Comparative Study of Permanent-Magnet Synchronous Machines with Concentrated Windings for Railway Application A. Soualmi 1, 2, F. Dubas2, A. Randria1, C. Espanet2 1
Alstom transport Ornans, France University of Franche-Comte, FEMTO-ST Institute, ENISYS Department, Belfort, France E-mail:
[email protected]
2
Abstract—The paper presents a comparative study of 3-phase permanent-magnet (PM) synchronous machines (PMSM) with concentrated windings. The purpose of this study is to find a machine giving the better electromagnetic performance (torque, losses, back electromotive force…) for railway traction. Three PMSM with concentrated windings having identical output power, stator and rotor outer diameter, air-gap, axial length,…, are designed. Two machines have equal tooth widths, with one have a coil wound on every tooth and the other have a coil wound on alternate teeth, while the third machine has also coils wound on alternate teeth but these are wider than the unwound teeth. A
comparison of the performance for single layer and double layer concentrated windings is made using finite element analysis. Index terms—permanent magnet, single layer, double layer, concentrated winding, back EMF, cogging torque. I.
INTRODUCTION
The PMSM become attractive because of great improvement of PMs, electronics devices and exhibit a high torque density. Recently, they have found many applications, such as domestic appliances, automotive, aerospace and wind power generation, etc [1]. Recent attention has been given in the literature to the use of concentrated windings in permanent magnet (PM) machines due to their advantages. The PMSM with concentrated windings become increasingly competitive regarding to those with distributed windings. The interest of this kind of machines is growing due to their simple winding structure, which enable cost effective automation methods in the manufacturing process. Concentrated windings became more attractive for several reasons [1]-[7]: the windings length is reduced, this means that the quantity of copper used is reduced and the copper losses (i.e., the efficiency is improved), a high flux weakening range is possible due to high inductances, the implementation is simplified, high efficiency, low torque ripple and good fault tolerance performance. The major drawback of this type of windings compared with distributed windings is that it has a large harmonic content; it results in the creation of eddy-current losses in the PMs and of magnetic forces (i.e., vibration and noise). In the winding, if there are two coil inside each slot the winding can be categorized as double layer, if there is only one coil inside slot, the winding will be categorized as single layer [see Tab. 1]. The choice of the number of layers depends mostly on the application. One of the aims of this paper is to define the most appropriate structure for railway application. The result should be meeting in railway application the following characteristics: • Lightweight machines. • High efficiency.
• Low radial force, vibration and noise. • Reduced maintenance. • Increased reliability. Traction motors for railway vehicles must be durable and sturdy [8]. Single-layer Fundamental winding factor End windings Slot fill factor Self inductances Mutual-inductance EMF Harmonic content of MMF Eddy current of MMF Overload torque capability
Double-layer
Higher
Lower
Longer Higher Higher Lower More trapezoidal
Shorter Lower Lower Higher More sinusoidal
Higher
Lower
Higher Higher
Lower Lower
Table I Comparison between single and double layer concentrated windings [4]. Table I compares some characteristics of single layer and double layer concentrated windings. II.
COMPARATIVE STUDY
The PMSM used in this study is 12 slots/10 poles [see Fig. 1]. The winding factor for these machines is 0.933 (double layer) and 0.966 (single layer). A comparison of the performance for single-layer (alternate teeth wound and alternate teeth wound on wider teeth) and double layer concentrated windings is achieved using two-dimensional (2D) finite-element method (FEM). This study consists in the comparison of electromagnetic performance of three machines [see Fig. 1]: back electromotive force (back EMF), the short circuit current, the 2-D PM eddy-current losses at no-load and at load, the cogging and electromagnetic torque.
a) machine A
b) machine B
c) machine C
Fig.1. Winding layouts for 12 slots/10 poles PMSM with: a) alternate teeth wound, b) all teeth wound and c) alternate teeth wound on wider teeth.
Fig.1 show prototype 10-pole/12-slot motors having single layer concentrated winding (machine A), double layer concentrated winding (machine B) and single layer winding with tooth widths. It is seen that machines A and B have equal tooth widths, with one having a coil wound on every tooth and the other only having a coil wound on alternate teeth, while the third one also has coil wound on alternate teeth (the wound teeth are wider than the unwound teeth). A. Windings layout and winding factor The most interesting winding layout is the one that gives the highest fundamental winding factor. There are different methods to find the winding layout [5]. The winding layout has a significant influence on the self and mutual inductances [3]. In our case the distribution of coils is as follows [4]:AA’A’AB’BBB’CC’C’C for double layer windings and AA’B’BCC’ for single layer windings. The winding factor is [9]: All teeth are wound:
K f = sin ( n ⋅ p ⋅ π / N s ) . 2
(1)
Alternate teeth are wound:
K f = sin(n ⋅ p ⋅ π / N s ) .
