Fractional-Slot PMSMs With One Coil Parallel Branches Made Phases—Part 2: Circulating Harmonic Current Rejection Potential

The paper is aimed at a class of fractional-slot permanent magnet- synchronous machines (FSPMSMs) equipped with phases made up of one coil parallel branches, with emphasis on their potential to reject the circulating harmonic currents. Following the identification and topological characterization of this class of machines treated in Part 1, the star of slots approach is extended to the investigation of their back-EMF harmonic content, and the possible resulting circulating harmonic currents. It is found that all identified candidates exhibit the potential to reject the circulating harmonic currents. A case study dedicated to a candidate equipped with three phases made up of six parallel branches of one coil each, is treated. Following an analysis of its back-EMF harmonic content, the torque-speed characteristic is analytically-predicted and validated by 2D finite element analysis and by experiments. The study is achieved by a special attention paid to the iron loss and thermal analysis.


I. INTRODUCTION
In recent years, there is an increasing attention to develop fault-tolerant electric drives especially in transportation applications. The emergence of the ''More Electric Aircraft'' trend makes it necessary the development of new electric drives with emphasis on their fault-tolerance capabilities in presence of extreme emergency situations [1]- [3]. Enhanced fault-tolerance capability represents the most vital requirement in aerospace applications in so far as the safety of the passengers is intimately linked.
Fault-tolerant electric drives are also highly coveted in sustainable propulsion systems equipping electric and hybrid vehicles (EVs and HEVs) [4]- [6]. Beyond the zero green house gas emissions, the high efficiency, the possibility to The associate editor coordinating the review of this manuscript and approving it for publication was Shaopeng Wu . recover the wheel kinetic energy during regenerative braking, the fault tolerance enhances the superiority of the electric and hybrid vehicles over their internal combustion engine propelled counterparts.
A synthesis of a literature review revealed that the faulttolerant-oriented design of electric machines is dominated by multiphase candidates. The latter are commonly equipped with phases made up of series-connected coils. Nevertheless, such an arrangement compromises their faut-tolerance with respect to open-circuit faults. Moreover, multiphase machines equipped with phases made up of series-connected coils require non conventional inverters with a relatively high DC-bus voltage for their power supply. This results in bulky battery packs in the case of electric and hybrid propulsion systems. Reduced DC-bus voltage drives represent attractive concepts for electric propulsion systems, particularly with the current trend aimed at the integration of the 48V technology in automotive applications. Among the 48V automotive applications, one can distinguish the mild hybrid propulsion system which has been introduced in early 2000 [7] and manufactured by Audi in 2016.
Recently, Fatemi et al. proposed an approach to optimise the design optimization of an electric machine for a 48V mild hybrid vehicle with rotor technology and the slot-pole combinations [8]. To do so, they considered a comparison study of three candidates: (i) a PM synchronous machine (PMSM) with V-shaped rare-earth magnets in the rotor, a PMSM with deep V-shaped ferrite rotor magnets, and a synchronous reluctance machine with four layers of conforming flux barriers. Predictive current control strategies dedicated to a 48V 600W brushless DC motor have been assessed and implemented in [9]. This has been carried in an attempt to accurately track the ideal hexagonal trajectory described by the armature current phasor in the stationary plane.
48V automotive actuators could be suitably-equipped with low-voltage FSPMSMs where the phases are arranged by connecting in parallel branches incorporating a single or several coils. In light of this, a significant improvement in the fault-tolerance capability is gained, such that under an opencircuit fault, the machine would lose the torque produced by the faulty branch, rather than the one developed by a total phase in series-connected coils machines. Furthermore, thanks to their reduced DC bus voltage, EVs and HEVs would have the merit to definitely discard the risk of electrocution of their passengers in case of accidents.
FSPMSMs equipped with odd number of phases, arranged in parallel branches incorporating one coil or suitable combinations of coils, have been partly treated in [10]. A special attention has been paid to assess their torque production capability under open-circuit faulty conditions. Following the identification of the slot/pole combinations enabling the above-described arrangement, two case studies of a 12-slot/10-pole 3 phase and a 20-slot/16-pole 5 phase FSPMSMs have been treated. Their healthy and open-circuit faulty operations have been investigated by 2D FEA.
A comprehensive survey dedicated to a systematic identification and topological characterisation of all FSPMSMs equipped with phases made up of single coil parallel branches, has been proposed in [11]. The targeted topologies exhibit the highest open-circuit fault-tolerance potential on one hand and require the lowest DC-bus voltage on the other hand. A star of slots-based approach enabled the identification of the slot-pole combinations fulfilling the targeted FSPMSMs as well as their winding factors. This has been achieved considering the cases of odd and even number of phases, arranged in single-and double-layer slots.
The present paper takes back the candidates identified in [11], in order to investigate the possible circulating harmonic currents in the loops created by the parallel branches. These would be harmful for the features of the targeted topologies. The investigation is based on an extension of the star of slots approach that enables the prediction of the back-EMF harmonic content. The possible circulating harmonic currents would result from phase shifts between the harmonic back-EMFs induced in the parallel branches. In absence of shifts, harmonic current exist in the parallel branches but not in a circulating form, with their sum flowing in the machine lines.

