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The Journal of Engineering
The 9th International Conference on Power Electronics, Machines and
Drives (PEMD 2018)
Novel 24-slots14-poles fractional-slot
concentrated winding topology with low-
space harmonics for electrical machine
eISSN 2051-3305
Received on 22nd June 2018
Accepted on 27th July 2018
E-First on 16th April 2019
doi: 10.1049/joe.2018.8085
www.ietdl.org
Shaohong Zhu1,2 , Tom Cox1,2, Zeyuan Xu1,2, Chris Gerada1,2
1Institute for Aerospace Technology, University of Nottingham, Nottingham, UK
2Power Electronics, Machines and Control Research Group, University of Nottingham, Nottingham, UK
E-mail: hiteezsh@gmail.com
Abstract: This paper proposes a novel winding layout for the electric machines with fractional-slot concentrated windings
(FSCW) using a stator shifting concept, with which all the non-working harmonics can be completely cancelled or significantly
reduced and the non-overlapping winding can be kept. First, the basic winding layout with a 24-slot 14-pole machine to reduce
the significant 1st 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 105° mechanical
angle shift with respect to each other, it is not necessary to use overlapping windings. With this configuration, the 1st sub-
harmonic will be completely cancelled and the parasitic 5th 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, namely,
conventional 12-slot 14-pole and 24-slot 14-pole machine, will be designed and compared to validate the advantages of this
winding topology.
1Introduction
The fractional-slot concentrated winding (FSCW) permanent
magnet motor is a potentially excellent candidate for both
aerospace applications and electric vehicles (EVs) 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 localised 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 (DL) configuration
features less harmonic content and consequently lower torque
ripple, but a weaker overload capability compared to single-layer
(SL) 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 a 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.
Here, 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
1st sub-harmonic has been completely cancelled and the parasitic
5th harmonic has been significantly reduced. In order to validate
the proposed winding layout, two PM machines with different DL
winding layout, namelt, conventional 12-slots/14-poles and 24-
slots/14-poles, will be designed and compared, with particular
regard to the losses and output torque.
2Basic winding layouts
The FSCW machine incorporates significant MMF harmonics due
to its non-sinusoidal windings. This is especially serious for
machines with a SL winding which has two opposite coils on each
side. A significant 1st sub-harmonic will be induced and its
magnitude may be even higher than that of working harmonic [3].
For example, 12-slot 14-pole machines with both SL and DL
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 7th, so the 1st, 5th, 11th, and 13th etc. are undesired harmonics.
These non-working harmonics will result in torque ripple, rotor
loss, and localised saturation, which is undesirable for the machine.
It should be noted that the working harmonic can be the 5th for a
10-pole machine. It can be observed from Fig. 2b that a significant
1st sub-harmonic has been generated by the SL winding
configuration, while the DL winding design can reduce the 1st sub-
harmonic.
In fact, it is also apparent from Fig. 2a that a significant 1st 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
1st sub-harmonic for the machines with SL 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
J. Eng., 2019, Vol. 2019 Iss. 17, pp. 3784-3788
This is an open access article published by the IET under the Creative Commons Attribution License
(http://creativecommons.org/licenses/by/3.0/)
3784
the flux generated by one coil can be closed in a short flux path
through an adjacent opposite coil, as shown in Fig. 3a. This is a 24-
slots/14-poles machine with SL winding derived from 12-slots/14-
poles with SL winding. The Fourier analysis of the MMF spectrum
of this configuration is shown in Fig. 3b. It can be observed that the
MMF harmonic distribution is quite similar to 12-slots 14-poles
with DL winding and the 1st sub-harmonic 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 that 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.
3New 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.
3.1 Cancellation of the 1st sub-harmonic
Fig. 3 shows the 24-slot 14-pole motor with a three-phase SL
winding. The MMF distribution of this configuration can be
expressed as Fourier series.
F(θ,t) = ∑
k= 1, − 5, 7
∞
vksin kθ −wt −kπ
24
(1)
vk =12N I
kπ sin kπ
24 sin kπ
24
(2)
where vk is the amplitude of kth 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 30°, of
which corresponding electric angle is equal to 30° as well (30 × 7–
180). Thus, a possible winding configuration is a dual three-phase
windings (ABC&A1B1C1) with phase shifting to each other in
Fig. 1 Conventional winding layouts for 12slots/14poles machine
(a) Single layer, (b) Double layer
Fig. 2 Stator MMF harmonics distribution for 12Slots/14poles machine
Fig. 3 24Slots/14Poles machine with single layer winding
J. Eng., 2019, Vol. 2019 Iss. 17, pp. 3784-3788
This is an open access article published by the IET under the Creative Commons Attribution License
(http://creativecommons.org/licenses/by/3.0/)
3785
time by 30°. The MMF distribution under the dual three-phase
configuration can be written as Fourier series as well.
Fd(θ,t) = ∑
k= 1, − 5.7
∞
vdksin kθ −wt −k− 1
12 π
(3)
vdk =12NI
kπ sin kπ
24 sin k− 1
12 π
(4)
where vdk is the amplitude of kth MMF space harmonic.
From (4), the amplitude of each MMF space harmonic
including an item of sin(((k− 1)/12)π) is different from that of the
one 3-phase winding set. When k = 1, namely the 1st sub-harmonic,
the amplitude of the 1st MMF space harmonic vd1 is equal to 0,
which means the 1st 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. 3b. As can be seen, with
dual three-phase configuration, the 1st sub-harmonic is completely
cancelled while the working harmonics (either 5th or 7th) are
improved by 3.6% at the same time compared to the one 3-phase
winding configuration. On the other hand, the 11th, 13th, 23rd,
25th, 35th, 37th are cancelled as well. These are in accordance with
the above theoretical analysis from the Fourier series. Thus, the
dual three-phase winding set configuration is a good method to
cancel the 1st 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.
