Magnetic Pole Equivalence and Performance Analyses of Multi-Layer Flux-Barrier Combined-Pole Permanent-Magnet Synchronous Machines Used for Electric Vehicles

: Multi-layer ﬂux-barrier combined-pole permanent-magnet synchronous machines (MLFB-CP-PMSMs) are especially suitable for machines used in electrical vehicles (EVs), as they represent a tradeoff between electromagnetic performance and the consumption of high-priced rare-earth permanent magnets (PM). In this paper, magnetic pole equivalence and performance analyses of the MLFB-CP-PMSM are investigated. Firstly, three types of PM arrangements of combined poles are introduced, namely, parallel, series and series–parallel. Then, the magnetic circuit model and magnetic pole equivalence principle of MLFB-CP-PMSMs with different PM arrangements are analyzed. After that, the accuracy of the equivalence method is studied by comparing the machine electromagnetic performance before and after equivalence. Finally, the MLFB-CP-PMSM’s performance, including the loss, efﬁciency and electromagnetic torque, is analyzed. The results prove that the MLFB-CP-PMSM has the advantage of high efﬁciency, and the equivalence method can retain precision when the MLFB-CP-PMSM armature reaction degree varies.


Introduction
Global carbon dioxide emissions have increased rapidly in recent years, causing a series of climate problems [1][2][3]. Traditional vehicles use non-renewable fossil fuels to provide power and, at the same time, they produce large amounts of carbon dioxide emissions that are harmful to the environment. Hence, electric vehicles (EVs) are gradually replacing traditional vehicles due to their advantages of energy conservation and environmental protection [4][5][6]. The sales volume of EVs and hybrid electric vehicles (HEVs) is expected to exceed 48 million and thus exceed the sales volume of traditional vehicles by 2040 [7]. As the core component of EVs' driving systems, the motor plays an important role in the performance of EVs [8]. The multi-layer flux-barrier combined-pole permanent-magnet synchronous machines (MLFB-CP-PMSMs) are appropriately used for EVs as driving motors based on a tradeoff between performance and the consumption of high-priced rare-earth permanent magnets (PM).
The multi-layer flux-barrier structure can improve reluctance torque and reduce PM usage. In [9], a magnetic circuit model of a multi-layer flux-barrier permanent-magnet synchronous machine (PMSM) is established. The optimal machine scheme with the least PM usage was obtained by taking the anti-demagnetization ability and output torque into consideration. The torque harmonics of a multi-layer flux-barrier PMSM are analyzed and the method of reducing the torque ripple is studied in [10,11]. The PM working point of a multi-layer flux-barrier PMSM is calculated in [12], and the machine's anti-demagnetization ability is analyzed. magnetization direction, and the different colors represent different PM materials. As shown in Figure 1, the PMs of the parallel type are arranged left and right in the magnetization direction; the PMs of the series type are arranged up and down in the magnetization direction; and the PMs in the series-parallel type are arranged up and down, as well as left and right, in the magnetization direction. The machine structure is the same except for the PM structure when the MLFB-CP-PMSMs adopting different magnetic pole types are analyzed.
Energies 2023, 16, x FOR PEER REVIEW 3 of 24 According to the PM arrangements, the magnetic pole of the MLFB-CP-PMSM can be divided into three types, namely, parallel, series and series-parallel. Figure 1 shows the PM arrangements of three magnetic pole types. In Figure 1, the arrows are the PM magnetization direction, and the different colors represent different PM materials. As shown in Figure  1, the PMs of the parallel type are arranged left and right in the magnetization direction; the PMs of the series type are arranged up and down in the magnetization direction; and the PMs in the series-parallel type are arranged up and down, as well as left and right, in the magnetization direction. The machine structure is the same except for the PM structure when the MLFB-CP-PMSMs adopting different magnetic pole types are analyzed.   Table 1 shows the main motor dimensions and parameters.
In this paper, the basic principle of magnetic pole equivalence includes the following conditions: (1) various PMs in the same flux barrier are equivalent to one PM material on the basis of keeping the machine's electromagnetic performance unchanged, i.e., keeping the machine's magnetic field distribution unchanged; and (2) the magnetic parameters of the PMs (including the remanence and relative permeability) are changed after equivalence, but the PM structure parameters remain the same before and after equivalence.    Table 1 shows the main motor dimensions and parameters.