II. INVESTIGATION OF POSSIBLE CIRCULATING HARMONIC CURRENTS
A. STUDY BACKGROUND From a fundamental point of view, by connecting in parallel magnetically-coupled circuits, the first issue, that comes in mind, is the possible circulation of harmonic currents in the loops resulting from the parallel connections of these circuits. Such a problem concerns the FSPMSM candidates identified in [11]. Indeed, these have been selected on the basis that all harmonic back-EMFs of rank p (fundamental) induced in the coils assigned to each phase are identical in magnitude and have similar or opposite phases.
With this said, the question that arises immediately is: How about the harmonic back-EMFs of rank n, with n = p ? Any phase shift between the harmonic back-EMFs would result in the circulation of harmonic currents that make the one coil parallel branches arrangement of the phases totally useless. Indeed, the circulating harmonic currents in the loops resulting from the one coil parallel branches would affect the machine torque production and power efficiency. This section puts light on this possible drawback.

B. HARMONIC BACK-EMFs CHARACTERIZATION
Referring to [14], the Fourrier expansion of the no-load air gap flux density (produced by the PMs), assuming a slotless machine, could be expressed as: where θ is a mechanical angle counted in the air gap starting from the magnetic axis of a north pole magnet. Therefore, only harmonics of odd ranks should be considered in the investigation aimed to the possible circulating harmonic currents.
The investigation of the back-EMF harmonic content goes through the application of the star of slots approach considering an angular shift α (2n+1) between two successive phasors, expressed as [16], [25]: Then, the back-EMF phasors assigned to each phase, that have been identified by the star of slots corresponding to the fundamental, are reconsidered. In case the harmonic back-EMF phasors induced in all parallel branches of a phase would have the same initial angular shift, this would lead to a circulation of identical harmonic currents in the phase parallel branches. This statement would be true if the line harmonic current of the star-connected machine, is equal to the one of a branch multiplied by the number of parallel branches per phase. This confirms the absence of circulating harmonic currents in the loops created by the parallel connection of the phase coils.
In what follows, the FSPMSM topologies, enabling the one coil parallel branches made phases, identified in [11], are systematically re-investigated with emphasis on their back-EMF harmonic content.

