E. Cheng, T. W. Ng, and N. C. Cheung, Multi- Objective Optimization Design of In-Wheel Switched Reluctance Motors in Electric Vehicles, IEEE Trans. Ind. Electron., vol., no., pp.,. [] N. Bianchi, D. Durello, and E. Fornasiero, Multi-objective optimization of an Interior PM motor for a high-performance drive, in th International Conference on Electrical Machines,, pp.. [] C.-C. Hwang, C.-M. Chang, and C.-T. Liu, A Fuzzy-Based Taguchi Method for Multiobjective Design of PM Motors, IEEE Trans. Magn., vol., no., pp.,. [] D. Lim, K. Yi, D. Woo, H. Yeo, J. Ro, C. Lee, and H. Jung, Analysis and Design of a Multi-layered and Multi-segmented Interior Permanent Magnet Motor by using an Analytic Method, IEEE Trans. Magn., vol. PP, no., p.,. [] Y. Huang, J. Dong, L. Jin, J. Zhu, and Y. Guo, Eddy-Current Loss Prediction in the Rotor Magnets of a Permanent Magnet Synchronous Generator with Modular Winding Feeding a Rectifier Load, IEEE Trans. Magn., vol., no., p. -, Oct.. VIII. BIOGRAPHIES Minos E. Beniakar received the B. Eng. and M. Eng. degree in electrical and computer engineering from the National Technical University of Athens, Greece, in. He is currently working toward the Ph.D. degree in the Department of Electrical and Computer Engineering, Laboratory of Electrical Machines and Power Electronics, at the National Technical University of Athens, Greece. His current research involves design optimization of electric motors for aerospace and electric traction applications and industrial drives. Mr. Beniakar is a Registered Professional Engineer in Greece. Panagiotis E. Kakosimos received the B. Eng. and M. Eng. degree in electrical and computer engineering from the Aristotle University of Thessaloniki, Greece, in and the Ph.D. degree in from the Department of Electrical and Computer Engineering at the National Technical University of Athens, Greece. His current research involves power generation from renewable energy sources, industrial drives, as well as electric machine design optimization for aerospace and electric vehicles applications. Dr. Kakosimos is a Registered Professional Engineer in Greece. Christos T. Krasopoulos received the B. Eng. and M. Eng. degree in electrical and computer engineering from the National Technical University of Athens, Greece, in. He is currently working toward the Ph.D. degree in the Department of Electrical and Computer Engineering, Laboratory of Electrical Machines and Power Electronics, at the National Technical University of Athens, Greece. His current research involves design optimization and assembling techniques of electric motors for electric traction applications. Athanasios G. Sarigiannidis received the Diploma degree in electrical and computer engineering from the University of Patras, Greece in. He is currently working toward the Ph.D. degree in the Department of Electrical and Computer Engineering, Laboratory of Electrical Machines and Power Electronics, at the National Technical University of Athens, Greece. His current research involves permanent magnet motor losses analysis, design and control for traction applications, with emphasis on field weakening techniques for electric motor optimal efficiency control. Mr. Sarigiannidis is a member of the Technical Chamber of Greece. Antonios G. Kladas was born in Greece in. He received the Diploma in Electrical Engineering from the Aristotle University of Thessaloniki, Thessaloniki, Greece, in and the D.E.A. and Ph.D. degrees from the University of Pierre and Marie Curie (Paris ), Paris, France, in and, respectively. From to, he was an Associate Assistant with the University of Pierre and Marie Curie. During the period to, he joined the Public Power Corporation of Greece. Since, he has been with the Department of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece, where he is currently a Professor. His research interests include transformer and electric machine modeling and design, analysis of generating units by renewable energy sources and industrial drives. Dr. Kladas is member of the Technical Chamber of Greece.