According to the PM arrangements, the magnetic pole of the MLFB-CP-PMSM can be divided into three types, namely, parallel, series and series-parallel. Figure 1 shows the PM arrangements of three magnetic pole types. In Figure 1, the arrows are the PM magnetization direction, and the different colors represent different PM materials. As shown in Figure  1, the PMs of the parallel type are arranged left and right in the magnetization direction; the PMs of the series type are arranged up and down in the magnetization direction; and the PMs in the series-parallel type are arranged up and down, as well as left and right, in the magnetization direction. The machine structure is the same except for the PM structure when the MLFB-CP-PMSMs adopting different magnetic pole types are analyzed.   Table 1 shows the main motor dimensions and parameters.
In this paper, the basic principle of magnetic pole equivalence includes the following conditions: (1) various PMs in the same flux barrier are equivalent to one PM material on the basis of keeping the machine's electromagnetic performance unchanged, i.e., keeping the machine's magnetic field distribution unchanged; and (2) the magnetic parameters of the PMs (including the remanence and relative permeability) are changed after equivalence, but the PM structure parameters remain the same before and after equivalence.   In this paper, the basic principle of magnetic pole equivalence includes the following conditions: (1) various PMs in the same flux barrier are equivalent to one PM material on the basis of keeping the machine's electromagnetic performance unchanged, i.e., keeping the machine's magnetic field distribution unchanged; and (2) the magnetic parameters of the PMs (including the remanence and relative permeability) are changed after equivalence, but the PM structure parameters remain the same before and after equivalence. Figure 3 shows the magnetic circuit model of the MLFB-CP-PMSM with a parallel PM arrangement, and it is rewritten in Figure 4. In this paper, only the magnetic circuit model of the half pole is established, as the magnetic circuit is symmetrical. The silicon steel reluctance is ignored due to the high permeability of silicon steel.   Figure 3 shows the magnetic circuit model of the MLFB-CP-PMSM with a parallel PM arrangement, and it is rewritten in Figure 4. In this paper, only the magnetic circuit model of the half pole is established, as the magnetic circuit is symmetrical. The silicon steel reluctance is ignored due to the high permeability of silicon steel. In Figures 3 and 4, Fi is the magnetomotive force (MMF) produced by the stator current; RBai and Rgi are the flux barrier reluctance and air gap reluctance, respectively; RBri_Pi is the reluctance of the saturated bridge; FP_(2i−1) and RP_(2i−1) are the equivalent MMF and reluctance of the NdFeB in the i-layer flux barrier; and FP_(2i) and RP_(2i) are the equivalent MMF and reluctance of the ferrite in the i-layer flux barrier. FP_(2i−1), RP_(2i−1), FP_(2i) and RP_(2i) can be expressed as: where Br1 and μr1 are the remanence and relative permeability of NdFeB; Br2 and μr2 are the remanence and relative permeability of ferrite; hP_(2i−1) and bP_(2i−1) are the thickness and width of the NdFeB in the i-layer flux barrier, as shown in Figure 5; hP_(2i) and bP_(2i) are the thickness and width of the ferrite in the i-layer flux barrier, as shown in Figure 5; μ0 is the vacuum permeability; and L is the stack length. Table 2 shows the values of hP_(2i−1), bP_(2i−1), hP_(2i) and bP_(2i).   In Figures 3 and 4, F i is the magnetomotive force (MMF) produced by the stator current; R Bai and R gi are the flux barrier reluctance and air gap reluctance, respectively; R Bri_Pi is the reluctance of the saturated bridge; F P_(2i−1) and R P_(2i−1) are the equivalent MMF and reluctance of the NdFeB in the i-layer flux barrier; and F P_(2i) and R P_(2i) are the equivalent MMF and reluctance of the ferrite in the i-layer flux barrier. F P_(2i−1) , R P_(2i−1) , F P_(2i) and R P_(2i) can be expressed as:

Equivalent Principle Analysis
where B r1 and µ r1 are the remanence and relative permeability of NdFeB; B r2 and µ r2 are the remanence and relative permeability of ferrite; h P_(2i−1) and b P_(2i−1) are the thickness and width of the NdFeB in the i-layer flux barrier, as shown in Figure 5; h P_(2i) and b P_(2i) are the thickness and width of the ferrite in the i-layer flux barrier, as shown in Figure 5; µ 0 is the vacuum permeability; and L is the stack length. Table 2 shows the values of h P_(2i−1) , b P_(2i−1) , h P_(2i) and b P_(2i) .
where Br1 and μr1 are the remanence and relative permeability of NdFeB; Br2 and μr2 are the remanence and relative permeability of ferrite; hP_(2i−1) and bP_(2i−1) are the thickness and width of the NdFeB in the i-layer flux barrier, as shown in Figure 5; hP_(2i) and bP_(2i) are the thickness and width of the ferrite in the i-layer flux barrier, as shown in Figure 5; μ0 is the vacuum permeability; and L is the stack length. Table 2 shows the values of hP_(2i−1), bP_(2i−1), hP_(2i) and bP_(2i).  Figure 5. Diagram of the PM width and thickness with a parallel PM arrangement.