C. CASE OF ODD NUMBER OF PHASES 1) CASE OF DOUBLE-LAYER SLOTS
The star of slots of the back-EMF harmonic of rank (2n + 1) with n = 0 of the FSPMSMs identified in paragraph II-A1 (case 1) of Part 1 [11], are shown in Fig. 1. In the case where two successive harmonic back-EMF phasors are shifted by q − 1 q π, the corresponding harmonic back-EMF phasors of rank (2n+1) are shifted by π −(2n+1) π q . In the case where two successive fundamental back-EMF phasors are shifted by q + 1 q π, the corresponding harmonic back-EMF phasors of rank (2n + 1) are shifted by π + (2n + 1) π q . In the manner of the fundamental back-EMF, one can notice that the phasors of all harmonic back-EMFs induced in the coils assigned to the phases given in Fig. 1 of Part 1 are aligned, having the same magnitude and initial phase. This results in null circulating harmonic currents in the loops created by the parallel connections of the coils. Referring to the star of slots of Fig. 1, the winding factor of the back-EMF harmonic of rank (2n + 1) could be expressed as follows: Concerning the topologies fulfilling the star of slots treated in paragraph II-A1 (case 2) of Part 1 [11], the corresponding back-EMF harmonics are characterized by the star of slots shown in Fig. 2. The analysis of this latter reveals that all phasors of the back-EMF harmonics induced in the the parallel branches of a phase are identical (having the same magnitude and initial phase). Consequently, one can clearly confirm that no circulating harmonic currents exist in the loops created by the parallel connection of the coils. The winding factor of the harmonic back-EMF of rank (2n + 1) is deduced from Fig. 2, as:

2) CASE OF SINGLE-LAYER SLOTS
Following the removal of the phasors of even number from the star of slots illustrated in Figs. 1 and 2, the back-EMF harmonics induced in the one coil parallel branches of the considered phase remain similar, resulting in null circulating harmonic currents. The corresponding expressions of the winding factor K sl w(2n+1) are then the same as the ones of K dl w(2n+1) given by expression (3) and (4), respectively. The star of slots of the harmonic back-EMF of rank (2n + 1) with n = 0 of the FSPMSMs identified in paragraph II-A2 (second approach) of Part 1, are shown in Fig. 3. One can notice that the harmonic back-EMF phasors of a given phase are identical, resulting in null circulating harmonic currents. The winding factor K sl w(2n+1) is expressed as:

D. CASE OF EVEN NUMBER OF PHASES 1) CASE OF DOUBLE-LAYER SLOTS
The star of slots of the harmonic back-EMF of rank (2n + 1)p with n = 0 of the FSPMSMs identified in paragraph II-B1 of Part 1 [11], are illustrated in Fig. 4. It reveals the absence of circulating harmonic currents.   Based on Fig. 4, the prediction of the winding factor K dl w(2n+1) of the back-EMF harmonic of rank (2n + 1) yields:

2) CASE OF SINGLE-LAYER SLOTS
Following the removal of the phasors of even number from the star of slots shown in Fig. 4, the similitude of the harmonic back-EMFs induced in the one coil parallel branches of the considered phase, remains fulfilled, resulting in null circulating harmonic currents. The expression of the winding factor K sl w(2n+1)p is then the same as K dl w(2n+1)p given in (6). Moreover, Fig. 5 represents the star of slots of the harmonic back-EMF of rank (2n + 1) with n = 0 of the FSPMSMs identified in paragraph II-B2 of Part 1 [11]. Referring to Fig. 5, the prediction of the winding factor of the harmonic back-EMF K dl w(2n+1) of rank (2n + 1) has led to the following: To sum up, it has been found that: • all FSPMSMs equipped with phases made up of one coil parallel branches, identified in Part 1 [11], have the faculty to reject the circulating harmonic currents. With this said, two cases could be distinguished: 1) the harmonic winding factor is null. Consequently, the corresponding back-EMF harmonic is discarded, resulting in a null harmonic current in the phase parallel branches, 2) the harmonic winding factor is not null. This results in a circulation of harmonic currents in the phase branches but not in a circulating form in the loops created by the parallel connection of these branches. VOLUME 10, 2022 FIGURE 5. Star of slots of the harmonic back-EMF of rank (2n + 1) of FSPMSMs with even number of phases arranged in single-layer slots. Legend: (a) two successive harmonic back-EMF phasors shifted by π − (2n + 1) π q , (b) two successive harmonic back-EMF phasors shifted by π + (2n + 1) π q .
• in the manner of the fundamental back-EMFs, in both cases of odd and even number of phases and for a given harmonic rank, candidates arranged in single-layer slots exhibit a higher harmonic winding factor that the one arranged in double-layers slots.

