Fractional-Slot PMSMs With One Coil Parallel Branches Made Phases—Part I: Investigation Study

This work proposes an approach to design fractional-slot permanent magnet synchronous machines (FSPMSMs) equipped with phases made up of one coil parallel branches. These machines exhibit attractive potentialities, especially their enhanced open-circuit fault tolerance capability. Beyond their intrinsic fault tolerance, an open-circuit affecting the targeted topologies leads to a torque step-down limited to the one developed by the concerned coil rather than the torque produced by the total phase in FSPMSMs equipped with phases made up of series-connected coils. Furthermore, these topologies are suitably-adapted to low-voltage power supply that makes them viable candidates in automotive applications. This potentiality is by far vital in battery electric vehicles with the risk of electrocution in case of accident totally-eradicated thanks to the reduction of the DC bus voltage. Part 1 of the developed work is aimed at a star of slots-based identification and topological characterization of the FSPMSMs enabling the arrangement of the armature phases according to one coil parallel branches. The study distinguishes the topologies with odd and even number of phases, arranged in single- and double-layer slots. A case study is treated using a 2D finite element analysis and validated by experiments.


I. INTRODUCTION
Much attention is currently given to FSPMSMs to equip a variety of applications covering a wide range of power, from medical actuators and household appliances till wind turbines, going through electric and hybrid vehicles [1]- [5]. The great interest in FSPMSMs is motivated by [6]- [11]: (i) their low copper losses, (ii) their reduced cogging torque, (iii) their wide flux weakening range, and (iv) and their high fault tolerance capability thanks to their low mutual inductance. Further improvement of the fault tolerance is gained with the increase of the number of phases, yielding the so-called ''multi-phase FSPMSMs''. The design and post-fault feature recovery of multi-phase FSPMSMs have been widely reported in the literature. The most recent works are reviewed hereunder.
The associate editor coordinating the review of this manuscript and approving it for publication was Kan Liu . In [12], Qiao et al. treated the design and analysis of a class of six-phase semi-symmetrical FSPMSMs aimed to ship propulsion application. A special attention has been paid to the investigation of the electromagnetic vibration caused by radial magnetic forces. In [13], Liu and Zhu introduced the magnetic gearing effect and the gear ratio in FSMPSMs, considering different number of phases and slot-pole combinations. The influence of the gear ratio on the winding factor, the output and cogging torques, the inductance, and the rotor loss of 3 and 6 phase FSPMSMs has been investigated and experimentally-validated. In [14], Kuang et al. considered a thermal analysis of a 10kw 28-pole 30-slot fifteen-phase FSPMSM drive under different faulty scenarios affecting the machine and the associated converter. Steady-state and transient thermal behaviors have been investigated by a finite element analysis and confirmed by experiments. In [15], Gong et al. treated the design of double polarity five-phase FSPMSMs developing the same torque either by the first or the third current harmonic. In [16], Harke treated in detail the arrangement of six phase FSPMSMs. The possible slot-pole combinations have been discussed. Based on the star of slots approach, two winding arrangement techniques have been compared. An investigation of the fault tolerance highlighted the superiority of the design with two six phase belts. In [17], Zhang et al. considered the selection of the pole-slot combination and winding arrangement of a twelve-phase fractionalslot concentrated winding permanent magnet (PM) motor dedicated to ship propulsion. In [18], Wu et al. proposed a SiC-based integrated modular motor drive equipped with a five-phase FSPMSM. The motor and converter are cooled using a water jacket. A thermal analysis has been carried out with emphasis on the motor behavior, in order to improve the drive reliability at high-temperature operation. In [19], Fan et al. developed an approach to minimize the torque ripple caused by inter-turn short-circuit faults of a single-layer 20-slot IPM 18-pole 5-phase FSPMSM dedicated to electric vehicle application. In [20], Scuiller et al. treated the design and control of a seven-phase FSPMSM characterized by two fundamental harmonics. The so-called bi-harmonic design has been considered in an attempt to achieve a high torque density. In [21], Huang et al. considered the design 30-slot 24-pole 5-phase PMSM equipped with hybrid single/double layer fractional-slot concentrated winding applied to electric vehicles. A third harmonic current injection has been considered under healthy and faulty operations. In [22], Zhao et al. proposed a 20-slot 22-pole 5-phase outer rotor FSPMSM that exhibits a lower harmonic content of the air gap magnetomotive force compared to the conventional topology one. This has been achieved considering a star-pentagon connection of the 20 coils. In [23], Huang et al. proposed an equal-magnitude sinusoidal current compensation approach to improve the post-fault performance of a 10-slot 8-pole 5-phase FSPMSM under short-circuit faults. The proposed approach is based on the graphical rotating rhombus method. In [24], Yin et al. proposed a post-fault control strategy for a 10-slot, 8-pole 5-phase FSPMSM. Under a short-circuit fault, the d-axis armature magnetomotive force is changed from zero and the backward-rotating MMF components are kept null which enables the FSMPSM to recover a smooth torque. Finally, it should be underlined that a key step is required prior switching to any post-fault control strategy, that is the fault diagnosis [25]- [27].
An approach to improve the open-circuit fault tolerance has been proposed in [28]. It has the merit to be applicable to three and multi-phase machines. It consists in connecting in parallel the coils or suitable combinations of coils of each phase, so that in case of an open-circuit fault, only the concerned circuit turns to be passive rather than the total phase in series-connected coils. Furthermore, with their low-voltage power supply, FSPMSMs turn to be suitablyadapted to automotive applications. This approach has been extended to a class of FSPMSMs characterized by a star of slots including three phasors per phase and per winding period [29].
The approach introduced in [28] is deeply rethought in this work with emphasis on FSPMSMs equipped with one coil parallel branches made phases, considering: 1) both odd and even number of phases while only odd number of phases has been treated in [28], 2) a systematic identification allied to a topological characterisation of all candidates that makes it possible the phase arrangement according to one coil parallel branches, while limited number of slot-pole combinations have been considered in [28], 3) an investigation of the possible circulation of harmonic currents in the loops resulting from the parallel connection of the coils of each phase which affects the machine performance. Totally ignored in [28], this issue will be investigated in Part 2 of the present work.

