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0

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1

Space Harmonics

MM

F [

p.u

. ]

a) b)

Fig. 1: a). PM machine with the conventional 12-teeth /10-poles double-layer winding, b). Corresponding MMF winding harmonics.

Abstract — Two different costs effective and high efficiency methods for improving the main performances of tooth concentrated windings are presented. Using these simple techniques it is possible to reduce or even to cancel some space harmonics of low order resulting in lower magnet and iron losses induced by the armature reaction field. The presented techniques are applied for different 12-teeth/10-poles PM machines and the obtained results show enormous improvements on the machine performances.

I. INTRODUCTION

Permanent magnet (PM) machines with fractional slot concentrated winding (FSCW) are increasingly used in various industry applications, owing to their high power density, short and less complex end-winding, high filling factor (low copper losses), fault tolerance, and low manufacturing costs. However, they are characterized by high content of space harmonics in the air-gap magneto motive force (MMF) distribution which generate undesirable effects, such as localized core saturation, eddy current loss in the magnets [1 to 3], additional core losses in rotor and stator, and noise and vibration [4 to 6], which are the main disadvantages of these winding types. A PM machine with 12-teeth and 10-poles and tooth concentrated winding is illustrated in the figure 1-a, however, the space MMF winding harmonics are presented in figure 1-b. As well shown, the 1st, 5th, 7th, 17th and 19th are the

dominant space harmonics for this winding type. For the 10-pole machine, however, only the 5th stator space harmonic interacts with the field of the permanent magnets to produce continuous torque. The other MMF space harmonics, in particular the 1st, 7th, 17th, etc., which have relatively large magnitudes, are undesirable and in some cases they limits the usefulness of this winding type in different specific applications. To improve the MMF winding performances of the FSCW regarding to power losses and noise problems different methods and techniques are developed and investigated in the past [7 to 16]. References [7 to 14] show different methods for the reduction of winding sub-harmonics, however, in [15, 16] two another new methods for reduction simultaneously the sub- and high MMF harmonics are presented.

In this paper two novel methods for reduction of the MMF winding sub-harmonics developed in [9, 10] are considered and their effect on the machine performances are investigated. According to the first technique, the sub-harmonics of the FSCW are reduced or completely canceled by using winding coils with different number of turns per coil side [9], however, another new technique proposed in [10] solves the same problem by modifying the stator yoke in specific locations by using magnetic flux-barriers in stator yoke. The presented techniques are applied to improve the performances of

Different Novel Methods for Reduction of Low Space Harmonics for the Fractional Slot

Concentrated Windings Gurakuq Dajaku* and Dieter Gerling**

* FEAAM GmbH, D-85577 Neubiberg, Germany ** Universiteat der Bundeswehr Muenchen, D-85577 Neubiberg ,Germany

E-mail: gurakuq.dajaku@unibw.de, dieter.gerling@unibw.de

different 12-teeth/10-poles PM machines with single-layer and double-layer tooth concentrated windings. Of course, these methods are also useful also for any type of concentrated windings. Finite element methods (FEM) are used to determine the performances of the investigated machines.

II. CONCENTRATED WINDING WITH DIFFERENT TURNS PER COIL-SIDE

A novel solution for reduction of sub-harmonics for the FSCW by using winding coils with different number of turns per coil side is presented in [9]. Using the proposed technique the specific sub-harmonics can be reduced without influencing the working harmonic. The realization of the new 12-teeth/10-poles winding according to this technique is illustrated in the following figure 2, however, the comparison of the MMF harmonics for the conventional and the new 12-teeth/10-poles winding is presented in figure 3. With 1n is denoted the number of turns of coil sides in the slots which contain the coils of the same phase, however with 2n is denoted the number of turns of coil sides in the slots which contain the coils of different phases. For n1/n2=7/8, the 1st sub-harmonic of the considered winding type is reduced down to zero.

Fig. 2: New 12-teeth /10-poles winding topology with different turn per coil

side [9].

