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Abstract—  The paper presents a new method for torque ripple

calculation of permanent magnet assisted synchronous reluctance

motor (PMa-SynRM) by load angle curve simulations. We can

directly detect the load angle of minimum torque ripple and

maximum average torque by several load angle curves with

different current state. The analysis results were verified by the

experiment.

I.  I NTRODUCTION

In a synchronous reluctance motor (SynRM), high saliency

ratio is required to achieve high torque and power factor.

However it is very difficult to increase saliency ratio withsmall rotor. So, we insert permanent magnets into the barriers

for high torque. The advantages of PMa-SynRM compared to

IPM motor are low back emf and wide constant power region

with a small d-axis current at the field weakening control area.

On the contrary, PMa-SynRM has larger torque ripple due to

its complex barrier structure [1].

The magnitude of torque ripple as well as average torque

is changed by load angle. Therefore we should analyze the

characteristics of torque ripple according to load angle. This

 paper presents an efficient method for torque ripple

calculation by load angle curve calculation by FEM.

II.  A NALYSIS MODEL OF PMA-SYNRM 

We should design the optimal barriers of a rotor in order tomaximize the saliency ratio [2]. In the paper, we inserted PM

in the middle of barriers as shown in Fig. 1(a). Fig. 1(b) shows

the FEM analysis model for torque ripple calculation.

(a) Rotor of PMa-SynRM (b) FEM analysis model

Fig. 1. The analysis model of PMa-SynRM 

III.  A NALYSIS OF TORQUE A NGLE CURVE 

In order to analyze torque property according to load angle,

we just perform a FE analysis generally on an assumption that

the dc currents at 1st point of Fig.2 (a) flow into the three

 phase windings, and then rotor rotates up to 180 electrical

angles. However, the load angle curve by single condition of

dc current dose not presents average torque at each torque

angle, but shows torque property adding torque ripple. If so,

the superposition of toque angle curve by inputting the current

of each state from 2nd to 7th from Fig.3 gives us torque ripple

and average torque at the given torque angle. Fig. 2(b) shows

the results by proposed analysis method.

(a) Condition of Input currents (b) Analysis results of torque angle curve

Fig. 2. The torque ripple calculation method by torque angle curve

IV.  VERIFICATION OF TORQUE R IPPLE CHARACTERISTIC 

In the Fig. 2(b), we can see that torque ripple at the load

angle 90°  is smaller than that at 130°. In order to verify the

 proposed method, we perform the time stepping FE simulation

with sinusoidal rated current source and fixed load angle

 points. Fig. 3 shows the results of torque ripple waveform, and

it gives good agreement with results by proposed method.

We are going to presenting the effective magnet

distribution method in barriers by proposed method in order to

minimize torque ripple.

Fig. 3. Torque ripple waveform by time stepping FE analysis

V. 

ACKNOWLEDGMENT

This work was financially supported in part by Korea Energy Management

Corporation through the Energy Technology R&D program.

VI.  REFERENCES

[1] 

 Niazi, P. and Toliyat, H.A., “Design of a low-cost concentric winding

 permanent magnet assisted synchronous reluctance motor drive”,

Industry Applications Conference, Fortieth IAS Annual Meeting. Vol. 3,

 pp. 1744–1748, 2-6 Oct. 2005

[2] 

I. Boldea, T. Fukao, T.A. Lipo, L. Malesani, T.J.E. Miller and A. Vagati,

Synchronous Reluctance Motors and Drives A New Alternative, IEEE

IAS 29th Annual Meeting, Oct. 1994.

A Study on the Calculation and Reduction Method of Torque Ripple for

Permanent Magnet Assisted Synchronous Reluctance Motor by using the

Load Angle CurvesKi-Chan Kim, Joon Seon Ahn, Sung Hong Won and Ju Lee, Senior Member IEEE

Department of Electrical Engineering, Hanyang University

Haengdang, Seongdong, Seoul, 133-791, Koreachannykim@ihanyang.ac.kr

PA8-6

1-4244-0320-0/06/$20.00 ©2006 IEEE   76