A. CASE OF ODD NUMBER OF PHASES
This case is characterized by a star of slots with the back-EMF phasors, induced in the coils of a given phase, aligned in one or the two opposite sectors assigned to that phase.

1) CASE OF DOUBLE-LAYER SLOTS
Let us call N s the number of slots in the stator, p the number of pole pairs in the rotor, and q the number of phases. Odd and even fundamental back-EMF phasors are successively-shifted in the star of slots by an angle α p = p 2π N s . The case where the FSPMSM phases are made up of one coil parallel branches, is achieved when the star of slots fulfills the following criteria: Case 1: all back-EMF phasors assigned to a phase are aligned in one sector as illustrated in Fig. 1. This case covers both even and odd number of coils N s , with: The winding factor K dl wp is obtained from Fig. 1 as: where E is the amplitude of the coil back-EMF phasor. Case 2: the back-EMF phasors assigned to a phase are aligned and equally-distributed in the two opposite sectors, as shown in Fig. 2. This case is only feasible with an even number of coils N s , with: successive back-EMFs shifted by ( q − 1 q )π, (b) two successive back-EMFs shifted by ( q + 1 q )π.
Referring to Fig. 2, K dl wp is expressed as follows: The parallel connection of the coils of a phase in both cases is illustrated in Fig. 3. Referring to equations (2) and (4), one can clearly notice that the FSPMSMs characterized by the star of slots of Fig. 1 exhibit interesting K dl wp . Three phase candidates, characterized by their slot-pole combinations, have been identified in [28]. While the candidates characterized by the star of slots of Fig. 2 are penalized by their low fundamental winding factors. The slot-pole combinations of three phase machines are identified in table 1.

