FEAAM GmbH
D-85577 Neubiberg, Germany
E-mail: Sachar.Spas@unibw.de
Institute of Electrical Drives
Universitaet der Bundeswehr Muenchen
D-85577 Neubiberg, Germany
E-mail: Dieter.Gerling@unibw.de
Abstract —Permanent magnet synchronous machines with tooth concentrated windings are widely used in today´s hybrid electric vehicles (HEV). This is due to several well-known advantages provided by concentrated windings. Nevertheless, excessive heat generation in the rotor, caused by magnet losses, continues to be a major challenge for vehicle manufacturers.
Usually magnet segmentation is proposed to meet the overheating challenge.
This paper presents a PMSM that hardly generates any magnet losses over the whole operating speed range. In contrast to conventional approaches, the reduction of eddy current losses is achieved using a simple two-tooth winding with reduced harmonic content. 3D-FEM analysis of magnet losses shows that the magnet segmentation is no longer required for this winding topology. To demonstrate the great potential of this alternative, the winding is used for a 60-teeth/20-poles PMSM and is compared to a commonly used 30-teeth/20-poles PMSM with concentrated windings.
Keywords—concetrated windings; eddy current losses; field weakening capability; magnet loss reduction; two-tooth windings segment them. This reduces magnet losses, but decreases generated torque [11] and is cost intensive at the same time.
This paper presents an alternative 6-teeth/2-poles winding topology, which is used for a 60-teeth/20-poles PMSM, Fig. 1.
A comparison with widely used 30-teeth/20-poles machine (3teeth/2-poles winding topology) shows that the proposed alternative hardly generates any magnet losses over the whole operating speed range, which makes magnet segmentation unnecessary. For a fair comparison both machines were analyzed under the same geometrical and electrical boundary conditions. Both, analytical estimations and 3D finite element calculations of magnet losses show that the 6-teeth/2-poles winding produces almost no magnet losses.
II.
6-T EETH /2-P OLES W INDING T OPOLOGY
The alternative winding consists of two 3-teeth/2-poles windings. Combining a 3-teeth/2-poles winding [A+, B+, C+] and a 1.5 slots space shifted, vice versa supplied [A-, B-, C-] winding, within the same geometry, leads to researched 6teeth/2-poles winding topology. Figure 1 illustrates the mentioned winding formation. As can be seen from Figure 1 the resulting winding is a two-tooth winding with q = 1 (q is the number of slots per pole per phase).
I.
I
NTRODUCTION
Requirements for better performance, more safety, higher reliability and lower costs drive the development of electrical machines forward. For automotive applications in particular, features such as high efficiency, high torque density, short axial length and wide operating speed range are on demand.
Concerning these demands permanent magnet synchronous machines (PMSM) with concentrated windings turned out to be a good solution. Concentrated windings offer advantages over conventional distributed windings, such as short and less complex end-winding, high filling factor, low cogging torque, greater fault tolerance and low manufacturing costs [1].
However, the magnetic field produced by concentrated windings has higher harmonic content compared to the magnetic field caused by distributed windings. These undesired field components are responsible for eddy current losses in magnets, noises, vibrations and torque ripples [2]-[6]. A lot of work has been recently done to decrease the harmonic content of concentrated windings [7]-[10]. Nevertheless, high eddy current losses produced by concentrated windings still lead to unacceptably high heat generation in the rotor. To prevent overheating of rotor magnets, it is a common practice to
It is worth mentioning that two-tooth windings are the
“shortest” distributed windings, since they have the shortest possible winding pitch of y = 2 slots, otherwise you get a concentrated winding. This offers a possibility to combine the advantages of both, concentrated and distributed windings.
Fig. 1.
Formation of 6-teeth/2-poles winding
978-1-4673-7637-2/15/$31.00 ©2015 IEEE

It is a good practice to analyze the magneto motive force
(MMF) of the stator winding, since main machine characteristics, such as air-gap flux density, electromagnetic torque, torque ripple and magnetic radial forces depend on the
MMF distribution function. Using superposition principal the
MMF distribution function of the 6-teeth/2-poles winding
Θ can be deduced from the MMF distribution of the 3teeth/2-poles winding Θ as follows:
According to [13], where x, t
Θ x, t x, t Θ m 2 w ξ
2 π ν
/
I cos ωt ν
τ
π x δ 2
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4
3/2-topology
6/2- topology
5 6 7 8 9 10 11 12 13 14 15 16 17 18
Harmonic order
Fig. 2.