From [11], the analytical function for the MMF of the 12-teeth/10-poles new winding can be described using the following equ. (1).

w,new

p

2 wm ˆ(x, t) i cos t x2

ν

ν

⎛ ⎞⋅ ⋅ ξ πΘ = ⋅ ⋅ ⋅ ω − ν + δ⎜ ⎟⎜ ⎟πν τ⎝ ⎠∑ (1)

where, m is number of phases (m=3), w,newν ξ is the winding

factor, i is the phase current amplitude, δ is the load angle, ω is the angular frequency, w is the number of turns per phase, and ν is the space (MMF winding) harmonic.

The winding factor for the new concentrated winding with different turns per coil side is

2 2 1,

2 1 2 1

sin sin sin2 3 3w new

n n nn n n n

ν −⎡ π π ⎤ π⎛ ⎞ ⎛ ⎞ ⎛ ⎞ξ = ν − ν + ν⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎢ ⎥+ +⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎣ ⎦

(2)

And the relation between n1 and n2 of the coil windings with different go-in and go-out turns is,

1 2 1 21, and 50% / 100%n n n n= − ≤ < (3)

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0.2

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0.6

0.8

1

Conv. Winding

New Winding

Fig. 3: Comparison of MMF winding harmonics.

The following figure 4 compares the eddy current losses in rotor magnets for a PM machine with the conventional and the new 12-teeth/10-poles winding and also for two different rotor types (surface magnet rotor – SPM, and inset magnet rotor – IPM). The investigated machine is designed for automotive application and is characterized with an outer diameter of 76 mm, axial length of 25 mm and maximal power of 600 W. Further, finite element methods (FEM) are used to derive the magnet losses, and for all considered machine cases the simulations are performed under the same load conditions (torque and speed).

Fig. 4: Comparison of rotor magnet losses.

MM

F (p

.u.)

harmonic order

Fig. 5. PM eddy current distribution: a). Conventional winding, b). New

winding.

As well shown from figure 4, depending on the rotor type the rotor magnet losses are different, however, using the new winding topology the magnet losses can be reduced more than 50%. Further, the magnet losses distributions for the SPM machine type are presented in figure 5. From the obtained results it can be concluded that for the conventional winding type as results of the first winding sub-harmonic the magnet losses are induced over the complete magnet region, however, using the new winding the magnet losses are distributed only on the magnet surface. These losses are induced mostly from the air-gap flux density high harmonics.

III. FLUX BARRIERS IN STATOR YOKE Different from the previous solution where the reduction of

winding sub-harmonics is performed by modification of the coil construction, another new technique proposed in [10] solves the same problem by modifying the stator yoke in specific locations. Of course, it is true that for influencing the winding harmonics it is required to modify something in the winding layout or construction, however, the method presented in [10] reduces the effect of winding sub-harmonics indirectly by using flux-barriers in stator yoke as follows.

Analogous to the above solution, the new method reduce the effect of winding sub-harmonics indirectly be increasing the magnetic resistance in specific machine location according to the well-known relation between flux density B, magnetic resistance mR and winding MMF SΘ ,

/S mB R= Θ (4)

Therefore, according to (4) the effect of winding sub-harmonics can be reduced by reducing the stator MMF in specific slots [9] or by increasing the magnetic resistances in specific stator core location. Figure 6 shows a simple magnetic equivalent circuit (MEC) for an electric machine with smooth rotor and the new 12-teeth/10-poles winding shown in figure 2. For simplicity only one part of phase-A is presented. With R0 to R3 are denoted the magnetic resistances of corresponding flux paths.

Fig. 6: Magnetic equivalent circuit for the new stator structure.

Applying the Ampers law around the stator slot-1,

Hdl I=∑∫ (5)

and for the case 1 2 1n n= − we have

( )1 0 1 2 3 12 2 2R R R R n Iφ + + + = (6)

The resulting magnetic flux for this condition is

1

10 1 2 3

22 2

n IR R R R

φ =+ + + (7)

In other side, from (4) the same condition as under (7) can be realized also using the convectional winding ( 1 2n n= ) however by modifying (increasing) the magnetic resistance

*2R 1) in stator yoke. Thus, for the new stator yoke structure we

have

2

1 *0 1 2 3

22 2

n IR R R R

φ =+ + + (8)

