A Novel 24-Slots 14-Poles Fractional-Slot Concentrated Winding Topology with Low Space Harmonics for Electrical Machine

This paper proposes a novel winding layout for the machines with fractional-slot concentrated windings (FSCW) using a stator shifting concept and non-overlapping windings, with which all the non-working harmonics will be completely cancelled or significantly reduced. First, the basic winding layout with a 24slot 14pole machine to reduce the significant 1 sub-harmonic will be presented for machines with single layer (SL) windings. From this, a novel double layer (DL) winding layout using the stator shifting concept will be introduced. By adopting two SL winding sets with a 105deg mechanical angle shift with respect to each other, it is not necessary to use overlapping windings. With this configuration, the 1 sub-harmonic will be completely cancelled and the parasitic 5 harmonic will be significantly reduced. Hence, the rotor losses, specifically magnet loss will be significantly reduced. Finally, two PM machines with different DL winding layout, viz., conventional 12slot 14pole and 24slot 14pole machine, will be designed and compared to validate the advantages of this winding topology.


Introduction
The fractional-slot concentrated winding (FSCW) permanent magnet motor is a potentially excellent candidate for both aerospace applications and electric vehicles due to its high reliability and good fault-tolerance [1] [2].However, one of the key challenges is the significant space harmonics in the armature MMF distribution including sub-and high-order harmonics, which may result in localized saturation, eddy current loss in magnets (rotor losses) and unbalanced magnetic force inducing noise and vibration [1] [3].A number of methods like multi-layer winding, stator shifting, and unequal coil numbers have been proposed to deal with this in recent times.The impact of layer numbers on the performance of surface permanent magnet (SPM) synchronous machines has been studied in [4], which suggests the double layer configuration features less harmonic content and consequently lower torque ripple, but a weaker overload capability compared to single layer counterpart.In [5] [6], the method of four layer winding or three layer winding has been proposed to reduce or even cancel some particular harmonics by shifting an specific mechanical angle between first and second winding sets and specifically in [6] the effect of four layer winding on the PM eddy-current loss and vibration/noise have been identified as well.Another method of using concept of stator shifting was introduced by Dajaku [7] with doubling the slot numbers.With this method associated with unequal coil numbers, almost all the harmonics have been cancelled, but the winding is no longer non-overlapped due to the coil pitch of two slots [7]- [9].However, as far as the authors' knowledge, the first use of this method to cancel all the low order space harmonics was presented for a linear induction motor in [10] [11].However, for either the method of four layer winding or the conventional stator shifting, it is believed that mutual inductance will be considerably higher since there are two coils belonging to different phases wound around a tooth for a four layer winding design, and there are overlaps of different phase windings for the method of conventional stator shifting.In addition to that, doubling slot numbers with overlapping windings (coil pitch of 2 slots) or using four layer windings and unequal coil numbers complicate the manufacturing process and can negatively affect the slot fill factor.In this paper, an improved winding layout based on the 24-slot 14-pole PM motor is presented to deal with these challenges by using stator winding shifting and multi three-phase winding sets, but without using an overlapping winding.With this new winding layout, the 1 st sub-harmonic has been completely cancelled and the parasitic 5 th harmonic has been significantly reduced.In order to validate the proposed winding layout, two PM machines with different DL winding layout, viz., conventional 12slots/14poles and 24slots/ 14poles, will be designed and compared, with particular regards to the losses and output torque.

Basic winding layouts
The fractional slot concentrated winding machine incorporates significant MMF harmonics due to its non-sinusoidal windings.This is especially serious for machines with a single layer (SL) winding which has two opposite coils on each side.A significant 1 st sub-harmonic will be induced and its magnitude may be even higher than that of working harmonic [3].For example, 12slot 14pole machines with both single layer and double layer winding configurations are shown in Fig. 1 and their corresponding stator MMF spectra and harmonic distributions are illustrated in Fig. 2. For the 14 poles machine here, the only working harmonic is the 7 th , so the 1 st , 5 th , 11 th , and 13 th , etc. are undesired harmonics.And these non-working harmonics will result in torque ripple, rotor loss, and localized saturation, which is undesirable for the machine.It should be noted that the working harmonic can be the 5 th for a 10 pole machine.It can be observed from Fig. 2 (b) that a significant 1 st sub-harmonic has been generated by the SL winding configuration, while the double layer winding design can reduce the 1 st sub-harmonic.In fact, it is also apparent from Fig. 2(a) that a significant 1 st sub-harmonic is obvious in the MMF distribution of SL winding design.The inherent reason under this phenomenon is the two opposite coils of each winding are distributed on the opposite side of the machine, which means the magnetic flux induced by one coil have to be closed by another opposite coil through a very long magnetic flux path.In order to deal with the problem of significant 1 st sub-harmonic for the machines with single layer winding configuration, a new type of machine with two opposite coils of each phase being distributed adjacent has been proposed [12] [13], which results in the flux generated by one coil can be closed in a short flux path through an adjacent opposite coil, as shown in Fig. 3 (a).This is a 24slots/14poles machine with SL winding derived from 12slots/14poles with SL winding.The Fourier analysis of the MMF spectrum of this configuration is shown in Fig. 3 (b).It can be observed that the MMF harmonic distribution is quite similar to 12slots 14poles with DL winding and the 1 st subharmonic has been considerably reduced with this winding configuration.However, there are still many harmonics in the stator MMF distribution.In addition, a negative effect of this is the pitch factor has been reduced as well since the pole number is much lower than the slot number and this correspondingly will lead to a lower winding factor.Winding factor is related to torque output, so generally a lower winding factor will lead to a lower output torque, though this is not always the case.