Comparison of MMF spectrum with
ξ
⁄ sin ν
π
3
, 3 where m is the number of phases, ξ
⁄
is the winding factor of the ν -th harmonic, I is the phase current amplitude, δ is the load angle, ω is the angular frequency, τ is the pole pitch and w is the number of turns per phase.
Considering a shift angle of α π and using the addition theorem for trigonometric functions (1) becomes
Θ
Θ
Θ m 2 w ξ
2 π ν
⁄
ξ
is given by (2)
⁄ x, t
2I sin ωt
ξ
⁄
Θ sin ν
2 x
ν
τ
π
α, t 1 x
π
2
δ ,
4 are winding factors of the 6-teeth/2-poles winding.
Fig. 2 compares the MMF spectra of both windings. It can be clearly seen, that the harmonic content of the 6-teeth/2-poles topology is reduced by far, namely every even harmonic is eliminated.
As only the fundamental (1st harmonic) wave of the stator field interacts with the rotor field to generate useful torque, waves with higher harmonic order (2nd, 4th, 5th, 7th, etc.) affect the machine negatively. Consequently, a reduction of harmonic content in MMF distribution improves machine’s performance. From MMF spectrum of the 6-theeth/2-poles winding (Fig. 2), one can expect this topology to produce far less magnet losses than the conventional one. This is mainly due to the fact that the first harmonic wave, that has an inducing effect on the rotor magnets, is the 5th harmonic. In case of 3-teeth/2-poles winding already the 2nd harmonic induces eddy currents in the magnets. An analytical estimation of eddy current losses confirms this statement, please refer to chapter III.
In addition, even if the alternative winding is a distributed two-tooth winding, the end windings of both topologies have almost the same length. This is due to the fact that the tooth width of the 3-theeth/2-poles winding corresponds to the tooth width of two teeth of the alternative winding. However, the end windings of the 6-teeth/2-poles topology will be a bit longer due to their diagonal arrangement (Fig. 1). Since the winding factors of both windings are equal, please refer to (3) and (4), this leads to slightly higher copper losses but the same torque production, by a given power supply.
Two further points should be mentioned here. Firstly, as each harmonic represents an inductance, they contribute to the back
EMF induced in the phase windings. So a reduction of harmonics results in a decreased phase inductance and therefore in a decreased back EMF for a given rotational speed. But at the same time a decreased phase inductance leads to a worse field weakening capability, due to higher currents needed to produce the opposite field. Therefore, using the 6-teeth/2-poles winding, one can assume that the nominal speed of the machine will be higher but the field weakening capability will be worse. Nevertheless, a comparison of the torque-speed characteristics of both machine topologies (Fig.
7) shows that the first effect predominates in total.
Secondly, since the directly adjacent harmonics are most harmful from the perspective of noise excitation, because they lead to radial forces (modes) of low order, the alternative winding topology will be advantageous also from this point of view.
III.
A
NALYTICAL
E
STIMATION OF
E
DDY
C
URRENT
L
OSSES
In order to predict the impact of a stator winding on eddy current losses in rotor magnets an analytical method has been derived in [13]. Assuming eddy current losses to be proportional to squared product of frequency and flux density
~ . 5 then, taking into account, that only asynchronous frequencies
~ | 1| induce eddy current losses in the magnets and considering the dependency of the flux density on winding factors and harmonic order (normalized to the winding factor of the working wave )

~
1 proportionality (5) becomes:
,
~ | 1|
1
. 6
Using (6) it is possible to calculate the impact on magnet losses for each harmonic and this permits an analytical comparison of winding topologies concerning magnet losses.
Fig. 3 shows the result of such a comparison for the analyzed windings. winding. The rms value of the sinusoidal supply current was fixed to Imax = 300A.
