Design and analysis of a hybrid-excited wound field synchronous machine with high reluctance torque utilization

Abstract

The paper proposes a hybrid-excited wound field synchronous machine (HE-WFSM), which can achieve high reluctance torque utilization. The key of the proposed HE-WFSM is that two permanent magnets (PMs) assist each rotor pole in forming an additional magnetic flux circle. It is opposite to the magnetic flux circle along the q-axis in the WFSM. The reduction of the q-axis flux can help to improve the saliency ratio and reluctance torque. Additionally, the asymmetrical flux linkage achieves a closest current phase angle between the maximum field torque and the maximum reluctance torque. To highlight the advantages of the proposed HE-WRSM, a general WFSM was adopted as the basic machine and analyzed under the same operating conditions. All performances of the basic machine and proposed HE-WFSM were predicted using finite element analysis (FEA) in Jmag-Designer. Finally, it was confirmed that the proposed HE-WRSM can achieve high reluctance torque utilization.

Keywords

Hybrid-excited wound field synchronous machine high reluctance torque utilization finite element analysis

1. Introduction

Recently, the high cost and limited supply of rare earth materials have motivated researchers to develop electric machines with less or without using rare earth materials [1]. Wound field synchronous machines (WFSMs) do not require any earth materials, and can be applied instead of permanent magnet (PM) machines in most cases. Therefore, they have been attracting increasing attention.

For a general WFSM, the total output torque is composed of the field torque and reluctance torque, which reach their maximum values at theoretical 45° (elec.) current phase angle difference [2]. Moreover, the general WFSM shows a lack of ability to produce high reluctance torque compared with the interior permanent magnet synchronous motors, owing to its poor saliency ratio (L_d∕L_q). In other words, the reluctance torque of the general WFSM occupies a very small component. However, the reluctance torque can be more talented due to loss reduction and achieving the satisfactory factor [3,4]. Therefore, hybrid torque combining field torque and reluctance torque is being developed. Additionally, achieving a high saliency ratio contributes to high reluctance torque utilization for the WFSM. In a previous study [5], because air is a poor magnetic field conductor, a single flux barrier was introduced into the rotor pole of the general WFSM to hinder the q-axis flux line and achieve a high saliency ratio. It was found that the single flux barrier could effectively improve the saliency ratio, but it is still slightly low.

Another method for high reluctance torque utilization is to reduce the current phase angle between the maximum field torque and the maximum reluctance torque below 45° (elec.). Then, a larger portion of each torque component is utilized. The utilization of each torque components can be improved by using an asymmetric magnet and improving the rotor design. In [6], the principle of the relationship between the structures of the PMs, airspace barriers, current phase angle of the maximum PM torque and maximum reluctance torque were thoroughly investigated. An axially sandwiched hybrid permanent magnet synchronous reluctance machine has been proposed to improve the PM torque and make full use of the PM torque and reluctance torque [7].

Hybrid-excited wound field synchronous machines (HE-WFSMs) for achieving high torque density are widespread. These machines combine PM excitation and wound field excitation to combine the advantages of PM machines and WFSMs. The wound field excitation can control the excitation flux in the air gap, which improves flux weakening. The PM excitation can reduce copper loss and improve torque density. Therefore, HE-WFSMs are an attractive research area for improving the energy efficiency, torque density, and flux weakening ability [8]. Almost all HE-WFSMs focus on hybrid torque, which combines the field torque and PM torque. The reluctance torque of the general WFSM because of low saliency ratio is ignored sometimes. Even for the HE-WFSM in [9], the saliency ratio is reduced owing to PM excitation. In [10], a novel HE-WFSM with PMs asymmetrically positioned on the pole surface was proposed to make full use of the field torque and reluctance torque, and thus to improve the torque, efficiency, and power factor. However, the saliency ratio was still low and relatively small reluctance torque was produced.

This paper proposes a novel HE-WFSM, which is analyzed to achieve a high saliency ratio and a closest current phase angle between the maximum field torque and the maximum reluctance torque for high reluctance torque unitization. To highlight the advantages of the proposed HE-WFSM, a general WFSM is adopted for comparison and operated under the same driving conditions. Finite Element Analysis (FEA) using by Jmag Designer is utilized to predict all the characteristics of the machines.

2. Modeling of the proposed HE-WFSM

2.1. Basic WFSM

A general WFSM, which is designed for low-power fan applications, is first adopted as the basic machine and analyzed for comparison. The stator has six slots with three-phase and concentrated-coil windings. The rotor has four poles with the DC field windings. The structural topology of the basic WFSM is shown in Fig. 1(a). The laminated silicon steel sheet is selected for the cores of the stator and rotor, and the main design specifications are listed in Table 1.

