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Performance Improvement of Ferrite-Assisted Synchronous Reluctance Machines Using Asymmetrical Rotor Configurations

Wenliang Zhao1, Dezhi Chen1, Thomas A. Lipo2, Life Fellow, IEEE, and Byung-il Kwon1, Senior Member, IEEE

1Department of Electronic Systems Engineering, Hanyang University, Ansan, 426-791, Korea

2 Department of Electrical and Computer Engineering, Florida State University, Tallahassee FL, 32306, USA

This paper proposes novel ferrite-assisted synchronous reluctance machines (FA-SynRMs) having the merit of highly improved machine performance including torque, efficiency, and power factor. The particular superiority of the proposed FA-SynRMs is the utilization of an asymmetrical rotor configuration that contributes to the full use of torque components by allowing the magnetic torque and reluctance torque to reach their maximum values near or at the same current phase angles. To provide visible insights into the contribution, a frozen permeability method (FPM) is utilized to separate the torque into the reluctance torque and the magnetic torque based on a two-dimensional (2-D) finite element method (FEM) by aid of JMAG-Designer. For highlighting the advantages of the proposed models, a conventional FA-SynRM with symmetrical rotor configurations is adopted for comparison under the same operating conditions. As a result, it is demonstrated that the proposed design is effective in improving the performance of FA-SynRMs.

Index Terms—Asymmetrical rotor, ferrite-assisted synchronous reluctance machines (FA-SynRM), finite element method (FEM), frozen permeability method (FPM), magnetic torque, power factor, reluctance torque.

I. INTRODUCTION

ITH increasing environmental and energy concerns, research and development of high performance electric

machines are gaining increasingly more attention. In particular, permanent magnet (PM) machines are widely employed due to their high torque/power density and high efficiency benefiting from the use of the properties of rare earth magnetic materials. However, recently, rare earth PMs have suffered from the problem of increased price as well as limited supply, which leads to a critical challenge in those applications where a high quantity of PMs and mass production are required such as large direct-drive machines, automotive and home appliances [1]-[2].

Accordingly, various alternative solutions for designing electric machines with less or zero rare earth PMs have been proposed, mostly focusing in the field of switched reluctance machines [3], ferrite PM machines [4]-[5], and PM machines with minimized rare earth magnets [6]. It was found that the ferrite PM machines offer competitive advantages through an overall consideration of torque/power density, efficiency, torque pulsations, and production cost. In particular, the ferrite-assisted synchronous reluctance machine (FA-SynRM), designed by inserting low-cost ferrite PMs into a synchronous reluctance machine, is regarded as a better option that can effectively utilize both of the magnetic torque and reluctance torque. The design and performance analysis of FA-SynRMs have been extensively examined [7]-[8]. However, the reported research for FA-SynRMs are commonly performed based on the fact that the PMs are inserted in the central position of rotor flux barriers. Thus, the rotor shape maintains

circumferential symmetry such that the magnetic torque and the reluctance torque obtained from a d-q rotor frame equivalent circuit reach the maximum values at different current phase angles displaced theoretically by 45o (electrical). Hence, only a portion of each torque component is utilized. Nevertheless, the situation can be improved by taking advantage of the design concept presented in [9], in which the maximum values of the torque components can occur near or at the same current phase angle by flux barrier design in a V-type interior PM (IPM) machine.

In this paper, the FA-SynRMs designed by a novel strategy combining the rotor magnet design with rotor flux barrier design, are proposed for improving the machine performance including torque, efficiency, and power factor. The magnetic torque and the reluctance torque of the proposed FA-SynRMs will reach a maximum near or at the same current phase angles for torque enhancement benefiting from the adopted asymmetrical rotor configurations. A frozen permeability method (FPM) is utilized to provide visible insights into the separation of the magnetic torque and the reluctance torque based on a 2-D finite element method (FEM) by aid of JMAG-Designer. To highlight the advantages of the proposed models, a conventional FA-SynRM with symmetrical rotor configurations is adopted for comparison under the same operating conditions.

II. MODELING OF THE INVESTIGATED FA-SYNRMS

A. Conventional FA-SynRM and Torque Characteristics

A conventional FA-SynRM with three flux barriers per pole has been adopted as the basic model as illustrated in Fig. 1. The stator has six slots with concentrated windings as shown in Fig. 1(a). The low-cost ferrite PMs are inserted in a central position within the rotor flux barriers as shown in Fig. 1(b). The machine specifications are listed in Table I.