1) Of course each magnetic resistance can be modified to fulfill the required conditions, however the magnetic resistance of the stator yoke is the single resistance which fulfill the above requirements without influencing the flux density of neighbours slots.

a) b)

Flux barriers

From the above relations (7) and (8) the stator yoke resistance for the new stator structure should be

( )* 22 2

2 1e enR R R R

n′ ′= + −

− (9)

With,

0 1 32 2eR R R R′ = + +

III.1 PM MACHINE WITH 12-TEETH/10-POLES DOUBLE

LAYER WINDING The following figure 7 shows a PM machine with inset

magnets in rotor and with the 12-teeth/10-poles double layer concentrated winding. In the presented example six additional stator yoke components of non-magnetic material are used as flux-barriers and also for fixing (mounting) the complete stator structure. The main geometrical and electrical constrains are the same with PM machine investigated in the second section.

Fig. 7: Geometry of the 12-teeth/10-poles PM machine with the new stator

structure.

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Space Harmonics

B [

T ]

Conv. Stator

New Stator

Fig. 8: Comparison of air-gap flux density harmonics due to stator currents.

Figure 8 compares the air-gap flux density harmonics due to stator field, however, under a given load operation point the machine losses are presented and compared in figure 9. As well is shown, regarding to the air-gap flux-density harmonics and losses the machine performances clearly can be improved using the new technique with flux-barriers in the stator yoke. Furthermore, this technique is related also with additional advantages for the electric machine such as it enables a high efficiency cooling, solves the noise problems etc. [10, 13].

Fig. 9: Comparison of machine losses.

III.2 PM MACHINE WITH 12-TEETH/10-POLES SINGLE

LAYER WINDING

In some machines, e.g. 2 2Sp N= ± , either all the teeth (double-layer winding) or only alternate teeth (single-layer winding) can carry a coil. Figure 10 shows a PM machine with the 12-teeth/10-poles single layer winding and the corresponding MMF winding harmonics. The main advantages for this winding type are the high winding factor for the 5th and the 7th harmonics (about 0.966), high slot filling factor and simple realization (manufacturing). However, figure 10-b shows that the 1st sub-harmonic is relative too high which deteriorate the performances of the machine. Therefore, the new technique with flux-barriers can be used also for this winding type for reducing of the sub-harmonics as illustrated in figure 11-a. Comparison of the air-gap flux density harmonics due to stator reaction field presented in figure 11-b shows that the proposed technique is very efficiency also for the single-layer tooth concentrated windings. The air-gap flux-density sub-harmonics are reduced more than 70%. Furthermore, for a given operation point, the power losses for the convectional and the new stator structure are presented in the figure 12. Also here, using of the magnetic flux barriers in the stator yoke leads to enormous improvements on the machine characteristics. Power loss reduction for about 40% in stator core, 66% in the rotor core, and 75% in the rotor magnets are achieved. The magnet loss distribution for the conventional and the new stator structure are shown in the figure 13.

Flux-barriers

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0

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1

1.2

1.4

Space Harmonics

MM

F [

p.u

. ]

a) b)

Fig. 10: a). PM machine with the conventional 12-teeth /10-poles single-layer winding, b). Corresponding MMF winding harmonics.

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Space Harmonics

B [

T ]

Conv. Stator

New Stator

a) b)

Fig. 11: a). New stator core with flux barriers, b). Comparison of air-gap flux density harmonics due to currents.

IV. CONCLUSIONS Two simple and high efficiency techniques for reduction of

the sub-harmonics for the FSCW are presented and analyzed. According to the first method, the sub-harmonics of the FSCW are reduced or completely canceled by using winding coils with different number of turns per coil side, however, the second method solves the same problem by modifying the stator yoke in specific locations by using magnetic flux barriers. Furthermore, the second method is related also with additional advantages for the electric machines such as enables a high efficiency cooling, solves indirectly the noise problems and so on.

The presented techniques are applied to improve the

performances of different 12-teeth/10-poles PM machines with single-layer and double-layer tooth concentrated windings. Enormous improvements on the machine performances are achieved:

Sub-harmonic reduction more than 60%, Power loss reduction up to 40.6% for the stator iron

losses, 66.2% for the rotor iron losses, and 75.6% for the magnet losses.