Items Unit Value
mm 2 Figure 6 shows the magnetic circuit model of the MLFB-CP-PMSM with a parallel PM arrangement after equivalence, and it is rewritten in Figure 7. In Figures 6 and 7, R Bri_Pi is Energies 2023, 16, 4502 6 of 23 the reluctance of the saturated bridge after equivalence; F P_i and R P_i are the equivalent MMF and reluctance of the PMs after equivalence. F P_i and R P_i can be expressed as: where B r_Pi and µ r_Pi are the remanence and relative permeability of the PMs after equivalence in the i-layer flux barrier.
bP_5 mm 13 bP_2, bP_4, bP_6 mm 2 Figure 6 shows the magnetic circuit model of the MLFB-CP-PMSM with a parallel PM arrangement after equivalence, and it is rewritten in Figure 7. In Figures 6 and 7, R′Bri_Pi is the reluctance of the saturated bridge after equivalence; F′P_i and R′P_i are the equivalent MMF and reluctance of the PMs after equivalence. F′P_i and R′P_i can be expressed as: Where Br_Pi and μr_Pi are the remanence and relative permeability of the PMs after equivalence in the i-layer flux barrier.  According to the magnetic pole equivalence principle of keeping the machine's magnetic field distribution unchanged, we know that the reluctance of the saturated bridge remains unchanged before and after equivalence. By comparing Figures 4 and 7, it is found that only the equivalent MMF and reluctance of the PMs change after equivalence. Hence, the flux produced by all the PMs and the reluctance of all the PMs in the i-layer flux barrier should be unchanged before and after equivalence according to the equivalence principle. Therefore, the following equations are obtained: 1 R P_(2i−1) According to Equations (1)-(10), the following equations can be obtained: According to the magnetic pole equivalence principle of keeping the machine's magnetic field distribution unchanged, we know that the reluctance of the saturated bridge remains unchanged before and after equivalence. By comparing Figures 4 and 7, it is found that only the equivalent MMF and reluctance of the PMs change after equivalence. Hence, the flux produced by all the PMs and the reluctance of all the PMs in the i-layer flux barrier should be unchanged before and after equivalence according to the equivalence principle. Therefore, the following equations are obtained: According to Equations (1)-(10), the following equations can be obtained:

Equivalent Result Comparisons
The electromagnetic performances of the machines with a parallel PM arrangement before and after equivalence are compared to verify the equivalence method's accuracy.

Equivalent Result Comparisons
The electromagnetic performances of the machines with a parallel PM arrangement before and after equivalence are compared to verify the equivalence method's accuracy. Figures 8 and 9 show the no-load back electromotive force (EMF) and electromagnetic torque at the rated current obtained through the FEA of the MLFB-CP-PMSMs with a parallel PM arrangement.  As found in Figures 8 and 9, the waveforms of no-load back EMF and electromagnetic torque before and after equivalence match well. The fundamental amplitude of no-load back EMF and the constant component of electromagnetic torque before and after equivalence have the errors of 0.04% and 1.04%, which can be considered negligible. As found in Figures 8 and 9, the waveforms of no-load back EMF and electromagnetic torque before and after equivalence match well. The fundamental amplitude of no-load back EMF and the constant component of electromagnetic torque before and after equivalence have the errors of 0.04% and 1.04%, which can be considered negligible.  As found in Figures 8 and 9, the waveforms of no-load back EMF and electromagnetic torque before and after equivalence match well. The fundamental amplitude of no-load back EMF and the constant component of electromagnetic torque before and after equivalence have the errors of 0.04% and 1.04%, which can be considered negligible.  Figure 11 shows the magnetic circuit model of the MLFB-CP-PMSM with a series PM arrangement, and it is rewritten in Figure 12. In Figures 11 and 12, R Bri_Si is the reluctance of the saturated bridge; F S_(2i−1) and R S_(2i−1) are the equivalent MMF and reluctance of the ferrite in the i-layer flux barrier; and F S_(2i) and R S_(2i) are the equivalent MMF and reluctance of the NdFeB in the i-layer flux barrier.  Figure 11 shows the magnetic circuit model of the MLFB-CP-PMSM with a series PM arrangement, and it is rewritten in Figure 12. In Figures 11 and 12, RBri_Si is the reluctance of the saturated bridge; FS_(2i−1) and RS_(2i−1) are the equivalent MMF and reluctance of the ferrite in the i-layer flux barrier; and FS_(2i) and RS_(2i) are the equivalent MMF and reluctance of the NdFeB in the i-layer flux barrier. FS_(2i−1), RS_(2i−1), FS_(2i) and RS_(2i) can be expressed as:

Equivalent Principle Analysis
where hS_(2i−1) and bS_(2i−1) are the thickness and width of the ferrite in the i-layer flux barrier, as shown in Figure 13; hS_(2i) and bS_(2i) are the thickness and width of the NdFeB in the ilayer flux barrier, as shown in Figure 13. Table 3 shows the values of hS_(2i−1), bS_(2i−1), hS_(2i) and bS_(2i). hS_3 and hS_5 are small, which means that the corresponding PMs are thin. The method of dividing the PM into blocks in the axial direction can be used to manufacture a thin PM and ensure that the PM size meets the requirements.   F S_(2i−1) , R S_(2i−1) , F S_(2i) and R S_(2i) can be expressed as: Energies 2023, 16, 4502 10 of 23 where h S_(2i−1) and b S_(2i−1) are the thickness and width of the ferrite in the i-layer flux barrier, as shown in Figure 13; h S_(2i) and b S_(2i) are the thickness and width of the NdFeB in the i-layer flux barrier, as shown in Figure 13. Table 3 shows the values of h S_(2i−1) , b S_(2i−1) , h S_(2i) and b S_(2i) . h S_3 and h S_5 are small, which means that the corresponding PMs are thin. The method of dividing the PM into blocks in the axial direction can be used to manufacture a thin PM and ensure that the PM size meets the requirements.

Figure 12.
Rewriting of the magnetic circuit model with a series PM arrangement. Figure 13. Diagram of PM width and thickness with a series PM arrangement.   , h S_(2i) and b S_(2i) . Figure 14 shows the magnetic circuit model of the MLFB-CP-PMSM with a series PM arrangement after equivalence, and it is rewritten in Figure 15.

Items Unit Value
In Figures 14 and 15, R Bri_Si is the reluctance of the saturated bridge after equivalence; F S_i and R S_i are the equivalent MMF and reluctance of the PMs after equivalence. F S_i and R S_i are calculated as: where B r_Si and µ r_Si are the remanence and relative permeability of the PMs after equivalence in the i-layer flux barrier.
Energies 2023, 16, x FOR PEER REVIEW 11 of 24 Figure 14 shows the magnetic circuit model of the MLFB-CP-PMSM with a series PM arrangement after equivalence, and it is rewritten in Figure 15.  In Figures 14 and 15, R′Bri_Si is the reluctance of the saturated bridge after equivalence; F′S_i and R′S_i are the equivalent MMF and reluctance of the PMs after equivalence. F′S_i and R′S_i are calculated as:  Figure 14 shows the magnetic circuit model of the MLFB-CP-PMSM with a series PM arrangement after equivalence, and it is rewritten in Figure 15.  In Figures 14 and 15, R′Bri_Si is the reluctance of the saturated bridge after equivalence; F′S_i and R′S_i are the equivalent MMF and reluctance of the PMs after equivalence. F′S_i and R′S_i are calculated as: According to the equivalence principle, the following equations can be obtained on the basis of keeping the magnetic field distribution unchanged before and after equivalence: According to Equations (13)- (22), the following equations are obtained:

Equivalent Result Comparisons
In this section, the electromagnetic performances of the MLFB-CP-PMSM with a series PM arrangement before and after equivalence are compared. Figures 16 and 17 show the no-load back EMF and electromagnetic torque at the rated current of the MLFB-CP-PMSM with a series PM arrangement. As seen in Figures 16 and 17, the fundamental amplitude of no-load back EMF and the constant component of electromagnetic torque before and after equivalence have the errors of 0.94% and 0.3%, respectively.
where Br_Si and μr_Si are the remanence and relative permeability of the PMs after equivalence in the i-layer flux barrier. According to the equivalence principle, the following equations can be obtained on the basis of keeping the magnetic field distribution unchanged before and after equivalence: According to Equations (13)- (22), the following equations are obtained:

Equivalent Result Comparisons
In this section, the electromagnetic performances of the MLFB-CP-PMSM with a series PM arrangement before and after equivalence are compared. Figures 16 and 17 show the no-load back EMF and electromagnetic torque at the rated current of the MLFB-CP-PMSM with a series PM arrangement. As seen in Figures 16 and 17, the fundamental amplitude of no-load back EMF and the constant component of electromagnetic torque before and after equivalence have the errors of 0.94% and 0.3%, respectively.