III. CASE STUDY
This study resumes the candidate treated in Part 1 [11]. It consists in a FSPMSM equipped with three phases in the armature arranged in eighteen double-layer slots and twelve poles in the rotor achieved by interior PMs. The slot-pole combination makes it possible the arrangement of each phase by connecting in parallel six coils.

A. BACK-EMF HARMONIC CONTENT
Following a start of slots-based investigation of the back-EMF harmonic content, three cases have been distinguished. These are characterized by three electrical shifts between adjacent back-EMF phasors, such that: α (2k+1) = 2π, 2π 3 , and 4π 3 . The corresponding star of slots and winding factors are regrouped in table 1.

B. TORQUE PRODUCTION CAPABILITY
This paragraph deals with both analytical and FEA predictions of the torque production capability of the FSPMSM under study. With its interior PMs, it belongs to the class of salient pole synchronous machines, developing an electromagnetic torque T em which is the sum of a synchronizing component and a reluctant one [12], [13]. The design of the machine has been carried out in order to meet the following: • a DC bus voltage V DC = 400V leading to a maximum armature voltage V max 255V.
• a maximum torque T max of 180N.m achieved for an armature current of 188.25A, • the corresponding base speed B = 2600rpm, Accounting for above specifications, the machine parameters have predicted. They are listed in table 2.  With the armature current kept constant equal 188.25A, the variation of the electromagnetic torque T em with respect to the torque angle ψ has been analytically-predicted and has led to the characteristic shown in Fig. 6. The same figure includes the results yielded by 2D FEA. One can notice a good agreement between the analytical and FEA results, with the maximum torque achieved for a torque angle, noted ψ M , almost equal to − π 6 . In addition to the high torque requirements at low speeds, aerospace and automotive applications require a flux weakening operation over a wide speed range. For a given armature current, to achieve speeds over the base one, the torque angle ψ should be varied from M to − π 2 . The corresponding range of the speed could be found out applying a numerical procedure such as the fixed point method.
The different steps of the developed fixed point-based numerical procedure dedicated to the prediction of the speed are listed hereunder: • for given values of the armature current I rms and torque angle ψ, • the speed is increased starting from the base one −B, while the armature voltage V rms is predicted using the phasor diagram characterizing the steady-state operation of salient pole synchronous machines with a reverse saliency [13], as follows: where: A( ) = p φ rms + L d p I rms sin(ψ) + rI rms cos(ψ) B( ) = L q p I rms cos(ψ) + rI rms sin(ψ) • V rms is compared to V max . If the difference is lower than a given error , then the corresponding speed would be the solution. The maximum speed N max , corresponding to the limit of the flux weakening range, is expressed as: 13437.3rpm (9) The torque-speed characteristic has been analyticallypredicted under a constant armature current of 188.25A. In the constant torque region, the torque angle has been kept constant ψ = ψ M leading to a base speed of 2600rpm. Then, for V rms = V max , the torque-speed characteristic in the flux weakening range has been predicted by reducing ψ from ψ M to − π 2 . The resulting characteristic is shown in Fig. 7. The torque-speed characteristic has been also predicted by FEA. The obtained results are illustrated in Fig. 7. One can notice a good agreement between analytical and FEA results.

C. LOSS AND EFFICIENCY ASSESSMENT
Taking into account the fact that the iron loss and particularly the PM eddy current ones could be critical in FSPMSMs, a special attention is paid to their prediction hereunder.

1) IRON LOSS PREDICTION
This paragraph deals with a FEA-based prediction of the iron loss of the studied FSPMSM. The eddy current, hysteresis, and excess loss have been predicted considering two on-load operating points, as:     Table 3 gives a summary of the mean values of the iron loss components predicted for a speed of 2000rpm. It is to be noted that the rotor iron loss are far from being negligible and that they are weighted by their PM eddy current component.

