Investigation of a Novel 24-slot/14-pole Six-phase Fault-tolerant Modular Permanent-magnet In-wheel Motor for Electric Vehicles

In this paper, a six-phase fault-tolerant modular permanent magnet synchronous machine (PMSM) with a novel 24-slot/14-pole combination is proposed as a high-performance actuator for wheel-driving electric vehicle (EV) applications. Feasible slot/pole combinations of the fractional-slot concentrated winding six-phase PMSM are elicited and analyzed for scheme selection. The novel 24-slot/14-pole combination is derived from the analysis and suppression of the magnetomotive force (MMF) harmonics. By making use of alternate-teeth-wound concentrated winding configuration, two adjacent coils per phase and unequal teeth widths, the phase windings of the proposed machine is magnetically, thermally isolated, which offers potentials of modular design and fault tolerant capability. Taking advantage of the leakage component of winding inductance, 1.0 per unit short-circuit current is achieved endowing the machine with short-circuit proof capability. Optimal design of essential parameters aiming at low eddy current losses, high winding factor and short-circuit-proof ability are presented to pave the way for a high-quality system implementation.


Introduction
Multiphase fault-tolerant permanent magnet (PM) in-wheel motors, equipped with alternated-teeth-wound fractional-slot concentrated windings (FSCWs), are quite promising candidates in applications of four-wheel-driving electric vehicles (EVs) attributing to their high torque density, high efficiency and high fault-tolerant capability [1][2][3].By employing excessive winding redundancy over three phases, the stator winding of the multiphase PM machine can keep on forming the circulating rotating magnetic field when a fault occurs in one or even more phases.By making use of neodymium-iron-boron (NdFeB) rotor PMs with high remanence, coercivity and energy product, the power density of the machine is superior to existing fault-tolerant alternating current (AC) machines such as switched reluctance motor, flux switching machine and doubly salient machines [4][5][6], which makes it prevalent in this field throughout the past years.
For the design principle of fault-tolerant PM machines, electrical, magnetic, thermal, physical isolation features are listed as the most essential ones [7,8].These isolation features aim to eliminate any impact induced by the faulty winding upon the remaining phases, so as to provide a reliable transition to the stage of post-fault control and continuous operation.The fractional-slot concentrated winding machines, in which the stator windings are non-overlapped and wrapped around all teeth or alternate teeth, cater to the requirement of the above isolation features [9][10][11].Especially, by employing the alternate-teeth-wound fractional-slot concentrated windings, the coils are alternatively wound around the stator teeth, which provides an advantage of thermal isolation and physical isolation of the stator phase windings [12,13].The electrical isolation feature can be achieved by making use of the full-bridge inverter topology manipulating the phase voltages rather than the line-to-line voltages [14,15].Such machines have relatively large self-inductance and small mutual inductance assuring that the faulty winding will not affect the healthy ones.Furthermore, a close slot/pole combination of the fractional-slot concentrated winding machine, i.e., 2p (pole number) = Q (slot number) ± 2, should be utilized in order to maximize the flux linkage and torque density [16,17].Hence, a high winding factor of more than 0.9 and negligible cogging torque can also be obtained.
Under the above type of slot/pole combinations, the winding-produced main magnetomotive force (MMF) component, which is defined as the component whose wavelength equals the pole pitch [18], is normally a high-order one while other low-order and higher-order components exist leading to a larger harmonic leakage inductance compared to that of the conventional distributed winding configurations.The numerical calculation methods for the leakage inductances are mentioned in references [19,20].Since the rotating speed of the harmonic component is reversely proportional to its order, the lowest-order one is at the maximum spin speed in a relative movement to the rotor PMs.Consequently, the eddy currents induced in the PMs are rather considerable.Segmentation technique that circumferentially and axially separates the PMs into blocks is often applied to deal with the issue [21,22].By doing that, the fabrication process gets tougher since the PM blocks repel one another.Ways to cope with the MMF harmonic components should be sought.
With the development of the theory of fractional-slot concentrated winding, the modular design concept has been introduced to the design of fractional-slot concentrated winding machines, in which the stator windings can be constructed with separated armature cores [23].A modular three-phase 18-slot/12-pole scheme formed with 18 stator armature core modules was used in the Honda Civic hybrid electric vehicle (HEV) with the advantages of short end winding and easy fabrication.For fault-tolerant purpose, such a kind of stator construction offers convenience for replacement when the winding in a module suffers a failure, thus reducing the maintenance costs.A five-phase five-slot/six-pole fault-tolerant modular PM prototype machine with five soft magnetic composite (SMC)-constructed modules was investigated for safety-critical applications [24,25].It is found that the SMC modules suffered cracks during the fabrication process with a non-uniform air gap left after assembly.More importantly, neither the phase windings of the m-phase/m-slot nor those of the other existing PM modular machines are completely magnetically isolated, which means that they are physically modularized but not magnetically.
This paper starts out with the analysis of feasible slot/pole combinations for the six-phase fault-tolerant fractional-slot concentrated winding machines.To solve the problem of high iron loss and temperature rise of rotor PMs due to excessive MMF harmonic components, several machine schemes including 24-slot/22-pole alternate-teeth-wound scheme, 24-slot/22-pole all-teeth-wound scheme, etc., are discussed and compared.A novel alternate-teeth-wound 24-slot/14-pole symmetric six-phase fault-tolerant permanent-magnet in-wheel motor is proposed and investigated.To advance the value of the winding pitch factor of the proposed machine, alternate-teeth-wound fractional-slot concentrated winding with unequal stator teeth widths are applied.With two adjacent coil per phase and excellent magnetically isolation features, it is suitable for the proposed machine to adopt the modular design conception for easy fabrication and post-fault operation.Besides, the outer rotor prototype machine is designed and optimized aiming at high power/torque density.