2.2. Proposed HE-WFSMs and PM effects

The proposed HE-WFSM with symmetrically positioned PMs is shown in Fig. 1(b). The PM in each pole consists of two PMs, which have the same magnetization direction. It shares the same stator and winding topologies with the basic WFSM, as well as the same operating condition. Additionally, the NdFeB with the remanence of 0.47 T is specified for the assisted PMs. In the proposed HE-WFSM, PMs are adopted to help increase the saliency ratio and improve the utilization of reluctance torque.

Fig. 1.

(a) Basic WFSM. (b) Proposed HE-WFSM.

Table 1

Main design specifications

Item	Unit	Value
Rotor poles/Stator slots	-	4/6
Stator outer diameter	mm	88
Air gap length	mm	0.5
Motor axial length	mm	52
Magnetic motive force	A∗turn	75
Rated armature current	A	1.6

2.3. Torque characteristics

In the basic WFSM, the d-axis is defined as the magnetic direction produced by the field winding. And the q-axis is positioned by 90° (elec.) counterclockwise from the d-axis. The theoretical flux line distributions in the d–q coordinates of the basic WFSM are shown in Fig. 2(a). The electromagnetic torque can be obtained in the elegant d–q rotor equivalent circuit as expressed in Eq. (1). $\begin{eqnarray}\displaystyle T\text{} & =\text{} & \displaystyle \displaystyle {\displaystyle \frac{3p}{2}}[L_{ad}I_{f}I_{s}\cos {\gamma}-0.5(L_{d}-L_{q})I_{s}^{2}\sin 2{\gamma}]\nonumber\\ \displaystyle \text{} & =\text{} & \displaystyle T_{f}+T_{re}.\end{eqnarray}$ (1) Where, p denotes the pole pairs, I_s is the peak value of the phase current, I_f is rotor field current, 𝛾 is the current phase angle, L_d and L_q are the inductances of the d-and q-axis, respectively. The first term T_f in Eq. (1) is called as the field torque, which is generated by the wound field excitation. Moreover the second term T_re is called as the reluctance torque, which is generated because the motor is moving to a position where the reluctance seen by the armature flux is declining.

The rotor position is initialized based on the no-load back-EMF in phase, and then the torque characteristics of the basic WFSM obtained from Eq. (1) are presented in Fig. 2(b), which displays that there is 45° (elec.) difference between the current phase angles at the maximum field torque and maximum reluctance torque. For the basic WFSM the saliency ratio defined as L_d∕L_q is slightly low, which will cause the low reluctance torque.

In the proposed HE-WFSM, there are two PMs symmetrically positioned on the two sides of each rotor pole with the same magnetization direction. The theoretical flux line distribution of the proposed HE-WFSM in the basic WFSM’s d–q coordinates is shown in Fig. 3. And Fig. 3 points out the direction of the PM magnetization, which is opposite to q-axis flux. It is helpful to reduce the inductance in the q-axis, which can benefit to produce the high saliency ratio and increase the reluctance torque in WFSMs.

Fig. 2.

(a) Theoretical d–q flux line distribution of basic WFSM. (b) Theoretical torque characteristics of the basic WFSM.

Fig. 3.

Theoretical q flux reduction of proposed HE-WFSM.

From the view of the topology analysis, the two PMs of each pole in the proposed HE-WFSM have the same magnetization direction. Figure 4 shows the topology analysis of the proposed HE-WFSM. When the excitation is only wound field excitation, the field torque and the reluctance torque are both produced in d_fq_f axis frame as shown in Fig. 4(a). When the PM excitation is added, the newly formed magnetic direction is produced by the vector sum of the field winding and the PMs, which is generally defined as the d-axis. Obviously, the dq-axis frame of the field torque for the proposed HE-WFSM is changed due to the asymmetrical magnetic flux distribution. However, the reluctance torque is still in the d_fq_f axis frame. When it transfers into the new dq-axis frame, the closest current phase angle between the maximum field torque and the maximum reluctance torque can be achieved in the proposed HE-WFSM as shown in Fig. 4(b). Above all, the high reluctance torque utilization is expected to be achieved in the proposed HE-WFSM.

Fig. 4.

Theoretical current angle displacement of proposed HE-WFSM. (a) Wound field excitation (b) PM and wound field excitation.

Fig. 5.

Magnetic flux density distribution. (a) Basic WFSM (b) Proposed HE-WFSM.

3. Performance and discussion

To validate the proposed HE-WFSM, all the characteristics of the basic WFSM and the proposed HE-WFSM, including magnetic flux density distribution, back-EMF, torques and saliency ratio, are predicted by the FEA using JMAG-Designer, under the same operating conditions.