New winding layout with low harmonic content
Machines with FSCW configuration have many advantages but in order to use them, it is necessary to avoid the disadvantage of significant MMF harmonics.Therefore, in this section methods to reduce or even cancel the non-working MMF harmonics will be studied.

Cancellation of the 1 st Sub-harmonic
Fig. 3 shows the 24 slot 14 pole motor with a 3-phase SL winding.The MMF distribution of this configuration can be expressed as Fourier series.
where   is the amplitude of k th order MMF space harmonic; k is the MMF harmonic order; N is the number of turns of each coil; I is the RMS value of current; θ is the space angle; w is the angular speed.It can be observed that the two adjacent coils for each phase winding have a mechanical phase difference in space by 30deg, of which corresponding electric angle is equal to 30deg as well (30*7-180).Thus a possible winding configuration is a dual 3phase windings (ABC&A1B1C1) with phase shifting to each other in time by 30 0 .The MMF distribution under the dual 3phase configuration can be written as Fourier series as well.
where   is the amplitude of k-th MMF space harmonic.
From Equation ( 4), the amplitude of each MMF space harmonic including an item ofsin ( −1 12 ), is different from that of the one 3-phase winding set.When k=1, namely the 1 st subharmonic, the amplitude of the 1 st MMF space harmonic  1 is equal to 0, which means the 1 st sub-harmonic has been completely cancelled.Moreover, when k equals to -11 or 13, their corresponding amplitudes are 0 as well.In fact, all the (12k±1) order harmonics have been cancelled.One thing that should be noted is that the rotational direction of (12k-1) or (6k-1) order harmonic is different from the working harmonic.
The MMF space harmonics under this condition are presented in Fig. 3 (b).As can be seen, with dual 3-phase configuration the 1 st sub-harmonic is completely cancelled while the working harmonics (either 5 th or 7 th ) are improved by 3.6% at the same time compared to the one 3-phase winding configuration.On the other hand, the 11 th , 13 th , 23 rd , 25 th , 35 th , 37 th are cancelled as well.These are in accordance with the above theoretical analysis from the Fourier series.Thus, the dual 3-phase winding set configuration is a good method to cancel the 1 st MMF sub-harmonic.However, the parasitic harmonics are not being reduced, but increased like the working harmonic.Hence, the method to reduce or cancel the parasitic harmonic has to be studied.

Reduction of parasitic harmonics
There are parasitic harmonics in the machines with fractionalslot concentrated winding like 5 th and 7 th for 12slots 10/14poles machine.They usually occur in pairs, e.g. 5 th and 7 th , which result in difficulty to reduce only one of them.For example, for the 24 slot 14 pole machine, the working harmonic is 7 th , but the parasitic 5 th harmonic exists as well, its amplitude is quite similar to that of 7 th working harmonic, and their corresponding winding factors are exactly the same.
A method of utilizing the concept of 'stator shifting' has been proposed in [7], with which the number of stator slots is doubled and this means the coil pitch has been changed from 1 slot to 2 slots, then another identical winding set is added to the same stator, but there is a certain mechanical shift angle between these two winding sets.In order to cancel the parasitic harmonic, the windings usually overlap each other, namely, a distributed winding with short pitch, which is undesirable for manufacturing and/or the fault-tolerant machine design.
In this section, by utilizing the concept of stator shifting, the parasitic harmonic can be considerably diminished or completely cancelled without using an overlapping winding.
One thing that should be noted is the pitch factor might be lower compared to previous design, and this will result in a lower winding factor if the distribution factor holds the same.
The process of realizing the stator shifting based on a 24 slot 14 pole machine with SL winding is as below: a.Using the 24 slot 14 pole machine with a dual 3-phase SL winding proposed in the section 2 as a base.b.Another dual 3-phase winding is added, whose coil distribution is the same as the first dual 3-phase SL winding set, but with a specific mechanical shift angle between these two winding sets.c.The stator and rotor remain the same; and these two winding sets are connected in series.

