[doi 10.1109_icelmach.2012.6349866] Prieto, D.; Daguse, B.; Dessante, P.; Vidal, P.; Vannier, J.-C. -- [IEEE 2012 XXth International Conference on Electrical Machines (ICEM) - Marseille,

8/10/2019 [doi 10.1109_icelmach.2012.6349866] Prieto, D.; Daguse, B.; Dessante, P.; Vidal, P.; Vannier, J.-C. -- [IEEE 2012 X

1/7

Abstract -- This paper presents the design of Synchronous

Reluctance Motors (SynRM) with four flux-barriers. Thestudy is focused on the use of ferrite magnets into flux-barriers and its impact on average torque, torque ripple and

power factor. The analysis uses Finite Element Method (FEM)for different pole pair numbers in order to choose an efficientstructure.

Index TermsElectric motors, Permanent magnet motors,Power factor, Torque ripple, Synchronous reluctancemachines.

I. NOMENCLATURE

dq ii , : stator electromagnetic current magnitudes

dq VV , : stator electromagnetic voltage magnitudes

dq , : stator flux linkage

dq LL , : quadrature and direct axis inductances

p : pole pair number

: current angle

II. INTRODUCTION

ermanent magnet synchronous motors are known for

their electromagnetic performances and their compactsize. Rare earths like NdFeB are the kind of material

usually used for permanent magnets, but now their cost is

incremented and therefore the machine becomes more

expensive. A usual solution is the replacement of the motor

by a synchronous reluctance motor which is used in

industrial applications and has a good torque-density [1].

The torque is produced by the saliency of rotor. Several

investigators have compared performances of synchronous

reluctance motors and induction motors [1]-[4]. Common

drawbacks of such motors are the low power factor and the

high torque ripple [5]. In [6] a formula is deduced for

calculating the power factor and its behavior versus the

saliency ratio (Lq/Ld). To improve performances of

synchronous reluctance motor, we must design a rotor with

a large inductance difference (Lq-Ld) and a large saliency

ratio (Lq/Ld) [7].

Fig. 1(a) shows a transversally laminated rotor, it is also

called multiple-flux barrier rotor. The interest of that rotor

Dany Prieto is with the Ecole Suprieure dElectricit, F-91192 Gif sur

Yvette CEDEX, France (e-mail: [email protected]).

Benjamin Dagus is with the Ecole Suprieure dElectricit, F-91192

Gif sur Yvette CEDEX, France (e-mail: [email protected]).

Philippe Dessante is with the Ecole Suprieure dElectricit, F-91192

Gif sur Yvette CEDEX, France (e-mail: [email protected]).Pierre Vidal is with the Ecole Suprieure dElectricit, F-91192 Gif sur

Yvette CEDEX, France (e-mail: [email protected]).

Jean-Claude Vannier is with the Ecole Suprieure dElectricit, F-

91192 Gif sur Yvette CEDEX, France (e-mail: jean-

[email protected]).

is its high saliency ratio. The barriers limit the d-axis flux

without obstructing the q-axis flux. We will call this motor

SynRM.

If permanent magnets are inserted into the flux-barriers

of SynRM rotor, Fig. 1(b), the torque-density and power

factor of SynRM can be increased [8]. The magnet flux is

lower than that produced by stator excitation. This structure

is called Permanent Magnet Assisted Synchronous

Reluctance Motor (PMA-SynRM).

(a) SynRM (b) PMA-SynRM

Fig. 1. Sketch of (a) a synchronous reluctance motor and (b) permanent

magnet assisted synchronous reluctance motor

This paper proposes the use of ferrite permanentmagnets. This material is another alternative and the paper

aims to assess the impact of these magnets on the

synchronous reluctance motors. It studies a methodology to

compare the performances (average torque, torque ripple

and power factor) of the SynRM and the PMA-SynRM for

different pole pair number with a same stator imposed for

all structures.

The assumption adopted here, is to use the same

geometry (flux-barriers thickness and opening angles of

flux-barriers) and same volume of magnets for all PMA-

SynRM structures treated in order to keep same price at therotor.

III. MATHEMATICAL MODEL

The compared structures are a Synchronous Reluctance

Motor (SynRM) and a Permanent Magnet Assisted

Synchronous Reluctance Motor (PMA-SynRM), both with

the same number of flux-barriers per pole, the pole pair

number being a parameter.

A. Axis d-q

The d-q reference frame is shown in Fig. 2. The d-axis is

aligned with the permanent magnet flux of the PMA-SynRM, and the same convention is used for the SRM.

