I. INTRODUCTION. Electric machines used in embedded applications such as electric or hybrid vehicles traction should have, in addition to high efficiency, very ...
Permanent Magnet Synchronous Machine Design for Hybrid Traction Applications: Impact of Magnetic Laminations Materials B. NEDJAR1, Student Member, IEEE, S. HLIOUI1, Student Member, IEEE, L. VIDO1, M. GABSI1, Member, IEEE, Y. AMARA2, Member, IEEE, E. HOANG1. A. MIRAOUI3, Member, IEEE. 1 SATIE, ENS Cachan, CNRS, UniverSud, 61, av President Wilson, F-94230 Cachan, France 2 GREAH, 25,Philippe Lebon,76063, Le Havre Cedex. 3 L2ES, UTBM, FCLab Belfort, 90010, Belfort, France Abstract— This paper examines the influence of lamination material on the performance of a flux focusing permanent magnet machine. This machine is designed for the traction of hybrid vehicles. The design optimization is performed by coupling a multi-objective particle swarm optimization algorithm with the finite element method. The optimization procedure is performed for three different lamination materials. Solutions from optimization procedure are then compared.
I.
INTRODUCTION
Electric machines used in embedded applications such as electric or hybrid vehicles traction should have, in addition to high efficiency, very high power and torque densities to meet volume constraints. Due to their performances permanent magnet (PM) machines are considerate as good candidates to meet constraints of such applications [1] [2]. This paper examines the influence of lamination material on the performance of a flux focusing PM machine. This machine is designed for the traction of hybrid vehicles. Fig. 1 shows desired torque/speed characteristics for the traction machine. The machine according to specifications should operate 10 % of operating time (r1s = 10 %) at a low speed/high torque point (maximum torque region) and the rest of time (r2s = 90 %) at a high speed/low torque point (flux weakening region). Table I gives the values of some geometric, electromagnetic and mechanical parameters of specifications data. The design optimization is performed by coupling a multiobjective particle swarm optimization (MOPSO) algorithm with the finite element method. The output of the MOPSO algorithm is the set of non-dominated (pareto-optimal) solutions. The objectives of optimization algorithm are the inverter size and the electric machine power loss (inverter loss are not considered). Kennedy and Eberhart [3] introduced the Particle Swarm Optimization (PSO) method as an evolutionary computation technique. The optimization procedure is performed for three different lamination materials. Solutions from optimization procedure are then compared.
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Fig. 1. Torque- speed characteristics.
TABLE I SPECIFICATION DATA Dc voltage (v) UDC 300
Geometric parameters (mm) Lext Rext 150 100
II.
Torque (Nm) & speed (rpm) T1s 250
Ω1s 2000
r1s 10%
T2s 40
Ω2s 9600
r2s 90%
MACHINE DESIGN
Fig. 2 shows the chosen structure of the PM machine. In order to have relatively strong air gar flux density values the flux focusing principle was used. The stator is constituted of concentrated non overlapping windings. This kind of winding configuration have a shorter end-windings (lower copper loss) and greater winding coefficient than classical distributed windings. Authors in [5] studied advantages of this winding configuration for hybrid vehicle application. The size of stator back iron is reduced by choosing a high number of poles. However, the number of poles was limited by the maximum operating frequency of the inverter (this parameter is fixed p = 6). The air gap thickness is fixed to 0.5 mm. The number of teeth per poles pairs was fixed to 3. Used permanent magnets are the Neodymium-Iron-Boron (NdFeB).
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2.5
flux density B(T)
2
FeSi 300-35 FeSi 330p35 FeCo17
1.5 1 0.5 0 1 10
This machine has been modelised using finite element (FE) method. The estimation of iron losses (only stator iron losses are considered) is done by dividing the stator into 36 blocks (Fig. 3). The number of blocks is chosen in such a way that the flux density in each block can be considered as homogenous over an electric period. SPECIFICATIONS DATA AND LAMINATION MATERIALS The external volume is constrained (exterior length Lext = 150 mm, Rext = 100 mm outer radius) and the maximum voltage is limited (DC bus voltage UDC=300 V). As indicated before, the operating cycle of the hybrid vehicle is featured by two points in the torque/speed plane (Fig. 1). Three different lamination materials were used (FeSi30035, FeSi330p35 and FeCo17 from Usinor). Fig. 4 shows B(H) characteristics of these materials. Table II gives iron loss for a sinusoidal flux density of 1 T of amplitude at a frequency of 1 kHz.