Series-Parallel Magnetic Pole Equivalence
The MLFB-CP-PMSM with a series-parallel PM arrangement is shown in Figure 18a. A sketch of the rotor details is shown in Figure 18b. Except for the PM configuration, the machine structure and PM materials in Figure 18 are the same as those of the MLFB-CP-PMSM with series and parallel PM arrangements.

Series-Parallel Magnetic Pole Equivalence
The MLFB-CP-PMSM with a series-parallel PM arrangement is shown in Figure 18a. A sketch of the rotor details is shown in Figure 18b. Except for the PM configuration, the machine structure and PM materials in Figure 18 are the same as those of the MLFB-CP-PMSM with series and parallel PM arrangements.

Series-Parallel Magnetic Pole Equivalence
The MLFB-CP-PMSM with a series-parallel PM arrangement is shown in Figure 18a. A sketch of the rotor details is shown in Figure 18b. Except for the PM configuration, the machine structure and PM materials in Figure 18 are the same as those of the MLFB-CP-PMSM with series and parallel PM arrangements.  Figure 19 shows the magnetic circuit model of the MLFB-CP-PMSM with a seriesparallel PM arrangement, and it is rewritten in Figure 20. In Figures 19 and 20 Figure 19 shows the magnetic circuit model of the MLFB-CP-PMSM with a seriesparallel PM arrangement, and it is rewritten in Figure 20. In Figures 19 and 20, R Bri_SPi is the reluctance of the saturated bridge; F SP_(3i-1) and R SP_(3i-1) are the equivalent MMF and reluctance of the ferrite in the i-layer flux barrier; and F SP_(3i-2) , R SP_(3i-2) , F SP_(3i) and R SP_(3i) are the equivalent MMF and reluctance of the NdFeB in the i-layer flux barrier. The calculation formulae of F SP_(3i-2) , R SP_(3i-2) , F SP_(3i-1) , R SP_(3i-1) , F SP_(3i) and R SP_(3i) are as follows:

Items
Unit Value hSP_1, hSP_4, hSP_7 mm 4 hSP_2, hSP_3 mm 2  , h SP_(3i-1) , h SP_(3i) , b SP_(3i-2) , b SP_(3i-1) and b SP_(3i) .   Figure 21. Diagram of PM width and thickness with a series-parallel PM arrangement.  Figure 22 shows the magnetic circuit model of the MLFB-CP-PMSM with a series parallel PM arrangement after equivalence, and it is rewritten in Figure 23. In Figures 2 Figure 21. Diagram of PM width and thickness with a series-parallel PM arrangement. Figure 22 shows the magnetic circuit model of the MLFB-CP-PMSM with a series-parallel PM arrangement after equivalence, and it is rewritten in Figure 23. In Figures 22 and 23, R Bri_SPi is the reluctance of the saturated bridge after equivalence; F SP_i and R SP_i are the equivalent MMF and reluctance of the PMs after equivalence.  F′SP_i and R′SP_i can be calculated as follows: F SP_i and R SP_i can be calculated as follows:

Items Unit Value
where B r_SPi and µ r_SPi are the remanence and relative permeability of the PMs after equivalence in the i-layer flux barrier. On the basis of the equivalence principles, the following equations are obtained, keeping the magnetic field distribution unchanged before and after equivalence: According to Equations (25)-(38), the following equations can be obtained: where X and Y are expressed as: On the basis of the equivalence principles, the following equations are obtained, keeping the magnetic field distribution unchanged before and after equivalence: According to Equations (25)-(38), the following equations can be obtained: where X and Y are expressed as:

Equivalent Result Comparisons
The electromagnetic performances of the MLFB-CP-PMSM with a series-parallel PM arrangement before and after equivalence are compared in this section. Figures 24 and 25 show the no-load back EMF and electromagnetic torque at the rated current of the MLFB-CP-PMSM with a series-parallel PM arrangement. The fundamental amplitude of no-load back EMF and the constant component of electromagnetic torque before and after equivalence have the errors of 1.6% and 1.2%. Moreover, the waveforms of no-load back EMF and electromagnetic torque before and after equivalence are in good agreement.