Winding Arrangements and Feasible Slot/Pole Combinations
On winding phase belt level, there are two schemes for the six-phase permanent magnet machines, i.e., symmetric six-phase PMSM with 60 degree phase belt and asymmetric six-phase PMSM with 30 degree phase belt, as shown in Figure 1.The symmetric six-phase PMSM has similar magnetic features referring to a 60-degree phase-belt three-phase PMSM [26].On the other hand, the asymmetric six-phase PMSM [27], with two three-phase windings shifting by 30 degree, is magnetically approximate to a twelve-phase machine.Thus, it can be called a semi-twelve-phase PMSM [28].Apparently, one of the differences between the two schemes is the winding-produced MMF harmonic components.The MMF harmonic components of the asymmetric six-phase PMSM is (12k ± 1)th, and that of the symmetric six-phase PMSM is (6k ± 1)th.Roughly speaking, the MMF harmonic components of the asymmetric six-phase PMSM are almost half of that of the symmetric one.There is no doubt that the asymmetric six-phase PMSM might have less iron loss and lower torque ripple.However, the situation depends on not only the numbers of harmonics but also the amplitudes of harmonics that should be discussed in specific situations.
It is known to all that, the flux linkage will enhance with a close slot and pole numbers, and thus, a high torque density is achieved.Based on that viewpoint, the machine used for direct-driving EV applications is proposed to employ slot and pole combinations satisfied with 2p = Q ± 2, where p denotes the pole number and Q denotes the slot number.The feasible slot and pole combinations are listed in Tables 1 and 2, where LCM denotes the lowest common multiple of slot and pole numbers; SPP denotes slot number per pole per phase.And, a larger LCM number indicates a lower cogging torque.Both alternate-teeth-wound and all-teeth-wound fractional-slot concentrated windings are taken into consideration.Although the pole and slot combinations have been introduced in the discussion of six-phase supply feasibility, the selections for the feasible six-phase supply are limited to two three-phase winding shifting by 30 degree [29].However, in Tables 1 and 2, two possible winding distributions-symmetric and asymmetric six-phase windings-are involved with the limitation of 2p = Q ± 2. With the design of close slot and pole numbers, there are more combinations for the symmetric six-phase PMSM as shown in Tables 1 and 2.
As shown in Table 1, only the schemes with 12k slot numbers allow the alternate-teeth-wound winding arrangements (marked with ▲).With alternate-teeth-wound windings, the machine is well protected against internal short-circuit failure between phases.The winding factor increases and cogging torque decreases when the slot and pole numbers get larger.Among all the slot/pole combinations shown in Tables 1 and 2, the 24-slot/22-pole or 24-slot/26-pole asymmetric six-phase scheme (marked with ■), which enables alternate-teeth-wound winding arrangement and has the largest winding factors, is more suitable for the in-wheel applications than the others.
Additionally, compared to symmetric six-phase PMSM, the winding axes of asymmetric six-phase PMSM are not coincident with each other, which enables a fault tolerance up to four-phase open circuit fault.For instance, assume that the open circuit fault occurs at the phases A, B, D and E in Figure 1b, the symmetric six-phase machine merely has two aligned phases C and F. Thus, it is impossible to reconstruct a circular rotating MMF field in some types of severe fault conditions.