Effect of Magnets on Average Torque and

PowerFactorofSynchronousReluctanceMotorsD. Prieto, B. Dagus, P. Dessante, P. Vidal, J.-C. Vannier

P

978-1-4673-0142-8/12/$26.00 2012 IEEE 213


2/7

Fig. 2. Sketch of d-q reference frame

B. Mathematical model of SynRM

The Parks equations for a synchronous reluctance

machine are expressed by [6]:

qsdtdd

disrdv

+= (1)

dsdt

qdqisrqv +

+= (2)

In steady-state the currents, idand iq, are constant, so the

derivative of flux, dand q, is zero. The equations (1) and

(2) lead to equation (3).

qIqjXdIdjXIsRV ++= (3)

The equivalent electrical phasor diagram is depicted in

Fig. 3. This diagram shows the low power factor of

synchronous reluctance motors.

Fig. 3. Electrical phasor diagram of SynRM. is the current angle, is the

torque angle, is the phase angle

Equations (4) and (5) give the SynRM torque. It dependson the large difference between Ldand Lq.

)(2

3diqqidpT = (4)

( ) ( )

= diqiqLqididLpT 2

3 (5)

C. Mathematical model of PMA-SynRM

By inserting permanent magnets into the flux-barriers of

SynRM rotor, the magnet flux linkage is in the d-axis flux

path. So the flux linkage expressions become:

adidLd += (6)

qiqLq= (7)

Equation (8) gives the torque of a PMA-SynRM. It

increases with the magnet flux linkage.

( ) ( ){ }diqiqLqiadidLpT += 23

(8)

The equivalent electrical phasor diagram is represented

on Fig. 4, where E is the electromotive force produced by

the permanent magnets. It shows the improvement of powerfactor with the insertion of permanent magnets.

Fig. 4. Electrical phasor diagram of PMA-SynRM, is the current angle,

is the torque angle, is the phase angle

IV. REQUIREMENTS

Motors characteristics are reported in Table I. The

stator is the same as that of an industrial motor. The

magnets are ferrite type and the amount of magnets is the

same for all designed motors. The pole pair number is the

parameter to be defined in order to have an efficient

structure.

TABLEI

REQUIREMENTS OF SYNCHRONOUS RELUCTANCE MOTOR

Quantity Value

Power [kW] 630

Speed [rpm] 1 500

External diameter [mm] 600

Inner stator diameter [mm] 425

Shaft diameter [mm] 180

Air gap [mm] 1.5

Number of slots 72

V. ANALYSIS

The analysis uses Finite Element Method (FEM).

A. PMA-SynRM Structures

In a first approach, if we increase the number of flux-

barriers, the flux in the d-axis decreases, consequently it is

possible to get a higher value for the reluctance torque. But

if we think of increasing the pole pair number, the size of a

pole becomes smaller, so it generates a geometric

constraint. Fig. 5 shows PMA-SynRM structures. The study

compares four structures with: 2, 3, 4 and 6 pole pair

numbers. For this paper we choose four flux-barriers per

pole for all motors, the structure with p=6 is almostgeometric limit. All motor structures have the same stator

because it is imposed. All flux-barriers have the same

thickness. The opening angles of flux-barriers are uniform

d-axis

q-axis

I

Iq

Id

jXdId

jXqIq

RsI

V

d-axis

q-axis

I

Iq

Id

jXdId

jXqIq

RsIV

E

214


3/7

and the magnets have the same thickness as the barriers,

Fig. 6.

(a) (b)

(c) (d)

Fig. 5. Structure motor (a) 2 pole pairs (b) 3 pole pairs (c) 4 pole pairs (d)

6 pole pairs

Fig. 6. Flux-barriers Geometry

B. Calculation Method

For each structure we set a current angle for the

calculation of average torque, torque ripple and power

factor. Fig. 7 shows the torque behaviors versus rotor

position for an electrical period for a PMA-SynRM four

pole pairs and a current angle =50. The periodicity for the

torque calculation is equal to the sixth part of the electrical

period, so the average torque and torque ripple will be

calculated on Te/6. It is shown in Fig. 8 and in the equations

(9) and (10).

Fig. 7. Torque versus rotor position PMA-SynRM, p=4 and =50

Fig. 8. Torque versus rotor position on Te/6 PMA-SynRM, p=4 and

=50

Average torque: )(TmeanaveT = (9)

Torque ripple:

aveT

TTrippleT

)min()max( = (10)

Fig. 9 shows the flowchart on the power factor

computation process. First we compute the flux vector abc

for each phase, then dq is obtained with Parks

transformation. The voltage vector and the torque angle

are computed from dq.

Fig. 9. Power factor computation flowchart

VI. RESULTS

All simulations are carried out with the same current

equivalent to maximal thermal current in one slot. For each

current angle, the average torque, the torque ripple and the

power factor are computed. The gap between SynRM andPMA-SynRM is expressed with the expression (11).