3.2 Reduction of parasitic harmonics
There are parasitic harmonics in the machines with FSCW like 5th
and 7th for 12-slots 10-/14-poles machine. They usually occur in
pairs, e.g. 5th and 7th, which result in difficulty to reduce only one
of them. For example, for the 24-slot 14-pole machine, the working
harmonic is 7th, but the parasitic 5th harmonic exists as well, its
amplitude is quite similar to that of 7th working harmonic, and
their corresponding winding factors are exactly the same.
A method of utilising 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 utilising 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 realising the
stator shifting based on a 24-slot 14-pole machine with SL winding
is as follows:
(a) Using the 24-slot 14-pole machine with a dual three-phase SL
winding proposed in section 2 as a base.
(b) Another dual three-phase winding is added, whose coil
distribution is the same as the first dual three-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.
From (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
vαdk =vαdkcos kα
2
(5)
It can be observed that an additional factor of cos kα /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°/z, where j is a
non-negative integer and z is the stator slot numbers. In this case,
each slot corresponds to an angle 15° (360°/24), so the mechanical
angle of α can only be j × 15°. 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 (6) and summarised 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 14-pole machine with dual three-phase
windings, the working harmonic is chosen as the 7th harmonic and
the main parasitic harmonic is the 5th harmonic. Therefore, it is
necessary to find out an appropriate angle to reduce or cancel the
5th harmonic while having no or not much negative influence on
the 7th 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 7th harmonic is almost equal to 1. Within
these areas, the angle of 105° is a good candidate, at which the
attenuation factor of 7th is 0.9914 while the attenuation factor for
1st and 5th is 0.6087 and −0.1305, respectively. This means the 5th
harmonic has been effectively reduced and there are no
considerably negative influences to the working harmonic (7th).
The 1st harmonic does not need to be considered as it has been
cancelled by using the dual three-phase winding configuration.
In fact, there is another angle of 108°, better than the 105° in
terms of reducing 5th harmonic, because the fifth-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 × 15°. Therefore, the best candidate of
shifting angle is 105°, 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 three-phase winding
sets. Since the DL winding and SL winding can be recognised as
all teeth wound and alternate teeth wound windings, the
concentrated windings can be expressed by the corresponding
teeth, namely, each tooth represents a corresponding wound
concentrated winding coil. Two identical dual three-phase winding
sets are adopted with the second three-phase winding set shifting
Fig. 4 Attenuation factor for different order MMF harmonics
3786 J. Eng., 2019, Vol. 2019 Iss. 17, pp. 3784-3788
This is an open access article published by the IET under the Creative Commons Attribution License
(http://creativecommons.org/licenses/by/3.0/)
105° (7slots) over the first winding set. This winding layout is
using the concept of stator shifting but without adopting
overlapping winding (coil pitch of two 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 fault-tolerant drive applications.
It is clearly from Fig. 6 that the 1st sub-harmonic is completely
cancelled and the 5th 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 three-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.
4Design 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, namely, 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 EV (HEV) or
pure EV. The insert-pm (IPM) configuration is adopted as the rotor
structure. The drive requirement used here is summarised in
Table 1.
For both machines, the outer dimension limitation is the same,
with an outer diameter of 285 mm and an axial length of 90 mm. 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 three-phase winding layout, which can be regarded as a
combination of two 24S-14P machines with a SL winding, with the
winding set of the second 24S-14P SL machine shifting seven slots
(105°) 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 three-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 summarises 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 three-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
demagnetisation 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
Fig. 5 Concept of ‘stator shifting’ based on a 24 slot 14 pole machine
Fig. 6 MMF distribution of two winding layout
Table 1 Design specification of electric drive system
Design specification Data
peak power 45 kW
rated power 22 kW
peak torque 170 Nm
maximum torque ripple ≤5%
based speed 2500 rpm
maximum speed 12,000 rpm
DC link voltage 600 V
Fig. 7 New configuration of 24S-14P with double layer winding
Fig. 8 Comparison of torque performances between two machines
J. Eng., 2019, Vol. 2019 Iss. 17, pp. 3784-3788
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(http://creativecommons.org/licenses/by/3.0/)
3787
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 45° 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 5°, 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 three-
phase winding system is a promising solution to the challenges of
high space harmonics for FSCW motors.
5Conclusions
A novel 24 Slot 14 Pole DL winding layout using stator shifting
method for FSCW permanent magnet motors was proposed, which
gives complete cancellation of the 1st sub-harmonic, and
significant reduction of the 5th sub-harmonic. 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 three-
phase motor and conventional 12S-14P motor have been designed
for a traction application. The comparative study shows that the
proposed 24S-14P dual three-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 three-phase system is a
promising solution to the challenges of significant space harmonics
for FSCW motor.
6Acknowledgments
This work is funded by the INNOVATIVE doctoral programme.
The INNOVATIVE programme is partially funded by the Marie
Curie Initial Training Networks (ITN) action (project number
665468) and partially by the Institute for Aerospace Technology
(IAT) at the University of Nottingham.
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Fig. 9 Comparison of output performances between two machines
Fig. 10 Average torque versus current angle
3788 J. Eng., 2019, Vol. 2019 Iss. 17, pp. 3784-3788
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