IV.
5
10
DESIGN STRATEGY
For each lamination material, the optimization algorithm helps calculate optimal values of geometric and control parameters. Geometric variables are: the air gap radius Rair (which is equal to A per cent of external radius) (1), the rotor radius Rrot, the stator yoke (back iron) height Hc, shaft radius Rarb, the difference of rotor radius and shaft radius X, the tooth width Ld, the permanent magnet thickness Ep, the permanent magnet height Hp and He (see Fig. 2). Table III gives intervals of variation for per unit values A, B, C, D, E and F. Control variables are the armature current and current to EMF phase shifting. The machines are water cooled, so the maximum current density is fixed to 30 A/mm2. Table III gives intervals of variation for control parameters.
(1)
TABLE II IRON LOSS OF THE THREE MATERIALS
FeSi 300-35 FeCo 17 FeSi 330p35
4
The FeCo17 has the highest saturation induction (Bs) but also the lowest relative permeability. Iron Silicon high permeability (330p35) has the highest relative permeability. Finally, the Iron Silicon 300-35 has the worst saturation induction, but his iron losses are the lower.
Fig. 3. Stator blocks used to estimate iron losses.
materials
3
10 10 field intensity H (A/m)
Fig. 4. Materials B(H) characteristics.
Fig. 2. Flux focusing PM machine.
III.
2
10
Loss @ (1 kHz, 1T) (W/kg) 100 118 120
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TABLE III PARAMETERS INTERVAL OF VARIATION.
components in x and y directions are calculated separately and added to estimate iron loss (2) [6].
Minimal
Maximal
60% 30% 40% 25% 9% 50% 20% 0 0
80% 70% 80% 40% 15% 95% 80% 30 90
A B C D E F G J(A/mm2) Ψ
TABLE IV IRON LOSSES COEFFICIENTS
FeSi 300-35 FeCo 17 FeSi 330p35
Kh1 [W/kg/Hz/T]
Kh1 [W/kg/Hz/T2]
αP [W/kg/Hz2/T2]
0 0 4 10-4
7.2 10-3 10.2 10-3 6.41 10-3
3.67 10-6 3.9 10-6 4.8 10-6
In order to achieve high efficiency losses must be minimized; therefore the first optimization objective is the minimization of the totals power losses. The second optimization objective is the minimization of the inverter size, which is proportional to the maximum inverter current and the maximum inverter voltage. Since the maximum inverter voltage is limited by the DC bus voltage thus the second objective is presented as a minimization of the inverter current. These two objectives may not appear contradictory at a first glance. However, since the machine should operate 90 % of the time in the high speed region (flux weakening region), iron loss should be greater than copper losses. To reduce machine iron losses the size of the permanent magnet must be reduced. For fixed external machines dimensions and maximum torque, the reducing of magnetic size involve an increasing the amplitude of armature current. The two objectives are then contradictory in this application, where the specification is separate in two points, first one with high torque and second one, must use, with high speed. 1.
Machine losses
The power losses are divided in to iron losses and copper losses. The calculation of iron losses requires induction in all machine regions, the machine inductions are depending on rotor position. To reduce the computing time, the induction symmetry in three tooth of stator is used, thus, only one third of electrical period are need to determinate the stator iron loses. The rotor inductions do not have this symmetry, therefore the computation time for estimate rotor iron losses are three times more. In next paragraph the rotor iron losses are neglected. The stator is split into 108 parts (36 blocks by tooth). Iron loss is calculated in each block. The losses due to flux density
(2)
Where kh1, kh2: coefficient of hysteresis losses. αp: coefficient of eddy current losses. T: electrical period (s). Bx and By: induction in x, y axes respectively (T). The stator losses are determined by calculating the sum of losses in each region: (3) Where Vi the volume of block “i”. p: pole numbers. The key physical, magnetic and electrical properties of the three lamination materials, which were derived from manufacturer’s data, are given in Table IV. Combining optimization algorithm with FE method is time consuming process. To reduce computation time geometric and electromagnetic symmetries are exploited. Reconstitution of flux density components waveforms over an electric period (60 mechanical degrees) (Fig. 5), in a given location of the machine, can be achieved by calculating flux density waveform only over 10 mechanical degrees. Thus, for two specification points, the time process of one tentative machine is 70s (One FE estimation is 3,5s in Intel Pentium Dual Core 3GHz). The copper loss is calculated by the classical formula: (4) Where rc: copper resistivity. Js: current density. Sc: copper conductor section. lc: copper total length.( Including end windings length). 2.