%100

)(

)()()(

=

SynRMX

SynRMXSynRMPMAXXGap (11)

A. Average torque comparison

Fig. 10 and Fig. 11 show respectively the SynRM and

the PMA-SynRM average torque (Tave) versus current angle

() for each value of pole pairs. Table II gives the values of

maximum average torque and their optimal current angle

for each pole pair number. It also shows the impact of

magnets on average torque. The increase percentage isbetween 34 and 45%. The best results are for the PMA-

SynRM with 3 and 4 pole pair number. For the PMA-

SynRM withp=4, the maximum average torque is 4257N.m

215


4/7


5/7

factor is increased around 0.72 and their optimal current

angles are high, above 60.

Fig. 14. Power factor versus current angle, SynRM.

Fig. 15. Power factor versus current angle, PMA-SynRM.

TABLEIV

IMPACT OF THE NUMBER OF POLE PAIRS

Structure Quantity 2 3 4 6

SynRMcos 0.476 0.549 0.514 0.398

() 74 68 62 58

PMA-SynRMcos 0.715 0.766 0.727 0.621

() 76 70 66 60

Gap (%) 50 40 41 56

D. Demagnetization of magnets

Permanent magnets keep their performance when the

magnetic field does not exceed their intrinsic coercivity

field. For the magnet ferrite, the intrinsic coercivity field

increases when the temperature decreases, to -20C its

value is 375 kA/m. The magnetic field in all magnets wasmeasured for each PMA-SynRM structure. Fig. 16 shows

the evolution of the field in the permanent magnets for each

value of pole pairs.

Fig. 16. Magnet magnetic field versus current angle, PMA-SynRM

The magnetic field in the magnets decreases when the

pole pairs increases (Fig. 16), because this field depends on

the magnetomotive force. In addition structures with more

than 3 pole pairs the magnet magnetic field value does not

exceed the limit value of the intrinsic coercivity field

(375kA/m). It gives the interest to increase the pole pair

number.

VII. DISCUSSION

In order to study performances, we construct three

curves for each structure: SynRM (Fig. 17, 19, 21) and

PMA-SynRM (Fig. 18, 20, 22). The figures show

respectively the Average Torque vs. Power Factor, the

Average Torque vs. Torque Ripple and the Power Factor

vs. Torque ripple. Each figure represents also the variation

of these values in function of the pole pair number.

Fig. 17 and Fig. 18 compare the average torque and

power factor. The region of high average torque and power

factor is situated in the upper right corner. The comparison

between these two figures shows the impact of insertion ofthe ferrite permanent magnets on the average torque and the

power factor. The PMA-SynRM withp=3 andp=4 presents

the best results, taking into account the requirements (Tave=

4000 N.m) and a power factor greater than 0.7.

Fig. 17. Average Torque versus Power Factor, SynRM.

Fig. 18. Average Torque versus Power Factor, PMA-SynRM.

The Fig. 19 and Fig. 20, compare the average torque and

torque ripple together. We want to maximize average

torque and minimize torque ripple, therefore points must be

closer to the upper left corner. It is clear that SynRM

structures have fewer points in this direction than PMA-

217


6/7

SynRM structures. In addition, PMA-SynRM withp=4 has

a low torque ripple for several points. It should be noted

that PMA-SynRM with p=3 has a high average torque but

its torque ripple is high, between 20 and 25%.

Fig. 19. Average Torque versus Torque Ripple, SynRM.

Fig. 20. Average Torque versus Torque Ripple, PMA-SynRM.

The Fig. 21 and Fig. 22 compare the power factor and

torque ripple together. The region of high power factor and

low torque ripple is also situated in the upper right corner.

PMA-SynRM structures have more points in this region,

thanks to the magnets that improve the power factor. PMA-

SynRM withp=4 has a high power factor and a low torque

ripple, around 8%, for several points. Also we can see that

PMA-SynRM with p=2 and p=3 have several points with

high power factors, but with torque ripple is high.

Fig. 21. Power Factor versus Torque Ripple, SynRM.

Fig. 22. Power Factor versus Torque Ripple, PMA-SynRM.

Based on the structures comparisons above. We have

chosen to illustrate the PMA-SynRM with p= 4, with the

curve of the Fig. 23. This figure plots in 3D the average

torque, versus the torque ripple and the power factor, each

point is plotted for a given current angle. This type of figurecan be used as a tool to compare the different structures and

pole number.

Fig. 23. Average torque versus torque ripple and power factor for the

PMA-SynRM withp=4

VIII. CONCLUSION

This paper has presented a methodology to compare

SynRM and PMA-SynRM structures by using finite

element method. We presented the characteristics of

average torque, torque ripple and power factor depending

on current angle for different pole pair numbers. We find

that the structure with four pole pair number has the best

performances, of course with the assumption of the same

volume of magnets and same production cost.