2) IRON LOSS PREDICTION IN THE CONSTANT POWER REGION
The iron loss characteristic P iron (B) of the used laminated material M270-35A for a frequency of 400Hz is provided   in Fig. 12, based on which the coefficients of the Steinmetz model have been identified as: C ec = 0.3875, C hyst = 187.5593, and C ex 0, respectively.
Figs. 13 and 14 illustrate the variation of the eddy current and hysteresis loss over time, for a speed of 4000rpm. Table 4 summarises the means values of the different iron loss components, predicted for a speed of 4000rpm. It is to be noted that the iron loss are lower in the stator magnetic circuit than in the rotor one, where the PM eddy current loss represent the major part (71.6% of the rotor iron loss).

3) EFFICIENCY MAPS
A combined FEA-analytical procedure has been developed in order to predict the drive efficiency. As previously treated, the iron loss have been computed by FEA. While, the Joule, mechanical, and inverter loss have been analyticallypredicted.   Two efficiency maps of the FSPMSM under study (motor EM1) have been considered, such that: • Fig. 15(a) gives the efficiency map under constant torque operation (increasing the armature voltage, the torque angle kept constant), • Fig. 15(b) gives the efficiency map under constant power operation (decreasing the torque angle, the armature voltage kept constant at its maximum value). As expected, high efficiencies are achieved under constant torque operation. While under constant power one, a part of the armature current is used for the flux weakening, along with an increase of the machine iron and friction loss and the inverter commutation ones.

D. EXPERIMENTAL VALIDATION 1) STUDY STATEMENT
The Institute of Vehicle Concepts of the German Aerospace Center (DLR) has been working on the development of future  vehicle concepts for road and rail within different transport research programs. The aim is to design efficient, sustainable and affordable mobility concepts, allied to new energy sources as well as to automation and digital traffic guidance network systems.
Within the DLR internal project Next Generation Car (NGC), the Institute of Vehicle Concepts is currently developing an Urban Modular Vehicle (UMV) that makes it possible the assessment and test of novel urban and aerospace technologies. Of particular interest is the NGC-UMV concept, shown in Fig. 16. Thanks to its modular design, the VOLUME 10, 2022  NGC-UMV concept could be equipped with different drive train topologies, among which the so-called ''two-in-one motor system'' which is currently under development. It consists in a dual motor concept, made up of: • EM1: a FSPMSM with a rated power of 50kW acting as propeller, • EM2: a FSPMSM with a rated power of 10kW driving the air conditioning compressor when required and boosting the propulsion when possible. as illustrated in the scheme of Fig. 17.
Photos of the stators and rotors of the prototyped EM1 and EM2 are shown in Fig. 18. EM1 and EM2 are mechanically-coupled by the electromagnetic clutch illustrated in Fig. 19. Both FSPMSMs may be separately-operated using independent inverters. A photo of the inverter feeding EM1 is given in Fig. 20. It is equipped with SiC power switches, and designed for water cooling. It has a rated power of 60kVA.
The motivation behind the development of a dual motor concept comes from a trend to design a single drive including most of the energy converters of electric cars, in an attempt to emulate the operation of their internal combustion engine (ICE)-propelled counterparts. Indeed, ICE powertrains have  been designed in such a way that most of the auxiliary units like starter, generator, air conditioning compressor, water pump, are driven by the ICE shaft through pulleybelt systems. Integrating different electric machines in one electro-mechanical set has emerged with the necessity to improve the compactness of hybrid propulsion systems.
Within this frame work, Ben Hamadou et al. proposed in [17] a single-stator dual-rotor PM machine intended to hybrid heavy vehicles. It consists in two concentric PM machines with a stator sandwiched between an inner rotor and an outer one. In [18], Sun et al. treated the analysis and control of a complementary magnetic-geared dual-rotor motor. This concept has demonstrated its effectiveness as an electrical power split device for series-parallel hybrid powertrains. The same application has been considered in [19] where a dualrotor magnetically-geared power device has been proposed. In [20], Dalal and Kumar proposed an electromagnetic concept equipped with a PM rotor and a cage one dedicated to automotive applications. In [21], Li et al. treated the design and optimization of a dual-rotor machine for traction applications. It has surface-mounted PMs in the outer rotor and a synchronous reluctance in the inner one.
Beyond automotive applications, dual motor concepts have been found viable in several other applications. In [22], Wu et al. developed an approach to design of a pulsed alternator which is based on a dual rotor PM concept dedicated to military applications. Both inner and outer rotors are equipped with a Halbach PM array. In [23], Golovanov et al. investigated the power density of different electrical machine topologies intended for transport applications with emphasis on the aerospace one. They have found that the dual-rotor topology exhibits the best power to mass ratio.