Number of turns and maximal inverter current
The maximum voltage in the machine is limited by the batteries voltage and control strategy. The voltage phase of the machine is written: (5) Where n: number of turns. Ф: flux per pole and per coil. θ: mechanical angle. Ω: mechanical speed For a space vector modulation, the maximum voltage Vmax is given by: (6) The number of turns can then be estimated using following equation: (7)
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Fig. 5 Bx flux density component waveforms.
For a given geometry, the number of turns is the minimum of the number of turns calculated for two operating points. The inverter current is calculated from the maximum current density of the two operating points, copper conductor section, the slot fill factor (Kb = 0.65) and the number of turns. 3.
Fig. 6 flowchart of optimization.
Optimization approach
Optimization is performed under constraints of torque and maximum voltage for the two operating points. The optimization algorithms choose the geometric and control parameters. The instantaneous torque and flux density waveforms of the machines are calculated by FE method for the two points. For each set of parameters previous equations (2) to (7) are used to estimate the performances: the number of turns, the maximum current and the two points power losses. Average power loss is then calculated using:
V.
RESULTS AND DISCUSSION
First we discuss optimize of machines for two points of specification separately, the FeSi 300-35 material is used to this optimization Fig. 7. We note that the machine of the first point (height torque 250Nm) present a large magnet size and a smaller isthmus which assures the torque with low current density. The machine optimized for the second point presents a small magnet, it due to low torque value and height speed specification (40 Nm and 9600 rpm).
(8) In the multi-objectives optimization the two objectives must be contradictory. The two objectives of this optimization are the armature current and the power losses. The machine losses are divided on copper and iron losses, the first one are decreased by the minimization of the current but the second one are increased in particular for high speeds operations. The second point of specification is characterized by a lower torque (40 Nm) and higher rotational speed (9600 rpm), therefore the iron losses are dominant for this point. All machines have one and/ or two best objectives are presented in the Pareto- solution. Fig. 6 lists the different parts of the optimization procedure. The number of particles is fixed to 20 and the number of generations to 150. The determination of performance of each particle need calculate for two specification points and for each point induction is recuperate over ten rotor positions.
a) Point 1 (250Nm/2000rpm) Fig. 7 Separate specification points.
b) Point 2 (40Nm/9600rpm)
Secondly the optimization combined the two points of specification by introducing operating rate. The optimization results for the three materials are presented in Fig. 8. We note that neither material is dominating the two others, each material has an interest in a parts of the plan current - losses.
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TABLE V COMPARISONS MACHINES FESI.
900 FeSi 300-35
Armature current (A-rms)
800
FeCo 17
700
500 400 300 2000
2500 3000 3500 Total pow er losses (W) Fig. 8 Pareto- solution machines.
4000
4500
In first the FeSi 330p35 Pareto- solution is discussed. The Fig. 8 shows a jump of the rms current in the Pareto-solution between 600 A and 350 A, this discontinuity is due to the passage of number of turn of 2 to 4. The comparison of FeSi 300-35 and FeSi 330p35, shows that in one hand the first material dominate in the lower power losses [1500- 1700] (W), however the rms current is important [700 - 740] (A). In the other hand the second material dominates the rest of the plan, his rms current is lower but the power losses are greater. Comparisons machines of the two materials are shown in Table V the corresponding machines are presented in Fig. 9. For machines with 1600 W power losses, they have the same number of turns, but the FeSi 300-35 machine have less notch surface (24%) thus the inverter current is less than FeSi 330p35 (720 A for FeSi 300-35 compared to 860 A for FeSi 330p35). For the two machines with 3500 W, we see that the number of turns are different (2 and 5 for the first and second respectively) in this case the FeSi 330p35 present lower inverter current (250 A compared to 570 A for the FeSi 30035). We can see the iron power losses are greater than the copper losses for the second point of specification, since this point present the most used points (in this case 90%) thus the iron power losses is most important than the copper losses. Although the FeCo 17 material does not dominate the two others materials in all plan rms current- power losses, it is better than the other in the largest part of the plan. This is because, in one side, has better saturation induction and in the other side an intermediate values iron losses. Table VI shows two machines at 1750 W the first is FeSi 330p35 materials and the second is FeCo 17, the second one present a higher notch surface and lower thickness yoke Fig.10 this is due to it higher saturation induction. The large notch surface of FeCo 17 machines allow use lower current density to create torque or/and deflexed machines for height speed, thus the number of turns can be greater and rms current in the inverter is lower.