2) CASE OF SINGLE-LAYER SLOTS
The star of slots enabling the arrangement of the coils in single-layer slots is deduced form the double-layer slots one VOLUME 9, 2021  by removing the even back-EMF phasors. In order to arrange the phases in one coil parallel branches, this approach has been applied to the star of slots of Figs. 1 and 2.
A second approach to arrange the phases in single-layer slots is proposed in this work. It consists in removing a spoke of aligned even back-EMF phasor(s) from each sector of the star of slots corresponding to the double-layer slots. This latter includes two spokes of back-EMF phasor(s) per sector, such that: • the ones made up of even back-EMF phasor(s) are co-linear and located in the two opposite sectors, • the ones made up of odd back-EMF phasor(s) are co-linear and located in the two opposite sectors.
as depicted in the star of slots of Fig. 4.
Following the removal of the even back-EMF phasors from the star of slots of Figs. 1 and 2, the resulting winding factors in the case of single-layer slots, noted K sl wp , are similar to the ones in the case of double-layer slots K dl wp . Considering the second approach, Fig. 4 enables the prediction of K sl wp as: It is to be noted that, for a given number of phases, the second approach exhibits a higher K sl wp than those given by expressions (2) and (4).

B. CASE OF EVEN NUMBER OF PHASES
It should be underlined that the star of slots in the case of even number of phases differs from the one in the case of odd number of phases, by the localisation of the two sectors assigned to a phase, such that: • in the case of odd number of phases, the two sectors are shifted by π, • in the case of even number of phases, the two sectors are shifted by π + π q [30].

1) CASE OF DOUBLE-LAYER SLOTS
Arranging the phases according to one coil parallel branches inserted in double-layer slots is feasible if the tow following conditions are fulfilled: • all phase back-EMF vectors are located in one sector, • the angular shift between two adjacent back-EMF phasors is equal to the electrical shift between two adjacent phases (α p = 2π q ), as shown in Fig. 5. This latter enables a graphical determination of the fundamental back-EMF winding factor K dl wp , as: The slot-pole combinations enabling the arrangement of the phases according to one coil parallel branches in the case of q = 4 and q = 6 are identified in tables 2 and 3, respectively.

2) CASE OF SINGLE-LAYER SLOTS
The removal of the even back-EMF phasors from the star of slots of Fig. 5, leads to the coil arrangement in single-layer slots. The resulting winding factor K sl wp is similar to one given by expression (6).
A second approach that makes it possible the arrangement of one coil parallel branches in single-layer slots, is proposed. It is characterized by the star of slots of Fig. 6 from which one can predict K sl wp as: It is to be noted that, for a given number of phases, the second approach leads to a higher K sl wp than the one yielded by expression (6). The possible slot-pole combinations, characterizing the cases of q = 4 and q = 6 arranged in single-layer slots, are regrouped in tables 4 and 5, respectively.

III. CASE STUDY A. TOPOLOGICAL DESCRIPTION
The FSPMSM under study is characterized by:      It has the star of slots depicted in Fig. 7, resulting in a fundamental winding factor K dl wp = √ 3/2 0.866. It belongs to FSPMSM class characterized by the star of slots of Fig. 1(a). Thus, in the case of one coil open-circuit faulty scenario, the machine would lose 1/18 of its torque production capability. However, considering a series connection of its coils, in the case of one coil open-circuit faulty scenario, the machine would lose 1/3 of its torque production capability along with a high torque ripple. A quarter of the machine cross-section is shown in Fig. 8 where the main geometrical parameters are identified. These are listed in table 6.
The iron parts of the magnetic circuit are made up of M270/35A. The permanent magnets are made up of rare earth NdFeB with a remanence of 1.1T and a coercitivity of -875352.187A/m. The total mass of the PMs is 2.736kg. The masses of the stator and rotor cores are 22,3kg and 12,5kg, respectively. The mass of the shaft is 5.8kg. The mass of the remaining parts of the rotor is 2.744kg. The copper mass is 1.719kg with 95.5g per coil. The slot fill factor is 0.3. The winding wire diameter is 0,94mm. The number of conductors per slot is 80.