Fig. 4 Attenuation factor for different order MMF harmonics
From Equation ( 4), the amplitude of each harmonic can be obtained.If there is a specific mechanical angle α between the two winding sets, the resulting amplitude of each harmonic after the two winding sets added together can be written as It can be observed that an additional factor of cos (  2 ) has been added to the amplitude of each MMF harmonic.To simplify the analysis, this factor is defined as 'attenuation factor'.For each harmonic, namely a given k, with different shifting mechanical angle α, the attenuation factor will be varied sinusoidally.However, it should be noted that the mechanical angle α is not varying continuously but will be stepwise, as the winding sets can only shifted between slots.Thus α is equal to j*360 0 /z, where j is a non-negative integer and z is the stator slot numbers.In this case, each slot corresponds to an angle 15deg (360deg/24), so the mechanical angle of α can only be j*15deg.Therefore, with an appropriate shifting angle of α, the attenuation factor of a specific harmonic or more harmonics can be reduced or cancelled without influencing the desired working harmonic.The attenuation factor for each order harmonic can be calculated according to Equation ( 6) and summarized in Fig. 4. As can be seen, for different order harmonics, their attenuation factor changed sinusoidally with different periods; kth order harmonics vary at a period of k/2, which is in accordance with the above analysis.
In the case of a 24 slot 14pole machine with dual 3-phase windings, the working harmonic is chosen as the 7 th harmonic and the main parasitic harmonic is the 5 th harmonic.Therefore, it is necessary to find out an appropriate angle to reduce or cancel the 5 th harmonic while having no or not much negative influence on the 7 th harmonic.It can be observed from Fig. 4, possible or feasible angle area is represented by the grey areas, in which the attenuation factor of the 7 th harmonic is almost equal to 1. Within these areas, the angle of 105deg is a good candidate, at which the attenuation factor of 7 th is 0.9914 whilst the attenuation factor for 1 st and 5 th is 0.6087 and -0.1305, respectively.This means the 5 th harmonic has been effectively reduced and there are no considerably negative influences to the working harmonic (7 th ).The 1 st harmonic does not need to be considered as it has been cancelled by using the dual 3-phase winding configuration.
In fact, there is another angle of 108deg, better than the 105deg in terms of reducing 5 th harmonic, because the 5 th order harmonic is completely cancelled under this shifting angle.However, this angle is not feasible for this design as the shifting angle can only be implemented in steps of j*15deg.Therefore, the best candidate of shifting angle is 105deg, which is corresponding to 7 slots for a 24 slot 14 pole machine.Fig. 5 illustrates a proposed stator shifting concept in the designs of a 24 slot 14 pole motor with dual 3-phase winding sets.Since the double layer winding and single layer winding can be recognized as all teeth wound and alternate teeth wound windings, the concentrated windings can be expressed by the corresponding teeth, viz., each tooth represents a corresponding wound concentrated winding coil.Two identical dual 3-phase winding sets are adopted with the second 3-pase winding set shifting 105deg (7slots) over the first winding set.This winding layout is using the concept of stator shifting but without adopting overlapping winding (coil pitch of 2 slots) that are usually used in conventional stator shifting [7] [8], since the coil pitch is not changed.Without overlapping winding coils, the effect of physical contact and larger mutual inductance could be avoided, which is preferable for faulttolerant drive applications.It is clearly from Fig. 6 that the 1 st sub-harmonic is completely cancelled and the 5 th harmonic is significantly reduced to 13%, and these two harmonics principally determine the rotor losses (magnet eddy current loss).Therefore, the magnet eddy current loss can then be significantly reduced.The pitch factor of the 24S-14P configuration is about 0.793, which is 21.8% lower than that of 12S-14P configuration, to achieve an equivalent ampere turns, more coil turns should be used in the 24S-14P machine under the same current which will result in more copper loss in the slots.However, due to the doubling of the number of slots, the end winding length is reduced significantly, more importantly, the magnetic field distribution has been changed so that a larger reluctance torque could be produced.Besides, the distribution factor is improved by 3.5% by using dual 3-phase winding set.Therefore, this should not have a big influence on the torque output of the proposed motor.This will be illustrated in the next section.