MMF Harmonic Analysis
In this paper, the MMF harmonic is represented by an integer harmonic system rather than a fractional harmonic system.For a fractional-slot concentrated winding machine, the main component of the stator MMF is commonly a high-order component instead of the 1st component [18].Thus, the harmonic leakage inductance is quite large compared to the conventional distributed winding machine.Furthermore, the harmonics of the stator MMF have impacts on the cogging torque, eddy-current loss and power factor.Among all the MMF harmonic components, the two-pole sub-harmonic component [22] which travels at a reverse different speed is particularly high.MMF harmonic analysis is performed to compare schemes with different winding arrangements and slot/pole combinations.
As mentioned earlier in Section 2.1, the 24-slot/22-pole (or 24-slot/26-pole) asymmetric six-phase scheme, which enables alternate-teeth-wound winding arrangement and has the largest winding factors, is more suitable for the applications.The winding arrangement and MMF harmonic analysis are shown in Figure 2, based on the MMF calculation theorem for concentrated winding machines [30].The MMF harmonic spectrum is obtained by analyze the winding-produced air-gap flux density.As can be seen in Figure 2c, the spectrum of the flux density produced by the stator windings consists of (12k ± 1)th harmonic components.Also, a strong 1st component can be observed with amplitude of 70.4% of the main component (11th).Thus it induces eddy current both in iron and PMs, which is determined by the amplitude and velocity contrast [31].Such a large harmonic content can drastically reduce the motor performance.Specifically, it can reduce the power factor and efficiency, The 24-slot/22-pole all-teeth-wound scheme changes the distributing winding factor of each harmonic component.It can be clearly seen that, the 1st component is prominently suppressed.By making use of the estimation formula illustrated in reference [32], the PM losses produced by the 1st harmonic are reduced by 95.01%attributing to a change from alternate-teeth-wound scheme to all-teeth-wound scheme.However, as for fault-tolerant drives, isolation between the phase windings is of great significance.Note that each slot of the above scheme contains two coil sides.Thus, there are possibilities of short-circuit failure between phases, which increases the probability of failures that are difficult to deal with.Hence, the challenge becomes how to suppress the 1st MMF harmonic with alternate-teeth-wound windings.One possible solution is presented in Figure 4.As can be seen in Figure 4a, the idea begins with employing two coils of the same phase shifting by 150 mechanical degree in order to change the distributed factor of the stator MMF vectors.The angle θ ν = 150ν° in Figure 4a denotes the electrical angle between two MMF vectors F 1ν and F 2ν for the νth MMF harmonic component.Thus, the synthetized MMF vectors for the νth harmonic component are given by: where the F mν denotes the amplitude of the 1st MMF component; K dν = cos(ν75 °) is defined to be the distributed factor for νth MMF component and calculated in Table 3, which indicates the suppression level of the harmonics.It can be clearly seen from Table 3 that, such a kind of winding arrangement pattern suppresses the 1st, 11th, 13th… MMF harmonic components effectively, while the 5th, 7th… components remain nearly unchanged.Furthermore, the two coils of one phase can be placed adjacent to each other as shown in Figure 4b without transferring the relationship between the MMF vectors established in Figure 4a.Therefore, the winding-produced flux can close within a short path so that a better magnetic isolation features can be achieved.And, the winding-produced air-gap flux density and MMF spectrum for the scheme shown in Figure 4b is illustrated in Figure 5.As can be seen in Figure 5, the 1st harmonic component of the MMF has been nearly eliminated while the fifth and seventh component has become the predominant MMF components amid the air-gap flux density spectrum.Consequently, the appropriate number of rotor poles should be 10 or 14 instead of 22 or 26, resulting in a specific 24-slot/10-pole or 24-slot/14-pole combination.With the decreased number of rotor poles, the pole pitch for the stator winding is much less than 1, which leads to a smaller pitch factor.The pitch factor for the hth harmonic component is given by: sin where b w is the coil-wound tooth tip span which is specified in Figure 4c; b eq is the tooth tip span when all tooth tip spans are equal; and Q is the slot number.Therefore, unequal tooth tip spans could be employed to enlarge the pitch span of the winding to advance winding pitch factor, as shown in Figure 4c.
Since the pole pitch of a 14-pole scheme is shorter than that of a 10-pole scheme and the maximum teeth span for the 24-slot scheme can be 1/12 of the circumferential length, it is only feasible to adopt a 24-slot/14-pole scheme.The air-gap flux density and spectrum are shown in Figure 6 regarding a 24-slot/14-pole symmetric six-phase PMSMs having two adjacent coils per phase and unequal teeth width.
As shown in Figure 6, by making use of the extended coil-wound tooth span, the 5th and 7th harmonic components become more dominant among all the MMF components compared with what is shown in Figure 5b.Imagine that the widths of the non-wound tooth tips are adjusted to be zero, the 24-slot/14-pole machine will actually transform into a 12-slot/14-pole one with all-teeth-wound windings.Here we provide the differences between the two schemes to clarify this point: (1) The all-teeth-wound 12-slot/14-pole scheme allows the underlying possibility of short-circuit fault between two different phases, which means that the scheme is not electrically isolated and inappropriate for fault-tolerant uses; (2) Referring to a winding short-circuit failure, the non-wound teeth play a role that provides the closest path for the flux linked by the short-circuit winding.Thus, the fault will not interfere the remaining phases as the other alternate-teeth-wound schemes did.
Additionally, some references have already focused on concentrated winding machines using an irregular distribution of the slots [33][34][35].Even though the irregular distribution of the slots is, essentially, the unequal teeth scheme, it can still be distinguished from what is talking in this article.What is concerned in references [33][34][35] is how the irregular distribution of the slots is derived from a conventional distributed winding step by step.Besides, high performances-reduced copper loss, low torque ripple and enhanced output torque-was obtained by employing the structure of irregular slot distribution.However, in our paper, the 24-slot/14-pole machine is derived from a 24-slot/22-pole machine (both of them are fractional-slot concentrated winding machines).The major concern is that whether the new pattern can suppress the MMF harmonics and achieve a better isolation feature.