3500
FeSi
FeSi
FeSi
FeSi
300-35
330p35
300-35
330p35
78.2 10 16.6 39 17.1 19 30 28.3 7.6 47.7 2.4 73.5 2 4500 375.58 292.36 924.59
73.6 10.0 16.6 36.7 15.6 18.6 27 27.1 5 45.3 2.7 96.3 2 4900 464.65 167.2 1100
70.4 9.8 14.7 17.8 24.6 13.6 13.5 1.57 11 68.08 2.8 130.2 2 1600 333.74 1000 2700
64.7 8.6 14.4 25.8 16.7 18.2 11.4 8.3 11.2 80.6 2.6 169.7 5 1500 437.17 1460 2200
Materials
600
200 1500
1600
Losses (W)
FeSi 330p35
Rair(mm) Hc(mm) Ld(mm) Rarb(mm) Hp(mm) Ep(mm) J1(A/mm2) ψ1 J2(A/mm2) ψ2 He(mm) Sn(mm2) N losses Copper S1(W) Iron losses Copper S2(W) Iron
a) FeSi 300-35
c) FeSi 300-35
1600 (W)
b) FeSi 330p35
d) FeSi 330p35 3500 (W) Fig. 9 Comparisons machines FeSi 35-300-35 and FeSi 330p35.
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TABLE VI COMPARISONS MACHINES FESI 330P35 AND FECO17. 1750
Losses (W) FeSi
materials
330p35 Rair(mm) Hc(mm) Ld(mm) Rarb(mm) Hp(mm) Ep(mm) J1(A/mm2) ψ1 J2(A/mm2) ψ2 He(mm) Sn(mm2) n losses Copper S1(W) Iron losses Copper S2(W) Iron
76.7 10.2 17 38.2 16.4 20.3 28 24.3 6.7 50.2 2.8 77 2 4200 422.83 234.85 1100
FeCo 17 60 5.1 8.5 23.8 20.2 13.4 8.4 32.16 6.9 80.53 2.9 321.2 6 1500 383.65 1030 674.36
REFERENCES [1] Z. Q. Zhu, David Howe, ‘‘Electrical Machines and Drives for Electric, Hybrid, and Fuel Cell Vehicles,’’ Proceedings of the IEEE, Vol. 95, No. 4, April 2007. [2] A. M. EL-Refaie and T. M. Jahns “Comparison of Synchronous PM Machine Types for Wide Constant-Power Speed Range Operation” , IAS, 2005. [3] J. Kennedy and R. Eberhart, “Particle swarm optimization,” Proc. IEEE Int. Conf. Neural Networks, 1995, Vol. IV, pp. 1942-1948. [4] G. T. Pulido and C.A. Coello Coello, “Using clustering techniques to improve the performance of a multi-objective particle swarm optimizer,” Proc. of the Genetic and Evolutionary Computation Conference, Seattle, Washington, USA 2004, In Springer-Verlag, Lecture Notes in Computer Science, June 2004, 3102, pp. 225-237.. [5] L. Vido, Y. Amara, E. Hoang, M. Gabsi, F. Chabot, M. Lecrivain, “Design and Comparison of Concentrate Winding and Distributed Winding Interior PM Machines for a Hybrid Vehicle Application”, ICEM, Poland, September, 2004. [6] E. Hoang, B. Multon, M. Gabsi ”Enhanced accuracy method for magnetic loss measurement in switched reluctance motor” ICEM, December, 1994.
a) FeCo17 b) FeSi 330p35 Fig. 10 Comparisons machines FeSi 330P35 and FeCo17.
VI.
CONCLUSION
The optimization of the machine for a hybrid vehicle application was developed; this optimization takes into account the effect of materials on the machine performances. The two optimizations objectives are power losses in the machines and the maximum inverter current. The Pareto- solutions shows that no material is completely dominated by the two others. Therefore according to the choice of the maximum inverter current the choice of material, geometry and control change. For the most important part of the current- losses the FeCo 17 machines have the best performance, however for lower power losses machines (approximately 1500 W) the FeSi 300-35 is better due to it lower iron losses compared to the two other materials. But because of its low saturation induction, the current in the inverter is high (> 700 A). The FeSi 330p35 will limit the current values (about 250 A) but at the cost of higher losses.
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