Design example of machine with new winding layout
In order to validate the theoretical analysis of the novel winding layout, two PM machines with different slot/pole combinations and winding layouts, viz., proposed 24 slot 14 pole and conventional 12 slot 14 pole, are designed and compared based on a powertrain drive system used for such as hybrid electric vehicle (HEV) or pure electric vehicle (EV).
The insert-pm (IPM) configuration is adopted as the rotor structure.The drive requirement used here is summarized in Table 1.
Table 1 Design Specification of Electric drive system Design Specification Data

Maximum speed 12000rpm DC link voltage 600V
For both machines, the outer dimension limitation is the same, with an outer diameter of 285mm and an axial length of 90mm.
In addition, the rotor dimensions and magnet thickness are kept the same.Fig. 7 shows the proposed 24 slot 14 pole motor with novel dual 3-phase winding layout, which can be regarded as a combination of two 24S-14P machines with a single layer (SL) winding, with the winding set of the second 24S-14P SL machine shifting 7 slots (105deg) over the first machine.
The electromagnetic torque of both machines has been calculated, as shown in Fig. 8.It can be seen that both machines can generate an average torque of 170 Nm, meeting the design torque requirement, but the proposed 24S-14P dual 3-phase machine features an approximately constant torque with a ripple of 1%, as the significant non-working harmonics resulting in torque pulsation have been cancelled or significantly reduced.The torque ripple of the conventional 12S-14P machine is about 8.8%, which is beyond the requirement.Although this can be diminished by stator skewing or staggered rotor poles, these methods will complicate the manufacturing process and increase the cost.In addition to that, the average torque will be negatively influenced.Fig. 9 summarizes the losses in the machine's different parts and total loss for both topologies.It is shown that the copper loss of the proposed 24S-14P dual 3-phase motor is slightly higher than that of conventional motor, which is reasonable since more coil turns are used due to the lower winding factor.Other than that, the iron loss and magnet loss is much lower than that of the conventional 12S-14P motor, and total loss of the former is almost half that of the latter.Specifically, the magnet loss of conventional 12S-14P machine is about 1,148 W whereas the magnet loss of the proposed motor is only 60.8 W, significantly decreasing thermal load in the rotor part, which consequently reduces the demagnetization risk to the magnets without using any additional methods like magnet segmentation or staggered rotor poles which may result in increasing manufacturing costs and/or negative influences on EM performance and mechanical stiffness.The efficiency of the proposed 24S-14P machine is 96.3%, while for the conventional 12S-14P machine it is about 93.7%, showing that the proposed machine has a significantly higher efficiency.As mentioned before, the winding factor of the proposed machine is lower than that of conventional 12S-14P machine, but their average torque is almost the same.This is because a larger reluctance torque is generated for the proposed machine, while there is not much reluctance torque for conventional 12S-14P machine.The average torques versus current angle for both machine is calculated and illustrated in Fig. 10.It is apparent that the maximum torque per ampere (MTPA) is 45deg for the proposed machine and the corresponding torque is much higher than the torque when id=0 control strategy is used.For the conventional machine, the MTPA is 5deg, and the corresponding torque is just slightly higher than the torque when id=0 control strategy is used.Therefore, the proposed 24S-14P machine with a dual 3-phase winding system is a promising solution to the challenges of high space harmonics for FSCW motors.

Conclusions
A novel winding layout using stator shifting, based on a 24 Slot 14 Pole winding for FSCW permanent magnet motors was proposed in this paper.This method gives complete cancellation of the 1 st sub-harmonic, and the 5 th sub-harmonic has been significantly reduced.Unlike the conventional stator shifting concept that normally requires overlapping coils, this novel winding layout can still keep a concentrated winding set, which avoids physical coil contact and can give lower mutual inductance, making it preferable for fault-tolerant drive applications.Both the proposed 24S-14P dual 3-phase motor and conventional 12S-14P motor have been designed for a traction application.The comparative study shows that the proposed 24S-14P dual 3-phase motor not only exhibits much lower space harmonic content and much lower iron losses but also has an improved torque capability and efficiency.Therefore, it is confirmed that the proposed 24S-14P dual 3phase system is a promising solution to the challenges of significant space harmonics for FSCW motor.

Fig. 5
Fig. 5 Concept of "stator shifting" based on a 24 slot 14 pole machine

Fig. 7
Fig. 7 New configuration of 24S-14P with double layer winding

Fig. 9
Fig. 9 Comparison of output performances between two machines