Modular Design of the Stator
Although the modular design conception has been introduced to the m-phase/2m-slot alternate-teeth-wound fractional-slot concentrated winding machinery series, in which the stator can be divided into several E-shape modules each consisting of one full tooth, its wrapped coil and two incomplete teeth, the phase windings are not magnetically isolated [36].Another fact is that the fit tolerances between the separated stator armature cores are inevitable during manufacturing process.Therefore, the magnetic resistance will be increased in the stator yoke, affecting the torque capability of the machine.The flux lines in the six-phase 12-slot modular machinery series are shown in Figure 7.It is obviously that the flux lines produced by the winding of the six-phase 12-slot modular machine will go long paths in the stator yoke.Hence, this kind of machines is not suitable for modular design.With two adjacent coils per phase and excellent magnetic isolation feature, it is more convenient for the proposed 24-slot/14-pole machine to adopt a modular design concept for easy fabrication and post-fault replacement.The stator modules can be constructed both from SMC or lamination stack.It is found that, the lamination-steel-sheet constructed modules are more suitable for a low-speed high-torque machine.In contrast, the SMC modules are suitable for a high-speed low-torque machine since the iron losses can be prominently reduced by employing SMC materials [37].
The divided stator core wound with concentric winding simplifies the construction of the stator and reduces the end winding loss.Moreover, it offers a convenience in maintenance that the faulty core can be readily substituted for a new one.Thus, the cost of maintenance is reduced.
The 24-slot/14-pole six-phase modular PMSM is shown in Figure 8.As can be seen in Figure 8a, the stator of the 24-slot/14-pole six-phase PMSM is made up of six modules.Semi-circular grooves are applied in the modules to assemble the separated armature cores together to form the whole stator.As shown in Figure 8b, each module consists of two alternate-teeth-wound four slot concentric coils.Besides, two half teeth are located in both two ends of the module.