Fig. 4a. 30-teeth/20-poles machine Fig. 4b. 60-teeth/20-poles machine
T ABLE I: G EOMETRICAL B OUNDARY C ONDITIONS
Inner rotor diameter
Outer rotor diameter
Outer stator diameter
Gap length
Maximum active length
200 mm
240 mm
300 mm
1 mm
63 mm
Fig. 3.
Impact on eddy current losses over harmonic order
It can be clearly seen, that the proposed 6-teeth/2-poles winding will generate only a small fraction of magnet losses generated by the 3-teeth/2-poles topology, mainly due to the absence of the most harmful 2 nd harmonic.
Expression (6) allows a comparison of windings that use fundamental wave as the working wave. In general, one could be interested in comparison of windings characterized by
5 or higher working harmonics, i.e. 7 .
This mostly occurs when using a concentrated winding. Based on above mentioned idea a generalized expression is given by
(7).
,
~ | |
1
. 7
IV.
C
OMPARISON OF
S
IMULATION
R
ESULTS
For a comparative study both winding topologies were applied to 20-poles PMSMs, resulting in a 30-teeth/20-poles and a 60-teeth/20-poles machine, respectively. Fig. 4 shows one-tenth part of each topology. Both machines have been designed and analyzed using FEM. For a fair comparison the machines were designed under the same geometrical and electrical boundary conditions, refer to Table I and Table II.
Copper losses were calculated considering different end windings and different filling factors, teeth/2-poles winding and k k 0.45
for the 6-
0.55
for the 3-teeth/2-poles
T ABLE II: E LECTROMECHANICAL B OUNDARY C ONDITIONS
Supply voltage
Supply current
Nominal rotational speed
Nominal torque
Nominal Power
Maximum rotational speed
Urms = 92 V
I rms
= 300 A n n
= 2500 rpm
M n
= 270 Nm
P n
≈ 71 kW n max
= 6000 rpm
A.
Simulation results for nominal operating speed
Table III compares the simulation results of both machines at nominal operating point. First of all, both topologies fulfill the torque requirement. However, the induced voltage and the torque ripple are reduced using the 60-teeth/20-poles machine.
As noted before, reduction of the induced voltage results in higher rated speed and thus leads to an extended constant torque region of this topology. On the other hand, the conventional machine has to be skewed due to the high torque ripple of 13.6 %, which causes considerable torque reduction.
Contrary to this, torque produced by the alternative design is far smoother and the torque ripple is 6.3%. Optimizing the rotor geometry the common torque ripple requirement of less than 5% can easily be achieved without skewing.
Regarding the magnet losses, it is important to underline that the magnets in both machines are assumed to be solid. As shown in Table III, the alternative topology generates far less magnet losses, which is in good agreement with analytical estimation. As already indicated above, copper losses of the alternative topology increase due to lower filling factor and longer end windings of the two-tooth winding.

T ABLE III C.
Torque-Speed Characteristics
B.
@2500 rpm
I rms
U i
M
P cu
P fe
P mag
30/20-topology 60/20-topology Finally, a comparison of torque-speed curves for Imax = 300A
300 A 300 A is given in Fig. 7. As expected, 60-teeth/20-poles machine
92 V 88 V
270 Nm / 13.6 %
1.6 kW
0.35 kW
1.3 kW
270 Nm / 6.3 %
1.67 kW
0.33 kW
0.048 kW provides an extended constant torque region. The torque of this topology remains constant until 3000 rpm, while the 30teeth/20-poles machine provides constant torque only until
2500 rpm. Therefore, the maximum output power is increased from about 71 kW (30-teeth/20-poles) to about 85 kW (60-
Magnet losses assuming unsegmented magnets
In order to show the difference of generated magnet losses, no method to reduce them is applied. In particular, rotor magnets are not segmented in any direction. Fig. 5 shows a comparison of magnet losses over the whole operating speed range, assuming unsegmented magnets. It can be clearly seen, that the 60-teeth/20-poles machine hardly generates any magnet losses. Even at maximum speed magnet losses remain below 100W, refer to Fig. 6. teeth/20-poles). At first sight it may seem surprising, that both machines have nearly the same torque-speed characteristic at speeds above 5000 rpm, resulting in the same operating speed range. But this is exactly the effect of the worse fieldweakening capability of the two-tooth winding due to its decreased phase inductance. However, in total the proposed topology shows better performance than the conventional one.