In general, based on the vector diagram derived from a d-q rotor frame equivalent circuit using the Park transformation as shown in Fig. 2(a), the electromagnetic torque is expressed as

W

Manuscript received March 20, 2015; revised May 13, 2015; accepted May 14, 2015. Corresponding author: Byung-il Kwon (e-mail: bikwon@hanyang.ac.kr).

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Fig. 1. Conventional FA-SynRM (basic model). (a) Stator and windings. (b) Rotor with ferrite magnets.

TABLE I SPECIFICATIONS OF THE CONVENTIONAL MODEL

Item Unit Value

Magnet poles/Stator slots - 4/6

Stator outer diameter mm 88

Rotor inner diameter mm 15

Airgap length mm 0.5

Motor axial length mm 52

Remanence of magnet T 0.41

Fig. 2. Characteristics of the basic model. (a) Vector diagram in the d-q reference frame. (b) Torque characteristics. T: Resultant torque, T-PM: Magnetic torque, T-R: Reluctance torque.

2e

3 1[ cos ( ) sin 2 ]

2 2m pm a d q a

pT I L L I (1)

where p is the number of pole pairs, Ia is the peak value of the phase current, β is the angle of the stator current vector measured with respect to the q-axis designated as current phase angle, Ld and Lq are the inductances of the d- and q-axes, respectively, and λpm is the peak fundamental value of magnet flux linking the stator windings. The first term in (1) is termed the magnetic torque, while the second term is the reluctance torque. Based on (1), typical torque characteristics of FA-SynRMs can be obtained as shown in Fig. 2 (b), where it is displayed that the magnetic torque and the reluctance torque reach maximum values at different current phase angles, theoretically displaced by 45o with respect to each other.

B. Topologies of the Proposed FA-SynRM

Essentially all conventional FA-SynRMs are designed such that the rotor shape maintains circumferential symmetry such that the two axes, namely the direct or d-axis and the quadrature or q-axis, are located such that the q-axis is 90o (elec.) from the d-axis. In the proposed designs, the rule is changed by creating rotor asymmetry realized by combining the rotor magnet design with the rotor flux barrier design.

Fig. 3. Proposed FA-SynRMs. (a) Proposed model 1 (Concentrated PM configuration). (b) Proposed model 2 (Asymmetrical flux barriers).

Fig. 4. Flowchart of the torque segregation using FPM.

Fig. 3 shows the topologies of the proposed FA-SynRMs.

The proposed model 1 shows a concentrated PM configuration as shown in Fig. 3(a), in which a radial flux barrier A is created to place the ferrite PMs within an asymmetrical U-type PM structure. The proposed model 2, featuring a second asymmetrical rotor configuration, is shown in Fig 3(b), in which the magnet in the flux barrier B is moved to C, while an oblique flux barrier D is added to prevent flux from flowing to the outside. Both of the proposed models assume the same machine size and magnet amounts as the basic model.

C. Toque Segregation Using FPM

The frozen permeability method (FPM) which can reveal the influences of the magnetic saturation and cross-coupling, is an effective technique to carry out the segregation of the torque components in salient PM machines [10]. By means of a commercial FEM software package, JMAG-Designer (14.0), the torque segregation process using FPM is shown in Fig. 4. The no-load analysis is performed first to initialize the rotor position and current phase angle. Second, the total torque is obtained with both the PM and current excitations producing magnetic fields. Then the PMs are removed and the reluctance torque is determined. The magnetic torque is then calculated by subtracting the reluctance torque from the total torque.

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Fig. 5. Magnetic flux line distribution at the no-load case. (a) Basic model. (b) Proposed model 1. (c) Proposed model 2.

Fig. 6. Back EMFs for each phase.

Fig. 7. FFT analysis of the back EMFs.

III. 2-D FEM ANALYSIS RESULTS

A. Magnetic Flux Line and Back EMF

The characteristics for the no-load condition were first carried out using a 2-D FEM. The magnetic flux line distribution of the investigated models is shown in Fig. 5. Different from that of the basic model in Fig. 5(a), the flux lines of the proposed models feature asymmetrical flux distributions as shown in Fig. 5(b) and (c), respectively. The back EMFs for each phase are compared in Fig. 6. Due to the asymmetrical rotor magnet and flux barrier design, the back EMFs of the proposed models exhibit considerable distortion but contain highly enhanced fundamental values and rms values as listed in Table II. Fig. 7 shows the corresponding fast Fourier transform (FFT) analysis, while the THD for the three models are 8.5%, 56.6%, and 46.1%, respectively.

