Design and optimization of HTS flux-switching permanent magnet machine

Received Mar 17, 2019 Revised May 7, 2019 Accepted Jul 17, 2019 Flux-switching permanent magnet (FSPM) machine with high temperature superconductors (HTS) bulks located between the rotor poles to eliminate the flux leakage in the rotor, termed as (HTS-FSPM) machine has been proposed in this paper. Using genetic algorithm, the HTS and the conventional FSPM machines having the same size constraints and load conditions have been globally optimized for max aveage torque. To highlight the advantages of the HTS-FSPM machine, a performance comparison between the conventional and HTS-FSPM machines has been presented. It is found that the HTSFSPM machine can increase the torque by 27%, however, this comes with the expense of higher torque ripple and power losses.


INTRODUCTION
High temperature superconductors (HTS) electrical machines have been a centre of research in the past three decades, since they deliver several advantages [1][2]. High power density may be considered as the most important feature of the HTS machines [3][4][5]. The absence of the electrical resistivity which allows for significantly high current density and the zero magnetic permeability (Meissner effect), which offers perfect magnetic insulation opened several new electrical machine architectures with high performance.
As a type of stator permanent magnet machines, flux-swiching perment magnet (FSPM) machines have been wiedly applied in many sectors, since they incorporate the advantages of permanent magnet and reluctance machines [6][7][8]. However, flux leakage in stator and rotor poles is the main demerit of such machines [9]. Enhancing the exciticon system of the machine would increase the flux linkage and overcome such problem. Hence, several flux-switching permeant magnet machines with HTS field windings have been developed and reported. Conventional structure FSPM machine with HTS field winding with stationary seal has been developed and tested in [10]. Similar design with different stator structure has been studied in [11]. Furthermore, FSPM with HTS field winding located around the outer surface of the stator has been proposed in [12]. In [13] and [14], FSPM machine with HTS field winding wound radially around the stator has been designed and tested. Moreover, double rotor, linear and axial FSPM with HTS field winding has been reported in [15], [16], and [17], respectively.
Since the stator of the FSPM machine hosts all the excitation sources [18], slot area of the armature windings would be reduced when the filed winding is utilized, which results in electrical loading reduction [19]. In order to tackle such obstacle as well as reduce the flux leakage of the FSPM machine,this paper presents a FSPM machine with HTS bulks placed between the rotor poles to minize the flux leakage of the rotor pole, consequently improve the machine torque density. Global optimization process combining FEA and genetic algorithm has been used to optimized the machine for maximum average torque. Finally, perfromance comparison between the FSPM machine with bulk HTS and the original FSPM machine is conducted to highlight the benefits of the proposed HTS-FSPM machine.

FSPM-HTS MACHINE
The proposed HTS-FSPM machine is presented in Figure1, it consists of the same structure of the conventional FSPM machine albeit of the space between the rotor poles is filled with bulks HTS material. The bulk HTS material provides a perfect insolation for the magnetic field and therefore eliminate the flux leakage between the rotor poles and the stator and rotor. Table I lists the dimensions of the design parameters for both topologies.

GLOBAL OPTIMIZATION
Electrical machines having high torque density are desirable for various applications. Thereby, optimizing the main machine parameters for maximum torque is very important during the machine design process. It has been shown that global optimization using FEA based on Genetic Algorithm (GA) is a powerful tool to achieve such task [20]. Therefore, global optimization has been carried out for both machines to obtain maximum average torque. It should be noted that the optimization conditions have been kept the same for both machines seeking for a fair comparison. The constant parameters throughout the process of the optimization are defined in Table 1. According to [20] the parameters, which significantly effect the performance of the FSPM machine are given in Table 2. It must be mentioned that Table 2 also illustrates initial, restriction and optimal values of such parameters that have been changed in the process of the optimization, a schematic of those parameters is shown in Figure 2. The cost versus optimization iterations is shown in Figure 3. It can be seen that both machines have the same (RPTA) and (SR), while each machine possesses its own value for both (RPBA) and (RTH). On the other hand, there is a slight difference between the values of (STW) and (SBI) for both machines.

PERFORMANCE COMPARTION 4.1. Open-circuit results
Flux distribution and flux density at no-load condition for the original FSPM and the HTS-FSPM machines are shown in Figure 4. Evidently the HTS-FSPM topology has no flux leakage between the rotor poles. In contrast, flux leakages are presented in the gaps between the rotor poles of the conventional FSPM machine. Thanks to the presence of the HTS material, which leads to eliminate the flux leakage between rotor poles of the proposed machine. Figure 5. compares open circuit flux linkage of phase A for the mentioned machines. As a consequent of the flux leakage elimination, the FSPM-HTS machine exhibits higher flux linkage compares to the conventional counterpart. Moreover, a comparison between back-EMFs of the pahse A for the mentioned machines is presented in Figure 6. The HTS-FSPM topology delivers about 20% higher fundamental back-EMF than that of the original FSPM counterpart, since the FSPM-HTS machine possesses higher flux linkage. Furthermore, cogging torque for both machines are given in Figure7. Clearly, higher cogging torque is for the FSPM-HTS machine, due to high magnetic variation around its air gap.

Electromagnetic static torque
The predicted 2D-FE electromagnetic static torque waveforms for one electrical cycle of the HTS-FSPM and the original FSPM machines are presented in Figure 8. Apparently, the FSPM-HTS topology has higher average toque than that of the original FSPM machine, about 27% higher average torque is obtained by the FSPM-HTS machine. In addition, Figure 9 illustrates the average electromagnetic static torque with varied current densities for the understudying machines. It can be clearly observed that at low current-density the differences between the average torques for both machines are small. In contrast, at high current-density, this difference is increased, due to the core saturation in the conventional FSPM machine. Figure 8. Electromagnetic static torque Figure 9. Average electromagnetic torque against current-density

Electromagnetic losses
The predicted 2D-FE losses including core and magnets eddy current losses of the understudying machines at two operating circumstances, i.e., no-load and load with current density of 12 A/mm2 for various speed are compared in Figures 10-11, respectively. The FSPM-HTS machine has higher core and magnetic eddy current losses for both conditions in comparsion with the original FSPM machine. The losses are higher in the FSPM-HTS machine because of the higher flux focusing, which is provided by the HTS bulks. It must be mentioned that at base speed (400 rpm) on load condition the value of core and eddy current losses for the convnetinoal machine are (1.4 W and 1.4 w, respectively). In contrast, such values for the FSPM-HTS machine are (1.5W and 4W, respectivey), while the copper loss are 30W for both machines.  Figure 11. Magnet eddy current loss

CONCLUSION
A new FSPM with HTS bulks placed in the rotor gaps to reduce the stator-rotor flux leakage is proposed, designed, optimized and compared with the conventional FSPM machine. The conclusions of this work are: By adding HTS bulks in the rotor poles gaps of the FSPM machine, the average torque can improve by 27% compared to the conventional FSPM counterpart, keeping in consideration that both machines are globally optimized. While, the torque ripple of the proposed machine is around twice of the conventional, since high magnetic variation around the air gap appears when the HTS bulks are used. Moreover, higher