Fig. 5. Comparison of magnet losses without segmentation
Fig. 6. Magnet Losses of 60/20-topology
In practical application it will be necessary to segment the magnets of the 30-teeth/20-poles machine, in order to suppress the eddy currents within the magnets. It is shown in [12] that at nominal speed of 2500rpm eight segments would be needed to obtain magnet losses comparable to magnet losses of the
60-teeth/20-poles machine. At maximum speed even more
(over 10) segments would be needed. This would undoubtedly lead to a noticeable decrease in torque output.
Fig. 7. Torque-Speed Curves
V.
C
ONCLUSIONS
Presented study compares two interior permanent magnet synchronous machines for hybrid electric vehicle or battery electric vehicle application. Under same geometrical and electrical boundary conditions the conventional design and the alternative design, using 6-teeth/2-poles winding, are considered and obtained results are compared. All in all, the proposed machine design generates very low magnet losses, provides smoother torque and better torque-speed performance. Furthermore, it is shown that using the proposed winding makes skewing for torque ripple reduction and magnet segmentation for magnet loss reduction unnecessary.
The mentioned advantages are countered by following disadvantages. Due to the two-tooth winding the end windings will be bigger, resulting in greater axial length and slightly higher copper losses. In addition to that, one should consider that the manufacturing costs of a stator with two-tooth windings will be higher, compared to a stator with concentrated windings.
Nevertheless, in particular for full electric vehicle applications, where the space requirement is less critical because the internal combustion engine is absent, the 6-teeth/2poles winding will be an advantageous alternative.

VI.
R EFERENCES
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Electric Machines and Drives Conference, IEMDC 2009, May 3–
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[2] M. Nakano, H.Kometani, "A study on eddy-current losses in rotors of surface permanent magnet synchronous machines", IEEE
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VII.
B IOGRAPHIES
Sachar Spas ; M.Sc. Sachar Spas is with FEAAM GmbH, Werner-
Heisenberg-Weg 39, D-85579 Neubiberg, Germany (e-mail:
Sachar.Spas@feaam.de
)
Sachar Spas was born in Lviv, Ukraine, in 1988. He got his M.Sc. degree in
Mathematical Engineering from the University of Federal Defense Munich,
Germany in 2012. Since 2012 he is a Research Scientist with FEAAM GmbH, an engineering company in the field of electric drives.
Gurakuq Dajaku ; Dr.-Ing. Gurakuq Dajaku is with FEAAM GmbH, Werner-
Heisenberg-Weg 39, D-85579 Neubiberg, Germany (e-mail:
Gurakuq.Dajaku@feaam.de
)
Born in 1974, Dr. Dajaku got his diploma degree in Electrical Engineering from the University of Pristima, Kosova, in 1997 and his Ph.D. degree from the University of Federal Defense Munich, Germany, in 2006. Since 2007 he is Senior Scientist with FEAAM GmbH, an engineering company in the field of electric drives. His research interest is in the field of electrical machines and drives.
Dr. Dajaku received the Rheinmetall Foundation Award 2006 and the ITIS
(Institute for Technical Intelligent Systems) Research Award 2006.
Dieter Gerling ; Prof. Dr.-Ing. Dieter Gerling is Head of the Institute of
Electrical Drives at the University of Federal Defense Munich, Werner-
Heisenberg-Weg 39, D-85579 Neubiberg, Germany (e-mail:
Dieter.Gerling@unibw.de).
Born in 1961, Prof. Gerling got his diploma and Ph.D. degrees in Electrical
Engineering from the Technical University of Aachen, Germany in 1986 and
1992, respectively. From 1986 to 1999 he was with Philips Research
Laboratories in Aachen, Germany as Research Scientist and later as Senior
Scientist. In 1999 Dr. Gerling joined Robert Bosch GmbH in Bühl, Germany as Director, being responsible for New Electrical Drives and New Systems.
Since 2001 he is Full Professor and Head of the Institute of Electrical Drives at the University of Federal Defense Munich, Germany.