It should be noted that the study is limited to a fixed

structure especially the stator, we havent changed nor the

flux-barriers thickness, nor the opening angles, which can

improve the performances. For example the PMA-SynRM

withp=6 can be improved by increasing the volume of the

inserted magnets. We must consider that if we change the

geometry of the stator results may vary, suitable for direct

structure with p=2, for example, if the thickness of thestator yoke is increased, it will less saturated and thus

torque increase.

218


7/7

The performance can be improved when we increase the

thickness of flux-barriers and the volume of permanent

magnets, because the flux of magnets increases and also the

torque and power factor, however, it will have a maximum

value because the increase in the size of flux-barriers also

generates a reduction of rotor iron for the passage of flux

and it produces saturation of the rotor.

This comparison methodology can be used as tool infuture geometrical optimizations of the different structures.

Another aspect that will be incorporated in future research

is the optimization of the total machine cost (production

cost and material cost) versus performance.

IX. REFERENCES

[1] A. Vagati, "The synchronous reluctance solution: a new alternative

in AC drives," IEEE 20th International Conference on Industrial

Electronics, Control and Instrumentation, 1994. IECON '94, vol. 1,

pp. 1-13, Sep. 1994.

[2] T.A. Lipo, "Synchronous reluctance machines A viable alternative

for AC drivers?"Electric Machines and Power Systems, pp. 659-671,April 1991.

[3] A. Fratta, A. Vagati and F. Villata, "On the evolution of AC

machines for spindle drive applications," IEEE Transactions on

Industry Application , vol. 28, N5, pp. 1081-1086, Sep. /Oct. 1992.

[4] A. Boglietti, A. Cavagnino, M. Pastorelli and A; Vagati,

"Experimental comparison of induction and synchronous reluctance

motors performance,"IEEE Industry Applications Conference, 2005.

Fourtieth IAS Annual Meeting. Conference Record of the 2005, vol.

1, pp. 474-479, Oct. 2005.

[5] A. Fratta, G. P. Troglia, A. Vagati and F. Villata, "Evolution of

torque ripple in high performance synchronous reluctance machines,"Records of IEEE Industry Application Society Annual Meeting,

Toronto, Canada, vol. 1, pp. 163-170, Oct. 1993.

[6] T. Matsuo and T. A. Lippo, "Rotor design optimization of

synchronous reluctance machine," IEEE Transactions on Energy

Conversion , vol. 9, N 2, pp. 359-365, June 1994.

[7] K.-C. Kim, J. S. Ahn, S. H. Won, J.-P. Hong and J. Lee, "A study on

the optimal design of SynRM for the high torque and power factor,"

IEEE Transactions on Magnetics, vol. 43, N 6, pp. 2543-2545,

June. 2007.

[8] N. Bianchi, S. Bolognani, D. Bon and M.-C. Dai Pre, "Rotor flux-

barrier design for torque ripple reduction in synchronous reluctance

motors," IEEE Industry Applications Conference, 2006. 41st IAS

Annual Meeting. Conference Record of the 2006, vol. 3, pp. 1193-

1200, Oct. 2006.

X. BIOGRAPHIES

Dany Prieto was born in Lima, Peru, in 1984. He received the M.S.

degree in Electrical Engineering from the University of Nantes, France, in

2011.

Since 2011, he has been working toward the Ph.D. degree in Electrical

Engineering with the Department of Energy and Power Systems in

Supelec.

Benjamin Dagus was born in La Rochelle, France, in 1984. He isgraduated from Ecole Polytechnique de lUnivert de Nantes in Electrical

Engineering, France, 2008 and he received the M.Sc. degree in Nantes,

France, 2009.

He is currently working toward the Ph.D. degree in Electrical

Engineering with the Department of Energy and Power Systems in

Supelec.

Philippe Dessante is Professor of Department of Energy and PowerSystems in the Ecole Suprieure dElectricit (Supelec) in France.

Pierre Vidalis Professor of Department of Energy and Power Systemsin the Ecole Suprieure dElectricit (Supelec) in France.

Jean-Claude Vannier is Professor and head of Department of Energyand Power Systems in the Ecole Suprieure dElectricit (Supelec) in

France.

His research interest is with energy conversion systems (motors,

actuators, generators) and concerns the modeling, the design and the

optimization of these equipments for specific applications.

219

Documents

[doi 10.1109_icelmach.2012.6349866] Prieto, D.; Daguse, B.; Dessante, P.; Vidal, P.; Vannier, J.-C. -- [IEEE 2012 XXth International Conference on Electrical Machines (ICEM) - Marseille,