It is important to point out that the presented techniques are used for improving the performances of a 12-teeth/10-poles concentrated winding, however, they are applicable to any tooth concentrated winding.

Fig. 12: Comparison of machine losses.

Fig. 13. PM eddy current distribution for: a). Conventional stator core, b).

New stator core.

V. REFERENCES [1] H. Polinder , M. J. Hoeijmakers, M. Scuotto : “Eddy-Current

Losses in the Solid Back-Iron of PM Machines for different Concentrated Fractional Pitch Windings”. 2007 IEEE International Electric Machines & Drives Conference (IEMDC 2007), 3-5 May Antalya, Turkey.

[2] M. Nakano, H. Kometani: “A study on eddy-current losses in rotors of surface permanent magnet synchronous machines”. IEEETransactions on Industry Application, vol. 42, No. 2, March/April 2006.

[3] N. Bianchi, E. Fornasiero: “Index of rotor losses in three-phase fractional slot permanent magnet machines”. Electric Power Applications, IET, vol. 3, No. 5, September 2009.

[4] G. Dajaku, D. Gerling: “Magnetic Radial Force Density of the PM Machine with 12-teeth/10-poles Winding Topology”. IEEE International Electric Machines and Drives Conference, IEMDC2009, Florida USA, May 3-6, 2009, pp.157-164.

[5] J. Wang, Zh. P. Xia, D. Howe, S. A. Long : “Vibration Characteristics of Modular Permanent Magnet Brushless AC Machines”. IEEE IAS Annual Meeting, 2006, Tampa, Florida, USA.

[6] Z. Q. Zhu, Z.P. Xia, L. J. Wu, and G.W. Jewell: “Analytical modelling and finite element computation of radial vibration force in fractional slot permanent magnet brushless machines”, IEEE International Electric Machines and Drives Conference, IEMDC2009, Florida USA, May 3-6, 2009, pp.157-164.

[7] H. Kometani, Y. Asao, K. Adachi: “Dynamo-electric Machine”, US Patent 6,166,471, Dec. 26, 2000.

[8] K. Ito, K. Naka, M. Nakano, M. Kobayashi: “Electric machine”, US Patent 7,605,514, Oct. 20, 2009.

[9] G. Dajaku: “Elektrische Maschine”, German patent, DE 102008 057 349 B3, July 15, 2010.

[10] G. Dajaku: “Elektrische Maschine”, German patent application No. 102008 054 284 A1.

[11] G. Dajaku, D. Gerling: “Eddy Current Loss Minimization in Rotor Magnets of PM Machines using High-Efficiency 12-teeth/10-poles Winding Topology”, International Conference on Electrical Machines and Systems (ICEMS-2011), Beijing, China ,August 20-23, 2011.

[12] G. Dajaku, D. Gerling: “Low Costs and High-Efficiency Electric Machines”, 2nd International Electric Drives Production Conference 2012 (EDPC-2012), 16.-17. October 2012, Erlangen-Nürnberg, Germany, (paper accepted).

[13] G. Dajaku, D. Gerling: “A Novel 12-Teeth/10-Poles PM Machine with Flux Barriers in Stator Yoke”, 20-th International Conference on Electrical Machines (ICEM’2012), 02.-05. September 2012, Marseille, France, (paper accepted).

[14] M. V. Cistelecan, F. J. T. E. Ferreira: “Three phase tooth-concentrated multiple-layer fractional windings with low space harmonic content”, IEEE on Energy Conversion Congress and Exposition (ECCE) 2010.

[15] G. Dajaku, D. Gerling: “A Novel 24-Slots/10-Poles Winding Topology for Electric Machines”, International Electric Machines and Drives Conference (IEMDC-2011), Niagara Falls (Ontario), Kanada, May 15-18, 2011, pp. 65-70.

[16] G. Dajaku, D. Gerling: “Efficiency Improvements of Electric Machines for Automotive Application”, 26th International Electric Vehicle Symposium (EVS26-2012), Mai 06-09, 2012, Los Angeles (CA), USA.

P [ W/m³ ]

P [ W/m³ ]

a) b)