Finite Element Method (FEM)-Based Design and Optimization
The alternate-teeth-wound 24-slot/14-pole scheme with unequal teeth widths is presented and proposed to be a promising candidate for improving the reliability of EV driving system, as mentioned in the above sections.For in-wheel application, an original model of the outer rotor 24-slot/14-pole scheme is established with Ansoft Maxwell 2-D Design, as shown in Figure 9a.And the key parameters and dimensions are listed in Table 4.  10a, the maximum flux density in stator yoke, stator teeth and teeth tips are 1.70T, 1.68T and 2.1T, respectively, aiming to take full use of the material and pursue high power density.As can be seen in Figure 10b, since the flux produced by a phase winding closes in a short path within the modular it belongs to except for some leakage components, the six modules are well magnetically isolated.
The back EMF waveform and spectral analysis are shown in Figure 12.As can be seen in Figure 12a, the back EMFs in the six-phase windings of the 24-slot/14-pole machine are presented with a duty cycle of 19.05 ms and a sequent electrical angle shift of 60 degree from phase A to F. The maximum value of the back electromotive force (EMF) during the period is 114.88V. From the spectrum analysis illustrated in Figure 12b, we can see that the main harmonic component of the back EMF waveform comprises the 3rd, 5th, 9th and 11th harmonics.The total harmonic distortion (THD) of the back EMF waveform is 17.8%.As mentioned in Section 2, the span of coil-wound teeth tips should be increased to advance the pitch factor of the proposed 24-slot/14-pole machine.All the dimensions of the machine model are fixed except for the span of coil-wound teeth tip to search for the optimal value.The impact of the tooth tip span upon the cogging torque and back EMF are shown in Table 5 and Figure 13, in which the tooth tip span is represented using the circumferential angle and broadened from 18° to 20.5°.

Teeth tip span
Cogging torque (Nm)  As can be seen in Figure 13a, the cogging torque reaches a maximum value of 6.80 Nm with the tooth tip span of 19°, and a minimum value of 1.63 Nm with the tooth tip span of 20.5°.For the back EMF spectrums shown in Figure 13b, the 1st component of the back EMF is slightly increased with the tooth tip span gets wider.The main harmonic components, i.e., 3rd, 5th, 9th and 11th, remain at low levels.And there is a downtrend for the 3rd, 9th and 11th harmonic components and an uptrend for the 5th one.The optimal tooth tip span of the coil-wound tooth is 20.5°.
The pole arc coefficient also affects the performances of the machine.The pole arc coefficient is varies from 0.5 to 0.9 to see the impact on the cogging torque and back EMF harmonics, as shown in Table 6 and Figure 14.
As can be seen in Figure 14a, the cogging torque reaches a minimum of 1.72 Nm with the pole arc coefficient of 0.75.However, a lower pole arc coefficient results in a lower power density.Thus, we choose a high pole arc coefficient of 0.9 to obtain a high power density design.

