4.1 Electromagnetic Performances
To assess the comparative merits and limitations of the IPM, VPM and FSPM machines in the context of All-Electric aircraft propulsion, a comprehensive analysis is performed through extensive FEA on their optimal solutions obtained in the previous section. The results are showcased in Fig. 7, providing a comprehensive overview of the performance characteristics of these machines for comparison.
Figure 7 (a) displays the harmonic spectrum of the no-load airgap flux density. It can be observed that the dominant harmonic of IPM is 7 pole-pair. Due to the modular stator, the flux density of 1 pole-pair and 5 pole-pair harmonics are relatively low. For the VPM machine, the dominant harmonics are the 2 pole-pair and 10 pole-pair harmonic components. The 10 pole-pair harmonic is generated by the magnetizing PM, while the 2 pole-pair harmonic arises from the modulation of the rotor PM by the salient stator teeth. The stator PMs of the FSPM machine establishes the 6th and 18th harmonics without any asynchronous modulation effect. However, the 4th, 8th, 16th, and 18th harmonics of are produced due to the asynchronous modulation of the stator PMs by the rotor poles. Specifically, the 4th and 16th harmonics, as well as the 8th and 28th harmonics, are of the same order modulation and have approximately the same amplitude.
Figure 7 (b) illustrates a comparison of the no-load induced voltage and the corresponding FFT analysis. It is evident that the VPM machine exhibits the highest amplitude of the fundamental voltage, reaching 1777 V, indicating its potential for offering the highest torque capability. However, the total harmonic distortion (THD) of the corresponding waveform for VPM is 11.01%, also ranking the highest among these machines, with the 5th harmonic being the primary contribution to the distortion. On the other hand, the FSPM machine demonstrates the lowest THD of 1.28% in its corresponding waveform, showcasing the advantages of winding consistency and winding complementarity [20].
The cogging torque waveforms of these three machines are displayed in Fig. 7 (c). An interesting observation is that the cogging torque curves of these machines consists of 6 cycles in one mechanical cycle, which is exactly half the number of stator slots. Among these machines, FSPM machine exhibits the highest peak cogging torque, measuring at 8.56 Nm. Figure 7 (d) demonstrates the torque waveforms at the rated speed of 13000 r/min. The VPM machine achieves the highest average output torque of 224.35 Nm, whereas the IPM and FSPM machines exhibit output torques of 179.91 Nm and 172.16 Nm, respectively. Importantly, all three machines successfully meet the design requirements for output power, with the IPM, VPM and FSPM machines achieving output powers of 244.92 kW, 305.42 kW, and 234.37 kW, respectively.
To further analyze the average output torque characteristics of the three machines, the contribution of harmonics to torque generation is depicted in Fig. 7 (e). The dominant working harmonics of the IPM and VPM machines are respectively 7 pole-pair and 10 pole-pair harmonics, which correspond to the dominant harmonic of the no-load airgap flux density given in Fig. 7 (a). For the FSPM machine, the main harmonics contributing to the average output torque are the 4, 6, 16, and 18 pole-pair harmonics, which account for 24.16%, 19.34%, 38.55%, and 22.13% of the average output torque, respectively. Interestingly, the harmonics of the 8 pole-pair harmonic result in a negative torque component, contributing − 12.14% to the overall average output torque. This occurs because the harmonics of the 8-pole pair rotate in the opposite direction to the rotor.
Figure 7 (f) and Fig. 7 (g) depict the average output torque of the three machines under different armature currents and current angles. The results indicate that the VPM machine exhibits a higher average output torque compared to the IPM and FSPM machine. Furthermore, the average output torque versus current curves for all three machines show a linear relationship, indicating their strong overload capability. Notably, both the VPM and FSPM machines achieve maximum torque when the current angle is zero, indicating the absence of a salient pole effect in these machines. The doubly-salient pole structure of the FSPM machine is primarily employed for magnetic field modulation to establish extra effective harmonics boosting the average output torque. In contrast, the IPM machine reaches its peak torque when the current angle is 15 degrees.
The losses and efficiencies of these machines under rated conditions are calculated and analyzed in Fig. 7 (h). It is worth noting that the PM eddy current loss contributes the highest percentage to the total losses in these machines. Comparatively, the combined PM eddy current loss and core loss of the VPM machine are nearly equivalent to the sum of those of the IPM and FSPM machine. Despite the VPM machine exhibiting the highest average output torque, its efficiency is relatively low. Therefore, reducing the eddy current loss of PMs in the VPM machine is a promising topic worthy of further research to improve its overall performance.
In industrial applications, machines operate within a range of variable torque and speed. To provide a more systematic comparison for the three machines, efficiency maps have been calculated and are shown in Fig. 8. However, due to calculation errors in the simulation software, the efficiency values of the marked rated points in the efficiency maps may be higher than those depicted in Fig. 7 (h). The percentages of operating areas with efficiencies greater than 90% for the IPM, VPM and FSPM machines are 82.33%, 68.23% and 61.21% of the overall operating area, respectively. It can be observed that the IPM machine has a wider range of high-efficiency operating areas compared to the VPM and FSPM machines, suggesting that this machine may achieve higher system efficiency in industrial applications. The operating points of maximum efficiency are also indicated in Fig. 8. While the average output torque at the maximum efficiency point of the FSPM machine is indeed higher than the rated point, it is also accompanied by higher torque pulsation. The key performance metrics of these machines are summarized in Table IV. The simulation results indicate that all machines meet the requirements for power, power density, and efficiency.