Fig. 8. Characteristics of the basic model. (a) Magnetic flux density distribution at the maximum torque condition. (b) Torque characteristics. T: Resultant torque, T-PM: Magnetic torque, T-R: Reluctance torque.

Fig. 9. Characteristics of the proposed model 1. (a) Magnetic flux density distribution at the maximum torque condition. (b) Torque characteristics. T: Resultant torque, T-PM: Magnetic torque, T-R: Reluctance torque.

Fig. 10. Characteristics of the proposed model 2. (a) Magnetic flux density distribution at the maximum torque condition. (b) Torque characteristics. T: Resultant torque, T-PM: Magnetic torque, T-R: Reluctance torque.

B. Torque Characteristics, Power Factor, and Efficiency

Figs. 8 to 10 illustrate the machine characteristics of the basic model, proposed models 1 and 2, respectively. Figs. 8(a) to 10(a) show the magnetic flux density distribution for the maximum torque case, and Figs. 8(b) to 10(b) show the torque characteristics obtained by the aforementioned FEM-based FPM, in which the electromagnetic torque is predicted by feeding the stator windings with sinusoidal current excitations of 4 Arms/mm2 at 4800 r/min. The results in Figs. 8(b) to 10(b) indicate that the two torque components in the basic model reach their maximum values at different current phase angles (45o) as shown in Fig. 8(a), while it shows that the two torque components of the proposed models reach the maximum values near the same current phase angle, which improves the total torque as shown in Fig. 9(b) and Fig. 10(b),

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TABLE II 2-D FEM ANALYSIS RESULTS

Item Unit Basic model Prop. model 1 Prop. model 2

Back EMF (rms) V 8.9 34.1 21.9

Torque (Max.) Nm 0.3724 0.3924 0.4083

Torque ripple % 52.9 91.5 64.8

Power W 187 197 205

Power factor - 0.49 0.53 0.60

Total loss W 25.2 24.0 22.4

Efficiency % 88.1 89.1 90.1

0 30 60 90 1200.2

0.3

0.4

0.5

0.6

0.7

Augular displacement [degree]

Ele

ctro

mag

netic

torq

ue [

Nm

]

Basic model Prop. model 1 Prop. model 2

Fig. 11. Comparison of the electromagnetic torques.

0 60 120 180 240 300 360-240

-120

0

120

240

Angular displacement [degree]

Inpu

t cur

rent

[A

/50]

-240

-120

0

120

240

Indu

ced

volt

age

[V]

Input current Induced voltage

Fundamental component of the induced voltage

Fig. 12. Power factor calculation.

respectively. As listed in Table II, the maximum torques of proposed models 1 and 2 are increased by 5.4% and 9.6%, respectively, compared to that of the basic model. The electromagnetic torques at the maximum torque condition are compared in Fig. 11. It shows that the proposed models exhibit higher torque ripple than the basic model although the torque ripple can be minimized by various techniques [11].

The displacement power factor in the maximum torque case is defined as cosΦ, wherein Φ is determined by the difference of the angular displacements between the fundamental components of the input current and the fundamental component of the induced voltage extracted from a harmonic analysis using a FEM, as shown in Fig. 12 [12]. The efficiencies of all the investigated models are estimated by the ratio of the output power to the sum of the output power and losses. The results show that the power factor and efficiency of the proposed models are greatly improved compared to those of the basic model as listed in Table II.

IV. CONCLUSION

This paper has proposed a novel design strategy for FA-SynRMs to improve the torque production by making full use of its magnetic torque and reluctance torque such that the two torque components reach their maximum values nearly at the same current phase angles. Based on the 2-D FEM analysis results, it was found that the torque, power factor, and efficiency of the proposed models have been greatly increased, i.e. increased by 9.6%, 22.4% and 2.3% in the proposed model 2, respectively, when compared to those of the basic model. It is worthy to mention that the increased torque in the proposed FA-SynRMs comes at the expense of a higher torque ripple. As a future direction, the proposed models will be further optimized by an overall consideration of torque, efficiency and torque ripple to meet the requirements of most applications.

ACKNOWLEDGMENT

This research was supported by the BK21PLUS program through the National Research Foundation of Korea funded by the Ministry of Education.

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