B. PREDICTION OF THE NO-LOAD FEATURES
The no-load flux density mapping and lines throughout the study domain have been computed by a 2D FEA. The obtained results are shown in Figs 9 and 10, respectively. One can notice that the flux density can reach a maximum of 2.3T, causing a local saturation in the rotor iron areas facing the PMs' edges close to the air gap as well as in the space separating the two pole PM pieces. Fig. 11 shows the no-load air gap flux density over a pole pair with a maximum value not exceeding 0.6T. Such a low value results from a remarkable pole edge leakage flux, as confirmed by the flux lines shown in Fig. 10. This drawback is due to a mis-sized PM length and does not have any link with the arrangement of the phases according to one coil parallel branches. This statement will be clearly demonstrated in paragraph III-D. Moreover, it is to be noted that the south pole is affected by a remarkable spike which is caused by the slotting effect. Fig. 12 shows the waveform of the phase back-EMFs of the FSPMSM under study for the base speed 2600rpm. One can notice that the back-EMFs are not sinusoidal. In case   the harmonics of the back-EMFs induced in the parallel branches of a given phase are not in phase, this would lead to circulating harmonic currents, resulting in a degradation of the machine performance. Part 2 of this work will be dedicated to the investigation of the possibility that FSPMSMs, with their phases arranged in one coil parallel branches, may be penalized by circulating harmonic currents.

C. EXPERIMENTAL VALIDATION
The topology described and investigated by FEA in the two previous paragraphs has been prototyped. Photos of the stator and rotor ((b) assembled and (c) PMs and shaft dismantled) are shown in Fig. 13. It has been developed at the German Aerospace Center within a project aimed at the design and performance assessment of a two-in-one-motor system. This latter is made up two FSPMSMs mechanically-coupled by an electromagnetic clutch. A photo of the developed test bench is shown in Fig. 14 where EM1 is the FSPMSM under study.
The back-EMF has been measured for a speed almost equal to 480rpm whose scope capture is shown in Fig. 15.  One can remark that the back-EMF has a waveform similar to the one shown in Fig. 12 with a peak-to-peak value of 46V. The back-EMF has been also predicted by FEA considering the same speed. Fig. 16 shows a single-period waveform of the measured and FEA-predicted back-EMFs. A quite acceptable agreement has been noticed. Further experimental results are provided and discussed in Part 2 of this work.

D. DESIGN IMPROVEMENT
As previously underlined in paragraph III-B, the prototyped machine suffers from a remarkable pole edge leakage flux   due to a mis-sized PM segment length PM l . A FEA-based investigation of its influence on the no-load features has been carried out considering the flowchart illustrated in Fig 17. It has been found that an increase of PM l from 10mm to 12mm leads to a significant improvement of the no-load features as depicted in Figs. 18 to 21.
Following the comparison of the flux lines shown in Figs. 10 and 18, it has been noticed that the pole edge leakage flux has been remarkably reduced. As expected, this improvement has a direct positive impact on the air gap flux  density waveform, as illustrated in Fig. 19. For the sake of comparison, the air gap flux density waveform illustrated in Fig. 11 is recalled in Fig. 19 (dashed line).
The investigation has been extended to the back-EMF waveform and has led to the results shown in Fig. 20. Compared to the back-EMF waveform depicted in Fig. 12, one can notice an improvement in both amplitude and harmonic content. This statement is confirmed by the spectra of Fig. 21, corresponding to the FFT of the back-EMFs illustrated in Figs. 12 and 20 where the amplitudes have been normalised to the one of the fundamental in the case of PM l = 12mm.
From the spectra of Fig. 21, one can notice that, following the increase of PM l from 10mm to 12mm, the back-EMF waveform turns to be more sinusoidal with a remarkable:   • increase of 34.28% in the amplitude of the fundamental, • decrease of 70.77% in the amplitude of the harmonic of rank 5, • decrease of 68.94% in the amplitude of the harmonic of rank 7. The resulting reduction of the harmonic content is characterized by an amelioration of the THD, such that:

THD
13% for L PM = 12mm 21% for L PM = 10mm VOLUME 9, 2021 The great interest in the reduction of the harmonic content is motivated by the risk that the back-EMF harmonics may generate circulating harmonic currents in the parallel branches. The investigation of this risk will be treated in Part 2.