Table IV Electromagnetic Performances
Parameters
|
Unit
|
IPM
|
VPM
|
FPM
|
Power
|
[kW]
|
244.92
|
305.42
|
234.37
|
Average output torque
|
[Nm]
|
179.91
|
224.35
|
172.16
|
Torque ripple
|
[%]
|
2.95
|
4.71
|
11.88
|
Power density
|
[kW/kg]
|
5.66
|
7.17
|
5.56
|
Torque density
|
[Nm/kg]
|
4.16
|
5.27
|
4.08
|
Pm utilization ratio
|
[kW/cm3]
|
0.82
|
0.92
|
0.62
|
d-axis inductance
|
[mH]
|
0.93
|
1.74
|
0.57
|
q-axis inductance
|
[mH]
|
1.07
|
1.74
|
0.51
|
Cogging torque
|
[Nm]
|
4.42
|
6.50
|
8.56
|
Induced voltage
|
[V]
|
1096
|
1777
|
1173
|
THD of induced voltage
|
[%]
|
4.45
|
11.01
|
1.28
|
Copper loss
|
[kW]
|
1.45
|
1.04
|
1.24
|
PM eddy current
loss
|
[kW]
|
10.21
|
21.42
|
12.84
|
Iron loss
|
[kW]
|
3.11
|
6.27
|
2.69
|
Total loss
|
[kW]
|
14.77
|
28.73
|
16.77
|
Efficiency
|
[%]
|
93.84
|
90.96
|
92.86
|
Power factor
|
-
|
0.69
|
0.67
|
0.80
|
Slot fill factor
|
-
|
0.55
|
0.37
|
0.60
|
PM volume
|
[cm3]
|
297.13
|
332.93
|
379.69
|
Total weight of machine
|
[kg]
|
43.27
|
42.60
|
42.15
|
The results reveal that the VPM machine possesses the highest power, average output torque, and power/torque density among the three machines. However, it is important to note that the VPM machine also exhibits the highest total loss of 28.73 kW, resulting in the lowest efficiency of only 90.96%, which is the lowest among the three. The discrepancy between the d-axis and q-axis inductance of the three machines is minimal, suggesting that the reluctance torque component of these machines is nearly zero. The optimization process has resulted in a reduction in the disparity of PM volumes among the three machines. The PM volumes of the FSPM machine, while still the largest, now represents only 95% of the original structure. It is approximately 114% and 128% of the PM volumes of the IPM and VPM machines, respectively. The slot fill factor of the VPM machine is 0.37, which is the smallest among these machines, allowing for more space to be available for winding installation. The VPM machine exhibits a low power factor of 0.67, necessitating a significant power supply capacity. Additionally, the total weight of the three machines is nearly identical, with the heaviest IPM machine weighing only 2.66% more than the lightest FSPM machine.
4.2 Comprehensive Discussions
In light of the performance comparisons, it is evident that each machine type, namely IPM, VPM and FSPM machines, exhibits its own distinct advantages and limitations as All-Electric aircraft propulsion machine. The key conclusions can be summarized as follows.
(1) Compared to the VPM and FSPM machines, the IPM machine demonstrates lower torque ripple and cogging torque, as well as higher efficiency. Moreover, the IPM machine exhibits a wider range of high-efficiency operating areas (> 90%). This characteristic is advantageous for enhancing the overall operational efficiency of the system.
(2) The VPM machine indeed exhibits a large torque capability (224.35 Nm), power density (7.17 kW/kg) and torque density (5.27 Nm/kg) within the same machine volume. Additionally, under the same average output torque, the PM machine requires lower current compared to the IPM and FSPM machines. This suggests that the VPM machine operates at a lower electrical loading for the same average output torque, indicating stronger magnetic loading due to the air-gap flux modulation effect of the stator teeth. However, the VPM machine experiences more severe PM eddy current loss (21.42 kW) and iron loss (6.27 kW), highlighting the need for careful consideration of losses and significant heat dissipation. Furthermore, the notable drawback of the VPM machine is its low power factor of 0.67, which necessitates a large power supply capacity for All-Electric aircraft applications.
(3) Among the three machines, the FSPM machine exhibits the lowest THD of no-load induced voltage (1.28%) and the highest power factor (0.8). However, it also has the largest torque ripple (11.88%).
(4) For All-Electric aircraft propulsion application, the IPM and FSPM machines have not much overwhelming advantages compared with the VPM machine under the same machine volume over the entire speed range, while the VPM machine indeed has highest average output torque. If other effective measures are adopted to reduce the PM eddy current loss and improve the power factor, the merits of the VPM machine as All-Electric aircraft propulsion machine can be much extended. Additionally, the characteristic of low slot fill factor is another merit of the VPM machine, which can be reflected on reducing the difficulty of machine winding process.