Performance Analyses
This section analyzes the loss, efficiency and electromagnetic torque characteristics of the MLFB-CP-PMSMs, which are vital for the performance of the machines used for EVs.

Loss and Efficiency Analyses
The stator core loss and rotor core loss when the MLFB-CP-PMSMs adopting different PM arrangements operate at the rated current and rated speed (2000 rpm) are shown in Figure 26. As shown in Figure 26, the stator core loss is larger than the rotor loss in the MLFB-CP-PMSMs adopting three different PM arrangements. This is because the speed of

Performance Analyses
This section analyzes the loss, efficiency and electromagnetic torque characteristics of the MLFB-CP-PMSMs, which are vital for the performance of the machines used for EVs.

Loss and Efficiency Analyses
The stator core loss and rotor core loss when the MLFB-CP-PMSMs adopting different PM arrangements operate at the rated current and rated speed (2000 rpm) are shown in Figure 26. As shown in Figure 26, the stator core loss is larger than the rotor loss in the

Performance Analyses
This section analyzes the loss, efficiency and electromagnetic torque characteristics of the MLFB-CP-PMSMs, which are vital for the performance of the machines used for EVs.

Loss and Efficiency Analyses
The stator core loss and rotor core loss when the MLFB-CP-PMSMs adopting different PM arrangements operate at the rated current and rated speed (2000 rpm) are shown in Figure 26. As shown in Figure 26, the stator core loss is larger than the rotor loss in the MLFB-CP-PMSMs adopting three different PM arrangements. This is because the speed of rotor is the same as that of the fundamental magnetic field, which results in the reduction in rotor core loss. Moreover, it is known that the stator core loss and rotor core loss of the equivalent machine are close to those of the machine before equivalence. The PMs' eddy current loss, copper loss, core loss and mechanical loss and the efficiency of the MLFB-CP-PMSMs with the three PM arrangements are given in Table 5. The mechanical loss pfw is calculated using the following equation: where p is the machine pole pairs; v is the circumferential speed of the rotor. As shown in Table 5, the PMs' eddy current loss is negligible compared with the core loss and copper loss. The stator winding is applied with the same rated current in all three MLFB-CP-PMSMs; hence, the copper loss is the also same. The efficiencies of all three MLFB-CP-PMSMs reach 94.8%, which means that the MLFB-CP-PMSMs have the advantage of high efficiency and meet the high efficiency requirements of the driving motors used for EVs.  Figure 27 shows the average electromagnetic torque of the MLFB-CP-PMSMs with the three PM arrangements applying different winding currents. In Figure 27, IN is the rated current. The PMs' eddy current loss, copper loss, core loss and mechanical loss and the efficiency of the MLFB-CP-PMSMs with the three PM arrangements are given in Table 5. The mechanical loss p fw is calculated using the following equation:

Electromagnetic Torque Analysis
where p is the machine pole pairs; v is the circumferential speed of the rotor. As shown in Table 5, the PMs' eddy current loss is negligible compared with the core loss and copper loss. The stator winding is applied with the same rated current in all three MLFB-CP-PMSMs; hence, the copper loss is the also same. The efficiencies of all three MLFB-CP-PMSMs reach 94.8%, which means that the MLFB-CP-PMSMs have the advantage of high efficiency and meet the high efficiency requirements of the driving motors used for EVs. Figure 27 shows the average electromagnetic torque of the MLFB-CP-PMSMs with the three PM arrangements applying different winding currents. In Figure 27, I N is the rated current.

Electromagnetic Torque Analysis
Mechanical loss (W) 11.6 11.6 11.6 Efficiency (%) 94.8 94.8 94.8 Figure 27 shows the average electromagnetic torque of the MLFB-CP-PMSMs with the three PM arrangements applying different winding currents. In Figure 27, IN is the rated current.  When the winding current changes, the results obtained before and after equivalence match well, which means that the equivalence method retains its precision as the MLFB-CP-PMSM armature reaction degree varies. The electromagnetic torque consists of reluctance torque and PM torque. The reluctance torque and PM torque increase with the increment in the winding current; hence, the electromagnetic torque increases when the winding current increases.

Electromagnetic Torque Analysis
The three types of PM arrangements of combined poles use the relatively small amount ferrite to replace the NdFeB in order to avoid a significant decrease in machine performance. The ferrite volume for the three types of PM arrangements is also the same. Hence, the electromagnetic torque and loss of the MLFB-CP-PMSMs adopting the three types of PM arrangements have a small difference, as can be seen in Figures 26 and 27 and Table 5.