2) TORQUE-SPEED CHARACTERISTIC
A vector control strategy has been implemented in the motor EM1 drive. A scope of the phase current for a torque of 4N.m   and a rotor speed of 600rpm is ilustrated in Fig. 21. The measured waveform has a relatively lower harmonic distortion than the back-EMF one because, even with the parallel connection of the phase coils, the inductive behavior of the FSPMSM circuits remains dominant. The torque and speed are measured using dedicated sensors which are mounted between the two-in-one-motor and the load machine. A photo of both sensors is given in Fig. 25.
The torque-speed characteristic has been experimentallyaccessed, considering a constant armature current equal to 188.25A. The torque angle has been initially kept constant equal to − π 6 , and the speed has been increased until reaching 2600rpm, corresponding to the maximum armature voltage. Then, the flux weakening operation has been practically-implemented by keeping the armature voltage at its maximum value and increasing its frequency while  reducing the torque angle. Due to mechanical constrains, the speed has been limited to 12000rpm. The resulting torque-speed characteristic is shown in the top of Fig. 23. Furthermore, a special attention has been also paid to the generator operation which corresponds, in the case of propulsion applications, to the regenerative braking. The corresponding torque-speed characteristic is illustrated in the bottom of Fig. 23. For the sake of comparison, Fig. 24 brings together the characteristics given in Figs. 7 and 23. A quite acceptable match between FEA and experimental results has been found.

3) POWER FLOW ANALYSIS a: NO-LOAD TEST: LOSS
The sum of the iron and mechanical loss have been measured at no-load according to the EN 60034-2-1 standard. For that, current sensors have been linked to the armature phases as shown in Fig. 25. These have been interfaced to the wattmeter given in Fig. 26 to measure the electric power absorbed by motor M1 at no-load operation. This latter is characterized by low values of the armature current so that the copper loss P c VOLUME 10, 2022 could be neglected. The measurements of the no-load power P 0 are provided in table 5.
Accounting for the difficulties to extract the mechanical loss P m from P 0 , they have been predicted using the data sheet of the bearings equipping motor M1. The bearing loss can be approximated by a constant frictional torque. This latter has been predicted using [24] which has led to the variation of the mechanical loss due to the bearing friction P b versus the rotor speed N (rpm) as: Moreover, due to the grooves in the surface of the rotor, the latter generates ventilation loss P v . These increase quadratically with the speed as follows: Finally, the mechanical loss P m are expressed in terms of the speed as follows: The iron loss P i are extracted from the no-load loss as: Table 5 provides de mechanical and iron loss for the speeds considered in the no-load test. Table 6 recalls the FEA results given in paragraph III-C1 and compare them to the iron loss extracted from the no-load test. The shift between the   FEA and experimental results is mainly due to fact that the experimental test has been carried out at no-load operation with a negligible armature magnetic reaction. Fig. 27 shows P 0 , P m , and P i versus the speed N .

b: ON-LOAD TEST: EFFICIENCY AND POWER DENSITY
An on-load test has been carried out at a constant load torque of 50Nm and for a linear variation of the speed. Following the measurement of the power absorbed by the armature P a and the output power available in the shaft P s using the torque  and speed sensors, the efficiency η has been determined as follows: The obtained results are shown in Fig. 28. One can notice that the efficiency remains lower than 90% which is due the high pole edge leakage flux of the prototyped machine [11]. Let us call L t and D o , the total axial length and the outer diameter of M1 with L t = 0.3m and D o = 0.2m, one can predict the power density as follows: which gives for the considered load torque and speed range:

4) THERMAL BEHAVIOUR ASSESSMENT
Accounting for the FEA-analytical procedure considered in paragraph III-C3, a thermal replacement model, based on the approaches developed in [25], [26], has been established. It has been numerically-implemented considering the study domain illustrated in Fig. 29. For the sake of validation of the established thermal model, four temperature sensors have been appropriately-installed in the stator as shown in Fig. 29. With the temperature of the water in the cooling jacket kept constant equal to 13 • C (sensor 1), a load step characterized by an armature current of 50A, applied during 22min, has led to the evolution with respect to time of the temperatures, measured by sensors 2, 3, and 4, illustrated in Fig. 30. The same figure shows the temperatures analytically-predicted using the established thermal model. One can notice a quite acceptable agreement between the analytical and experimental results.

IV. CONCLUSION
This work was devoted to a class of FSPMSMs equipped with phases made up of one coil parallel branches. These are reputed by their enhanced open-circuit fault-tolerance capability. The second part of the work was aimed at an investigation of the possible circulation of harmonic currents in the loops created by the parallel connections of the coils. This has been carried out considering a systematic application of the star of slots approach to investigate the harmonic content of the back-EMFs. It has been found that all identified candidates exhibit the potential to reject the circulating harmonic currents.
A case study has been treated considering a 3 phase, 18 double-layer slot, 12 pole FSPMSM. The slot-pole combination enabled the arrangement of the three phases in six parallel branches including a single coil each. A special attention has been paid to the torque production capability with emphasis on the torque-speed characteristic. The latter has been analytically-predicted and validated by FEA.
Moreover, a power flow analysis, with emphasis on the iron loss, has been carried out. It enabled the drawing of the drive efficiency maps considering, separately, the constant torque and flux weakening operations. The case study has been achieved by an experimental validation of the torque-speed characteristic and of a dedicated thermal model.
In light of this work, it has to be underlined that, in spite of their intrinsic potential to discard circulating harmonic currents, not all identified FSPMSMs could be regarded as viable candidates for applications requiring a high open-circuit fault tolerance. This latter is compromised by a low fundamental winding factor in some identified candidates which affect their torque production capability. Moreover, even with a high fundamental winding factor, a special attention should be paid to the selection of the slot-pole combinations in order to achieve a low cogging torque and reduced radial forces that cause noise and vibration. This said, and for viable candidates such as the case study one, there is some way to go before reaching a mature technology. Beyond the design improvement, an enhancement of the fault tolerance capability could be gained through the synthesis of dedicated torque recovery control strategies under open-circuit faulty scenarios. This represents one of the major outlooks of the present work. in 1994, and the Postdoctoral Research Habilitation degree from SENS, in 2001, all in electrical engineering.
In 1988, he joined Tunisian University, where he held different positions involved in both education and research activities. He is currently a Full Professor in electric power engineering with SENS. He is also the Head of the Research Laboratory on renewable energies and electric vehicles, and the Coordinator of the master on sustainable mobility actuators: research and technology. He is the author of more than 100 papers, 24 among which are published in IEEE TRANSACTIONS. He is the author and coauthor of four books and is the Co-Inventor of a U.S.-patent. He has presented up to 11 keynote speeches in international conferences. He has been the Chair of the Program and Publication Committees of the International Conference on Ecological Vehicles and Renewable Energie (EVER), annually-organized in Monaco, since 2007. He is the Head of the Founding Committee of the International Conference on Sustainable Mobility Applications, Renewables, and Technology (SMART) that has been organized in the Australian College of Kuwait, in 2015. His research interests include the design of new topologies of AC machines and the implementation of advanced and efficient control strategies in drives and generators, applied to automotive, and to renewable energy systems.