(2)
Fig. 3. Predicted cogging torque for the three machines
It can be seen that the machine C exhibit higher cogging torque compared with machines A and B. B. Back EMF and open circuit magnetic field The three phases back EMF and its harmonic content for the machine in Fig. 1a, 1b and 1c are shown in Fig. 4. The value of the no-load voltage E0 depends on the flux produced by the magnet in the air gap and the speed of the rotor.
A. Cogging torque Cogging torque results from the interaction of the rotor permanent magnets with the stator teeth [see Fig. 2]. This torque produces vibration and noise which is considered undesirable in most permanent magnets machines. The period of cogging torque cans be calculated by equation 3. Tcogging =
360 . LCM ( N s , N p )
(3)
Where LCM is the least common multiplier, N s the number of slot and N p the number of pole.
a) Machine A
b) Machine B
c) Machine C
Fig. 4. Open circuit field distribution for the three machines: a) alternate teeth wound, b) all teeth wound and c) alternate teeth wound on wider teeth.
As can be seen the machines with single layer exhibits the maximum flux linkage compared with double layer (flux linkage is lower).
Fig.2. Cogging torque [10]
The cogging torque for the three machines is shown in Fig. 3. Machines for which 2 p = N s ± 2 generally exhibit a very low cogging torque since the ration of the slot number to pole number is fractional and the smallest common multiple between the slot number and pole number is high [3]. Fig. 5. EMF waveforms for the three machines
It can be observed that the back EMF of three machines is purely sinusoidal and have nearly the same amplitude. The FEM harmonics content of the three machines is shown in Fig. 6.
The magnetic induction produced by magnets is given by the following expression [11]:
(
)
B θ s ,θ r , rg =
∞
∑
n =1,3,5,....
( )
Bn rg ⋅ cos ( n ⋅ p ⋅ (θ s − θ r ) )
(4)
Where Bn is the n th spatial harmonic component of the flux density (T), rg is the air gap radius (m), θ s is the angle along the stator periphery, θ r is the rotation angle of the rotor and p is the number of pole pairs. The permeance function can be represented as Fourier series [11]:
(
)
∞
( )
P θ s , rg = ∑ Pm rg ⋅ cos ( m ⋅ N d ⋅ θ )
The peak-peak value of the machine C is the reference and equal to one per unit. Table II show the amplitude of harmonics of the various machines (A, B and C).
Machine A Machine B Machine C
1 167,38 160,33 168,46
2 5,31 5,16 5,36
Harmonic order 3 4 5 4,73 2,46 1,34 3,37 2,18 1,48 4,73 2,50 1,51
6 1,33 1,31 1,29
(5)
Where Pm is the n th spatial harmonic component of the relative permeance function and N d is the number of teeth. The magnetic flux density in the air gap with the stator windings open circuit is expressed as:
Fig. 6. FEM harmonics content of the three machines
machines
m =0
7 1,22 1,23 1,35
(
)
(
) (
Bopen _ circuit θ , rg = P θ s , rg ⋅ B θ s , θ r , rg
)
(6)
The flux harmonic content for the machines is given by interaction between the harmonics of the magnet induction produced by magnets and harmonics of permeance function, i.e:
h = n ⋅ p ± m ⋅ Nd
(7)
Table II Amplitude of harmonics of the three machines (A, B and C). m and n 0 1 2 …..
1 5 17 and 7 29 and 19 ……
3 15 3 and 27 39 and 9 ……
5 25 37 and 13 49 and 1 ……
7 35 23 and 47 59 and 11 ……
… … … … …
Table III Interpretation of the open circuit harmonics flux density.
C. The inductance The phase self inductance can be calculated as follow: E Ls = 2 ⋅ π ⋅ f ⋅ I cc
(8)
Where E is the back EMF and f the frequency.
Fig. 7. Open circuit harmonics flux density for the three machines
The Fig.7 compares the flux density harmonic content for the three machines. It can be observed that the 5 th harmonic (synchronous harmonic) is very significant compared to anther harmonics.
Short circuit current (A) Back EMF (V) Frequency (Hz) Inductance (mH)
Machine A 158 113 83.33 1.36
Machine B 251 113 83.33 0.86
Machine C 170 113 83.33 1.28
Table IV Calculation of the inductance
The table II compares the inductance values of the three machines. It is seen that machines A and C have the highest value of the inductance. This means that the coil of machines A and C obtain more flux linkage than machine B and obtain a
higher degree of fault tolerance (the self inductance is high which limits the short circuit currents). D. Back MMF Once the winding layout is defined, it is possible to calculate the magneto-motive force (MMF) create by the stator currents. The magneto-motive force (MMF) is given by Ampere circulation law:
MMF = ∫ H ⋅ dl = N s ⋅ I
(9)
When: N s is the number of turns. The MMF harmonic content for the three machines is shown in Fig. 8.