Demagnetization Analysis
The ferrite and NdFeB temperature coefficients of intrinsic coercivity are positive and negative, respectively. This means that the ferrite is prone to demagnetization at low temperatures, but the NdFeB is prone to demagnetization at high temperatures. Hence, the demagnetization curve temperatures of the ferrite and NdFeB are selected as 20 • C and 100 • C in this section. In this paper, the NdFeB and ferrite grades are N35UH and DM4545. Their demagnetization curves at different temperatures are shown in Figure 28. As can be seen in Figure 28, the knee points of N35UH at 100 • C and DM4545 at 20 • C are below 0 T. This means that if the flux densities of the ferrite and NdFeB are not less than 0 T, i.e., the PM's flux density is consistent with the PM's magnetization direction, the ferrite and NdFeB will not demagnetize. Moreover, when the machine's demagnetization is studied, the stator current is selected as the maximum current (1.5 I N ), and the stator magnetomotive force (MMF) is completely against the PM magnetization direction. When the winding current changes, the results obtained before and after equivalence match well, which means that the equivalence method retains its precision as the MLFB-CP-PMSM armature reaction degree varies. The electromagnetic torque consists of reluctance torque and PM torque. The reluctance torque and PM torque increase with the increment in the winding current; hence, the electromagnetic torque increases when the winding current increases.
The three types of PM arrangements of combined poles use the relatively small amount ferrite to replace the NdFeB in order to avoid a significant decrease in machine performance. The ferrite volume for the three types of PM arrangements is also the same. Hence, the electromagnetic torque and loss of the MLFB-CP-PMSMs adopting the three types of PM arrangements have a small difference, as can be seen in Figures 26 and 27 and Table 5.

Demagnetization Analysis
The ferrite and NdFeB temperature coefficients of intrinsic coercivity are positive and negative, respectively. This means that the ferrite is prone to demagnetization at low temperatures, but the NdFeB is prone to demagnetization at high temperatures. Hence, the demagnetization curve temperatures of the ferrite and NdFeB are selected as 20 °C and 100 °C in this section. In this paper, the NdFeB and ferrite grades are N35UH and DM4545. Their demagnetization curves at different temperatures are shown in Figure 28. As can be seen in Figure 28, the knee points of N35UH at 100 °C and DM4545 at 20 °C are below 0 T. This means that if the flux densities of the ferrite and NdFeB are not less than 0 T, i.e., the PM's flux density is consistent with the PM's magnetization direction, the ferrite and NdFeB will not demagnetize. Moreover, when the machine's demagnetization is studied, the stator current is selected as the maximum current (1.5 IN), and the stator magnetomotive force (MMF) is completely against the PM magnetization direction. The PMs' flux density distributions are shown in Figure 29 when the demagnetization current is applied to the MLFB-CP-PMSMs with the three PM arrangements. It can be found that the PMs' flux density is more than 0 T in the MLFB-CP-PMSMs with the three PM arrangements, which proves that the PMs in the machine will not demagnetize.  The PMs' flux density distributions are shown in Figure 29 when the demagnetization current is applied to the MLFB-CP-PMSMs with the three PM arrangements. It can be found that the PMs' flux density is more than 0 T in the MLFB-CP-PMSMs with the three PM arrangements, which proves that the PMs in the machine will not demagnetize.

Structural Analysis
This paper investigates the structural analysis of the machine rotor to avoid mechanical damage of the rotor structure caused by centrifugal force when the machine operates at high speed. The rotor stress and deformation distributions of MLFB-CP-PMSMs with three PM arrangements at maximum speed are shown in Figures 30-32. The ultimate tensile strengths of the ferrite and silicon steel are approximately 30 MPa and 500 MPa, respectively. It can be seen that the maximum stresses of the ferrite and silicon steel are lower than their respective ultimate tensile strengths. Hence, the centrifugal force cannot cause mechanical damage of the MLFB-CP-PMSMs' rotors.
Moreover, it can be seen that the PMs' deformation is very small in Figures 30-32; hence, the influence of centrifugal force on the bonding performance between the NdFeB and ferrite is also very small.

Structural Analysis
This paper investigates the structural analysis of the machine rotor to avoid mechanical damage of the rotor structure caused by centrifugal force when the machine operates at high speed. The rotor stress and deformation distributions of MLFB-CP-PMSMs with three PM arrangements at maximum speed are shown in Figures 30-32. The ultimate tensile strengths of the ferrite and silicon steel are approximately 30 MPa and 500 MPa, respectively. It can be seen that the maximum stresses of the ferrite and silicon steel are lower than their respective ultimate tensile strengths. Hence, the centrifugal force cannot cause mechanical damage of the MLFB-CP-PMSMs' rotors.