Short Circuit Current Constraint
Winding short-circuit fault is the most severe failure that might occur in the stator windings.Conventional permanent magnet machines possess a short-circuit current that is several times higher than the rated stator current.Therefore, the short-circuit fault will overheat the stator conductors and bring about deterioration situations further.
The alternate-teeth-wound fractional-slot concentrated winding PMSM provides an inherent thermal isolation feature of the stator phase windings.Besides, all of the phases windings are magnetically isolated, signifying that the short-circuit fault in certain phase windings will not interfere the other phases.If only we restrain the short-circuit current within about 1.0 per unit, the motor can be prevented from the potential damage caused by the short-circuit current.The leakage inductance of a fractional-slot concentrated winding PMSM consists of harmonic leakage inductance, slot leakage inductance and end leakage inductance, which is quite large compare with the one with distributed windings [38].The main MMF component corresponding to the mechanical-electrical energy conversion is usually a high order MMF component.For instance, the main MMF component is the 11th one for a 24-slot/22-pole fractional-slot concentrated winding machine.It can be calculated that the harmonic leakage inductance could be several times larger than the main inductance by the analyses provided in references [19,20].Along with the slot leakage inductance, the self-inductance of the fractional-slot concentrated winding machine could be rather large in contrast to the distributed winding machine.
It should be noted that, the inner power factor of the machine declines although a lower short-circuit current can be achieved with large leakage inductance.The vector diagram of the equivalent circuit in d-q reference frame for PMSM with 1.0 per unit short-circuit current is illustrated in Figure 15.As can be seen in Figure 15a, the relationship of the vectors in case of the short-circuit fault can be written as: where the E 0 is back EMF; I s is the short-circuit current; X is the reactance of the stator winding; and R a is the resistance of the winding.Since the resistance of the winding is negligible compared to the winding reactance, Equation (2) can be reduced to: Thus, the angle between the phase voltage vector U 0 and stator current I with I d = 0 control is given by: where the stator current I equals the short-circuit current I s .The winding resistance R a can be disregarded again, then: Therefore, the inner power factor is given by: 45 0 707 cos .
Although the inner power factor is quite low under I d = 0 control, the actual power factor can be adjusted by changing the stator current vector I.

Optimal Scheme
Combing the above analyses of optimal coil-wound tooth tip span, pole arc coefficient and short-circuit current constraint mentioned in Sections 3.2 and 3.3, the key parameters for the optimal scheme are shown in Table 7 and Figure 16.To achieve the desired power, voltage and the other parameters, an analytical design program was firstly performed to calculate, adjust and obtain the sensible but relatively rough parameters [39].After that, FEA methods are employed to check and adjust the desired power, voltage, efficiency, etc.Therefore, an accurate design is achieved.Besides, circumferential segmentation of the rotor PMs is employed to restrain the eddy current within short paths [40].For the PM material of N45SH, the relative permeability μ r = 1.113 and the conductivity ρ = 160 μΩ•cm.Thus, the depth of penetration is calculated as 1.5 cm.Each piece of the PM is divided into four parts to reduce the eddy current loss.
The proposed outer rotor 24-slot/14-pole machine is designed for the in-wheel driving applications.The machine has a maximum speed of 1200 rpm and maximum torque of 250 Nm.For the constrain of DC-bus voltage of 288 V, the flux-weakening operation is applied to expand the speed to 1200 rpm.The efficiencies in all speed ranges are shown in Figure 17.Iron losses, joule losses and estimated mechanical losses are taken into consideration.The current regulation is based on the control strategy of maximum torque per ampere (MTPA).
As can be seen in Figure 17, the efficiency reaches the maximum value of 0.95.The area where the efficiency is greater than 0.90 covers approximately 78.2% of the whole region.The area where efficiency is greater than 0.80 accounts for 87.5%, which shows that the designed machine is high-efficient in most operating area.The presented design could be an interesting candidate for prototyping.