Fig. 9. Eddy current losses in the magnet for the three machines
It can be seen that the eddy current losses in the magnet increase with increasing of the speed. The losses in the machine A are the highest compared to the machines B and C, because the machine A is richer in harmonics. F. Torque ripple The torque ripples in the electrical machines are due to several factors: Space harmonics. Time harmonics. Cogging torque: it is generated by the variation of the magnetic permeance seen by the permanent magnet due to the slotting of the stator when there is no stator excitation.
Fig. 8. Total and fundamental three phase MMF harmonics content for the three machines
We can see that the three machines are very rich in harmonics particularly the machines A and C. The FMM harmonics spectrum shows for the machines A and C that the fundamental harmonic is very significant compared to synchronous harmonic (5 th), other significant harmonics are: 7 th and 11th. In the case of the machine B, we found the same significant harmonics in the other machines but with lower amplitude. E. Eddy current losses in the permanent magnet The permanent magnet iron losses are calculated by finiteelement analysis. The induced losses in the magnets provoke temperature arising that must be limited to avoid the risk of demagnetization. Loses in the permanent magnet due to: At no-load: eddy current losses are due to slot effect. At load: eddy current losses are due to slot effect, the space harmonics effect and the time harmonics effect. The losses for the three machines are shown in Fig. 9.
Fig. 10. Torque output with sinusoidal current excitations for the three machines
Fig.10 shows the torque for each machine configuration. It can be noted that the three machines have the same average torque but in torque ripple, the machine B has the lowest torque ripple because its cogging torque is the lower and it’s not rich in harmonics like the machines A and C. III.
CONCLUSION
This study is part of a project whose aim is to develop of new PMSM for railway transportation. It has been show that machines which have single layer windings (with equal or
unequal width of teeth) are preferred when a high fault tolerance is required (the phase of the windings are thermally isolated) and in application requiring a wide speed range of constant power operation (hither inductance). Otherwise, double-layer windings are preferable to limit the losses. As a perspective is to make a comparative study with an interior permanent-magnet synchronous machines (IPMSM) that are better adapted to the railway application (IPMSM has a lot of advantages compared to SPMSM). IV. REFERENCES [1]
Z. Q. Zhu, Z.P. Xia, L. J. Wu et G.W. Jewell, "Influence of Slot and Pole Number Combination on Radial Force and Vibration Modes in Fractional Slot PM Brushless Machines Having Single- and Double layer Windings", Energy Conversion Congress and Exposition, ECCE 2009. [2] J .Cros et P. Viarouge, “Synthesis of High Performance PM Motors With Concentrated Windings”, IEEE Transactions on Energy Conversion, vol. 17, NO. 2, JUNE 2002. [3] D. Ishak, Z. Q. Zhu, and D. Howe, “Permanent Magnet Brushless Machines with Unequal Tooth Widths and Similar Slot and pole Numbers,” IEEE Transactions on Industry Application, Vol. 41, N0.2, pp.584-590, April 2005. [4] F. Meier, “Permanent-Magnet Synchronous Machines with NonOverlapping Concentrated Windings for Low-Speed Direct-Drive Applications” Master thesis, Royal Institute of Technology. School of Electrical Engineering, Electrical Machines and Power Electronics. Stockholm 2008. [5] F. Meier et J. Soulard, “PMSMs with non overlapping concentrated windings: design guidelines and model references”, Ecologic Vehicles Renewable energy (EVER), Monaco, March 26-29 2009. [6] A.M. EL-Refaie, “Fractional-slot concentrated Windings Synchronous permanent Magnet Machines: Opportunities and Challenges”, IEEE Transactions on industrial Electronics, vol. 57, NO. 1, January 2010. [7] Z. Q. Zhu, “Fractional Slot Permanent Magnet Brushless Machines and Drives for Electric and Hybrid Propulsion Systems”, ”, Ecologic Vehicles Renewable energy (EVER), Monaco, March 26-29 2009. [8] K. Minoru, “Application of permanent magnet synchronous motor to driving railway vehicles”, Railway technology avalanche, No 1, January 1, 2003. [9] D. Ishak, Z. Q. Zhu, and D. Howe, “Comparative study of permanent magnet brushless motors with all teeth and alternative teeth windings”, ”, Printed and published by the IEE, Michael Faraday House, 2004. [10] A. Jassal, H. Polinder, G. Shrestha, C. Versteegh, “Closed Slot Topology for Reduction of Cogging and Noise in Permanent Magnet Direct Drive Generator for Wind Turbines”. [11] A. Jassal, H. Polinder, G. Shrestha, C. Versteegh, “Analysis of Surface Permanent Magnet Machines With Fractional-Slot Concentrated Windings” , IEEE Transaction On Energy Conversion, Vol. 21, NO.1, March 2006.