Structural Analysis
This paper investigates the structural analysis of the machine rotor to avoid mechanical damage of the rotor structure caused by centrifugal force when the machine operates at high speed. The rotor stress and deformation distributions of MLFB-CP-PMSMs with three PM arrangements at maximum speed are shown in Figures 30-32. The ultimate tensile strengths of the ferrite and silicon steel are approximately 30 MPa and 500 MPa, respectively. It can be seen that the maximum stresses of the ferrite and silicon steel are lower than their respective ultimate tensile strengths. Hence, the centrifugal force cannot cause mechanical damage of the MLFB-CP-PMSMs' rotors.
Moreover, it can be seen that the PMs' deformation is very small in Figures 30-32; hence, the influence of centrifugal force on the bonding performance between the NdFeB and ferrite is also very small.

Conclusions
This paper proposed three PM arrangements of MLFB-CP-PMSMs used for EVs, namely, the parallel type, series type, series-parallel type. The magnetic circuit models of the different MLFB-CP-PMSMs were determined, and the magnetic pole equivalence method was studied. The relationships of the PM magnetic parameters after equivalence with the PM structure parameters and PM magnetic parameters before equivalence were deduced. The errors in machine performance before and after equivalence are not more than 1.6%, which proves that the equivalence method has a high accuracy. The equivalence method can also be extended to MLFB-CP-PMSMs with more magnetic pole materials and more complex magnetic pole structures. Moreover, the MLFB-CP-PMSMs' performances were studied. The results show that the efficiencies of all three MLFB-CP-PMSMs reach 94.8%, which means that the MLFB-CP-PMSMs can meet the high efficiency requirements of the driving motors used for EVs. The electromagnetic torque increases as the winding current increases, and the equivalence method still retains a high accuracy when the MLFB-CP-PMSM armature reaction degree changes. Corresponding experimental research on the MLFB-CP-PMSMs will be carried out in future work.

Conclusions
This paper proposed three PM arrangements of MLFB-CP-PMSMs used for EVs, namely, the parallel type, series type, series-parallel type. The magnetic circuit models of the different MLFB-CP-PMSMs were determined, and the magnetic pole equivalence method was studied. The relationships of the PM magnetic parameters after equivalence with the PM structure parameters and PM magnetic parameters before equivalence were deduced. The errors in machine performance before and after equivalence are not more than 1.6%, which proves that the equivalence method has a high accuracy. The equivalence method can also be extended to MLFB-CP-PMSMs with more magnetic pole materials and more complex magnetic pole structures. Moreover, the MLFB-CP-PMSMs' performances were studied. The results show that the efficiencies of all three MLFB-CP-PMSMs reach 94.8%, which means that the MLFB-CP-PMSMs can meet the high efficiency requirements of the driving motors used for EVs. The electromagnetic torque increases as the winding current increases, and the equivalence method still retains a high accuracy when the MLFB-CP-PMSM armature reaction degree changes. Corresponding experimental research on the MLFB-CP-PMSMs will be carried out in future work.   Moreover, it can be seen that the PMs' deformation is very small in Figures 30-32; hence, the influence of centrifugal force on the bonding performance between the NdFeB and ferrite is also very small.

Conclusions
This paper proposed three PM arrangements of MLFB-CP-PMSMs used for EVs, namely, the parallel type, series type, series-parallel type. The magnetic circuit models of the different MLFB-CP-PMSMs were determined, and the magnetic pole equivalence method was studied. The relationships of the PM magnetic parameters after equivalence with the PM structure parameters and PM magnetic parameters before equivalence were deduced. The errors in machine performance before and after equivalence are not more than 1.6%, which proves that the equivalence method has a high accuracy. The equivalence method can also be extended to MLFB-CP-PMSMs with more magnetic pole materials and more complex magnetic pole structures. Moreover, the MLFB-CP-PMSMs' performances were studied. The results show that the efficiencies of all three MLFB-CP-PMSMs reach 94.8%, which means that the MLFB-CP-PMSMs can meet the high efficiency requirements of the driving motors used for EVs. The electromagnetic torque increases as the winding current increases, and the equivalence method still retains a high accuracy when the MLFB-CP-PMSM armature reaction degree changes. Corresponding experimental research on the MLFB-CP-PMSMs will be carried out in future work.