IV. CONCLUSION
This work investigated a class of FSPMSMs that make it possible the arrangement of their phases within one coil parallel branches. These are reputed by their enhanced open-circuit fault tolerance capability. Part 1 of the work developed a star of slots-based approach aimed at the identification and the topological characterization of all candidates which belong to the above-described class of FSPMSMs. This has been achieved considering the cases of odd and even number of phases, arranged in single-and double-layer slots. The identified candidates have been systematicallycharacterized by their winding factors and their slot-pole combinations.
It has been found that the identified candidates with their armature arranged in single-layer slots exhibit higher winding factors than their counterparts arranged in double-layer slots. Of particular interest are the candidates equipped with odd number of phases whose double-layer star of slots, prior the removal of even back-EMF phasors, are characterized by two spokes in each sector. These are expected to exhibit the highest torque production capability.
A case study has been treated considering a FSPMSM equipped with three phases in the armature having six parallel branches of one coil each. A 2D FEA-based investigation of its no-load features has revealed a remarkable pole edge leakage flux. It also enabled the prediction of the back-EMF which has been experimentally-validated. The paper has been achieved by a FEA-based resizing of the PM length aimed at the minimization of the pole edge leakage flux, thanks to which a reduction of the back-EMF harmonic content has been gained.
Prior to go in depth in the modelling and control of the identified candidates, especially the synthesis of dedicated post-fault strategies, an investigation of the possible circulation of harmonic currents in the loops resulting from the parallel connection of the phase coils is a mandatory step. Part 2 of this work develops this idea. SAHAR MKAOUAR received the B.S. degree in electromechanical engineering from Sfax Engineering National School (SENS), University of Sfax, Sfax, Tunisia, in 2019, and the M.Sc. degree in sustainable mobility actuators: research and technology (SMART) from SENS, in 2021. She is currently pursuing the master's degree and defended her thesis with Kassel University, Kassel, Germany, within the Erasmus Exchange Program 20210607-ENIS-KA107. Her current interests include the design, sizing, and optimization of permanent magnet machines dedicated to automotive and aerospace applications.
AICHA MAAOUI received the B.S. degree in electromechanical engineering from Sfax Engineering National School (SENS), University of Sfax, Sfax, Tunisia, in 2019, and the master's degree in sustainable mobility actuators: research and technology (SMART) from SENS, in 2020.
She is currently a Simulation, Modeling, and Support Engineer involved in motor design with Electro-Magnetic Works Inc., a golden partner of SOLIDWORKS.
MICHAEL SCHIER (Member, IEEE) received the Diploma and Ph.D. degrees in electrical engineering with specialization in energy technologies and electrical drives from the Technical University of Kaiserslautern, Germany.
From 1995 to 1999, he was involved in the development of electrical machines and power electronics for starter-alternators at the Department of Electric Vehicles, Siemens Company, in Würzburg, Germany. From 1999 to 2005, he was responsible for the development of blowers with electrical commutated motors and for automotive applications at Ebmpapst Company. Before his work at DLR, he was a Leader of power electronics development at Catem-Develec, a daughter company of Eberspächer Company. Since 2007, he has been working in the research area with the German Aerospace Center, Stuttgart, Germany, where he was first responsible for the development of alternative drives within the Institute of Vehicle Concepts. He is currently the Head of the Department of Vehicle Energy Concepts. The main topics of his scientific work were combined permanent magnet-electrically stator excited synchronous machines, starter-alternators for automotive application, electronically-commutated motors for axial and radial blowers, high-speed electric turbo-chargers, high torque machines for in-wheel motors for aircraft autonomous taxiing, and double motor systems with corresponding publications on international conferences. VOLUME 9, 2021