Conclusions
(1) A novel 24-slot/14-pole PMSM adopting alternate-teeth-wound FSCWs and unequal teeth widths is proposed for in-wheel application, with the advantages of completely isolation features and reduced MMF harmonics; (2) The magnetic isolation feature of the proposed alternate-teeth-wound 24-slot/14-pole six-phase PMSM having two adjacent coils per phase is superior to the alternate-teeth-wound 24-slot/22-pole scheme which is a conventional optimal choice; (3) A 24 kW outer rotor prototype machine is designed and optimized using the FEA method.The modular stator core is form of six armature cores which provides the convenient features of easy fabrication and post-fault replacement.The defect of lower winding factor regarding the proposed machine is solved by extending the tooth tip span of the coil-wound teeth.The winding leakage inductance is utilized to restrain the winding short circuit current to nearly 1.0 per unit but with low inner power factor; (4) An optimal design scheme with high winding factor, 1.0 per unit short circuit current, high efficiency in all speed ranges is obtained and presented for in-wheel application; (5) In order to obtain flexibilities of post-fault control, the proposed solution imposes twelve legs instead of six legs for dual-three phase windings resulting in high cost of the power converter, which should be considered in future work.
cause temperature rises in the PMs.To solve this problem, all-teeth-wound schemes are frequently employed, as shown in Figure3.

Figure 3 .
Figure 3. Winding arrangement and MMF harmonic analysis of the 24-slot all-teeth-wound asymmetric six-phase PMSM: (a) stator winding arrangement and the synthesized EMF vector; (b) air-gap flux density; and (c) winding-produced air-gap flux density spectrum.

Figure 4 .
Figure 4. Stator winding arrangements of the 24-slot alternate-teeth-wound six-phase PMSM: (a) two coils of same phase shifting by 150 degree; (b) two adjacent coils per phase; and (c) two adjacent coils per phase with unequal teeth widths.

Figure 5 .
Figure 5. MMF harmonic analysis of the 24-slot asymmetric six-phase PMSMs having two adjacent coils per phase and equal teeth widths: (a) winding-produced air-gap flux density; and (b) spectrum.

Figure 6 .
Figure 6.MMF harmonic analysis of the 24-slot symmetric six-phase PMSMs having two adjacent coils per phase and unequal teeth widths: (a) winding-produced air-gap flux density; and (b) spectrum.

Figure 10 .
Figure 10.Flux density distribution and flux lines@450 rpm with rated load: (a) flux density map; and (b) winding-produced flux lines.

Figure 12 .
Figure 12.Back EMF waveform@450 rpm: (a) six-phase back EMF; and (b) spectrum for the back EMF in phase A.

Figure 13 .
Figure 13.Performance varies with different span of coil-wound teeth tip: (a) cogging torque; and (b) spectrum for the back EMFs in all phases.

Figure 14 .
Figure 14.Performance varies with different pole arc coefficient: (a) cogging torque; and (b) spectrum for the back EMFs in all phases.

Figure 15 .
Figure 15.Vector diagram for PMSM with 1.0 per unit short-circuit current: (a) short circuit; and (b) normal condition.

Figure 17 .
Figure 17.Efficiency map in all speed ranges.

Table 1 .
Possible slot/pole combinations of the symmetric six-phase PMSM equipped with fractional-slot concentrated windings (FSCWs).Notes: ▲ means the combinations enable alternate-teeth-wound design.

Table 2 .
Possible slot/pole combinations of the asymmetric six-phase PMSM equipped with FSCWs.Notes: ■ means the combinations enable alternate-teeth-wound design and have highest winding factor.

Table 3 .
The distributed factor for νth MMF component.

Table 4 .
Key parameters and dimensions of the original design.

Table 6 .
Cogging torque and harmonic components of back EMF.

Table 7 .
Key parameters and dimensions of the optimal scheme.