3.1. Magnetic flux density distribution and back-EMF

The machine characteristics at the no-load condition is first predicted. The magnetic flux density distribution of the basic WFSM and the proposed HE-WFSM are compared in Fig. 5. Different from the basic WFSM which exhibits symmetrical flux density distribution, the proposed HE-WFSM features asymmetrical flux density distribution.

The back electromotive forces (back-EMFs) of both the basic WFSM and the proposed HE-WFSM are compared in Fig. 6(a). Due to the asymmetric magnetic flux density distribution of the proposed HE-WFSM, the corresponding back-EMF shows considerable distortion. However, the proposed HE-WFSM exhibits slight reduction of back-EMF in phase than the basic WFSM. The RMS value of the back-EMF is reduced by 6.5%, compared with that of the basic WFSM. It is caused by the additional flux leakage from the PMs. Figure 6(b) shows the corresponding fast Fourier transform (FFT) analysis, and the total harmonics distortion (THD) for the two models are 2.42% and 5.67%, respectively.

Fig. 6.

(a) Back-EMFs (b) FFT results of Back-EMFs.

Fig. 7.

Flowchart of the torque separation using FPM.

Fig. 8.

Torque characteristics. (a) Basic WFSM (b) Proposed HE-WFSM.

3.2. Torque characteristics and saliency ratio

To confirm the reluctance torque unitization is improved, the frozen permeability method (FPM) is utilized to separate the field torque and the reluctance torque. The process of predicting torque characteristics for the basic WFSM and the proposed HE-WFSM using FPM with the aid of the FEA are illustrated in Fig. 7. The field torque is obtained by sub-tracting reluctance torque from the total torque.

The torque characteristics of the basic WFSM and the proposed HE-WFSM with respect to the current phase angles are compared in Fig. 8. As can be seen in Fig. 8(a) the two torque components of the basic WFSM reach their maximum values at different current phase angles by 45°. And at the −20° (elec.), the total torque reaches the maximum value, in which the utilized reluctance torque is 0.048 Nm. It occupied 68.5% of its maximum value (0.07 Nm). In contrast, Fig. 8(b) shows that the two torque components of the proposed HE-WFSM reach the maximum values at different current phase angles by 10°. And at the −5° (elec.), the total torque reaches the maximum value, in which the utilized reluctance torque is 0.174 Nm. It takes up 99.6% of its maximum value (0.175 Nm). Therefore, the high reluctance torque utilization has been achieved in the proposed HE-WFSM, which benefits from the PMs.

The saliency ratios of both the basic WFSM and the proposed HE-WFSM are shown in Fig. 9. From the current phase angle working range, the saliency ratio of the proposed HE-WFSM shows much higher than that of the basic WFSM. At the maximum working point, the saliency ratio of the proposed HE-WFSM is improved by 57.9%. It has verified that the assisted PMs in the proposed HE-WFSM can help to improve the saliency ratio a lot. As well as the reluctance torque of the proposed HE-WFSM is improved by 262.5%, compared with that of the basic WFSM.

The detailed comparisons between the basic WFSM and the proposed HE-WFSM are presented in Table 2. The higher saliency ratio with the closest current phase angle between the maximum field torque and maximum reluctance torque, greatly improved the total torque by 39.7%. With the increase of the total torque, the power of the proposed model is increased. Consequently, the efficiency of the proposed HE-WFSM are highly improved by 4.6%, as compared to that of the basic WFSM.

Fig. 9.

Comparison of saliency ratios.

Table 2

Performance comparison of the investigated models

Item	Unit	Basic WFSM	Proposed HE-WFSM
Back-EMF (RMS)	V	12.68	11.85 (6.5 ↓)
Current phase angle	°	−20	−5
Maximum total torque	Nm	0.302	0.422 (39.7% ↑)
Maximum reluctance torque	Nm	0.07	0.175
Utilized reluctance torque	Nm	0.048	0.174 (262.5% ↑)
Saliency ratio	-	1.21	1.91 (57.9% ↑)
Efficiency	%	85.5	89.4 (4.6% ↑)

4. Conclusion

This paper has proposed and analyzed a novel HE-WFSM with symmetrically positioning two PMs in each pole to achieve high reluctance torque utilization. Based on the simulation results by FEM, it confirms that the proposed HE-WFSM has achieved the high saliency ratio and a closest current phase angle between the maximum field torque and maximum reluctance torque. The high reluctance torque utilization is achieved as expected with the improved torque and efficiency, as compared to those of the basic model. Hence, it can be concluded that the proposed HE-WFSM with symmetrically positioned PMs is promising for improving energy efficiency, and adopting to high-performance applications.

Footnotes

Acknowledgements

This work was supported in part by the BK21PLUS Program through the National Research Foundation of Korea within the Ministry of Education, and in part by the National Research Foundation of Korea grant funded by the Korea government (Ministry of Science) (No. NRF-2020R1A2B5B01002400).

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