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Recently, high-speed permanent magnet (PM) motors have high output and efficiency by using rare-earth PMs. However, rare earth magnets with such advantages have major environmental disadvantages, owing to the serious environmental pollution caused during the separation and purification of rare earth materials. In addition, rare earth magnets are highly dependent on rare earth production, which is likely to lead to a surge in rare earth values. From an industrial perspective, an increase in manufacturing costs owing to dependence on rare earth PMs is inevitable, which causes production disruptions. Therefore, research on the reduction of the amount of rare earth PMs used and rare earth PM alternatives are being actively pursued.&lt;br/&gt;For most high-speed motors, a lower frequency is advantageous from a control viewpoint. Accordingly, a two-pole cylindrical magnet rotor that has an advantage in terms of output is often used. Because this requires a large amount of magnet usage, in this study, research was conducted to reduce the number of magnets in the conventional high-speed motor. We applied a hollow rotor shaft to reduce the number of magnets used while maintaining the magnetic loading ratio of conventional high-speed motors. The reduction in motor power by reducing PM usage is complemented by the redesign process through the analytical method and finite element method (FEM). A manufacturing model based on the design results was then used to conduct the experimental verification.&lt;br/&gt;The model in this study is a high-speed motor with two poles, and in early design, we compare the characteristics of concentrated and distributed windings in a 6-slot stator. The electromagnetic properties were analyzed according to each winding method, and based on this, the MMF(magneto-motive fore) characteristics on a high-speed rotor were compared and analyzed. Then, comparative verification was performed by experimenting with a hollow-shaft rotor model with concentrated windings finally applied by comparing the electromagnetic and mechanical properties according to the type of rotor considering windings. Figure 1(a) shows the 3D structure of two different winding patterns, (b) shows the rotor shape 3D structure along the hollow shaft. Figure 1(c) shows the manufacturing model to which the hollow shaft and concentrated windings are applied.&lt;br/&gt;Fig. 2(a) shows the magnetic flux line according to the winding method of the 2 pole 6-slot model. It can be confirmed that the magnetic flux lines are different according to each model with a concentrated winding with a coil pitch of one and a distributed winding with a coil pitch of two. Accordingly, to analyze the winding method influence on the motor, an MMF analysis was first performed, and the mechanical properties were considered based on the results.&lt;br/&gt;The MMF analysis was performed as follows. When the air gap is uniform, the relative permeance is constant; therefore, the distribution of the magnetic flux density of the air gap has the same distribution as that of the MMF [3]. Therefore, MMF analysis was performed based on the magnetic flux density of the air gap owing to the armature reaction of the winding method. A space harmonic method, which is an analytical method, is used to derive the air gap magnetic flux density. The space harmonic method is an electromagnetic field analysis technique that obtains magnetic vector potential from the Maxwell equation, which was used to perform an MMF analysis according to the winding methods of a high-speed PM motor [4].&lt;br/&gt;Fig. 2(b) shows the MMF analysis results of the analytical method and FEM. When comparing these two methods, the results obtained are found to be generally well matched, although there are slight harmonic differences. When a current of 15-Arms is applied in the distributed winding case and 25.5-Arms in the concentrated winding case, a similar MMF is observed.&lt;br/&gt;Fig. 2(c) shows the density distribution of electromagnetic losses. This result compares the electromagnetic losses generated in the rotor and stator when a hollow shaft is applied to the rotor. It was confirmed that the reduction in stator saturation owing to the reduction in the number of magnets decreased the core loss generated in the stator, and the current increase to match the same existing model output had a slight effect on the eddy current loss.&lt;br/&gt;Finally, Fig. 2(d) shows the line voltage according to the rotor shape under load conditions. As a result, it was confirmed that 3D analysis considering leakage through the hollow rotor shaft shape was most similar to the actual experimental results. This suggests the validity of the design results of a high-speed PM motor. Further discussion and results, including mechanical properties, are provided in the full paper.

**References:**

&lt;br/&gt;[1]   A. Damiano, A. Floris, G. Fois, I. Marongju, M. Porru, and A. Serpi, “Design of a High-Speed Ferrite-Based Brushless DC Machine for Electric Vehicles”, IEEE Trans. Ind. Appl., vol. 53, no. 5, pp. 4279-4287, Sep./Oct. 2017.&lt;br/&gt;[2]   S. Musuroi, C. Sorandaru, M. Greconici, V.N. Olarescu, M. Weinman, “Low-cost ferrite permanent magnet assisted synchronous reluctance rotor an alternative for rare earth permanent synchronous motors”, Industrial Electronics Society, IECON 2013- 39th Annual Conference of the IEEE, 10-13 Nov. 2013, Vienna, pp. 2966-2970.&lt;br/&gt;[3]   Huilin Kang, Libing Zhou, Jin Wang, “Harmonic winding factors and MMF analysis for five-phase fractional-slot concentrated winding PMSM”, 2013 International Conference on Electrical Machines and Systems (ICEMS), 16 January 2014&lt;br/&gt;[4]   P. Virtic, M. Hadziselimovic, T. Marcic, B. Stumberger, &quot;Torque analysis of an axial flux permanent magnet synchronous machine by using analytical magnetic field calculation&quot;, IEEE Trans. Magn., vol. 45, no. 3, pp. 1036-1039, Mar. 2009.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/53e4f5f4e73feb3a9c70254c06e34acf.png)
Figure 1. 3D structure of (a) two different winding patterns, (b) two different rotors and (c) Manufacturing model of concentrated winding motor

![](https://assets.underline.io/uploads/markdown_image/1/image/a285ad692aa6179108fc21f93a86e7eb.png)
Figure 2 (a) Magnetic flux lines due to winding patterns and (b) MMF waveform comparison between analytical method and FEM, (c) The electromagnetic loss density distribution, (d) line voltage according to the rotor condition

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 Experimental verification and analytical approach for Electromagnetic characteristics of a high-speed permanent magnet motor with two different rotors and winding patterns

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Recently, high-speed permanent magnet (PM) motors have high output and efficiency by using rare-earth PMs. However, rare earth magnets with such advantages have major environmental disadvantages, owing to the serious environmental pollution caused during the separation and purification of rare earth materials. In addition, rare earth magnets are highly dependent on rare earth production, which is likely to lead to a surge in rare earth values. From an industrial perspective, an increase in manufacturing costs owing to dependence on rare earth PMs is inevitable, which causes production disruptions. Therefore, research on the reduction of the amount of rare earth PMs used and rare earth PM alternatives are being actively pursued. For most high-speed motors, a lower frequency is advantageous from a control viewpoint. Accordingly, a two-pole cylindrical magnet rotor that has an advantage in terms of output is often used. Because this requires a large amount of magnet usage, in this study, research was conducted to reduce the number of magnets in the conventional high-speed motor. We applied a hollow rotor shaft to reduce the number of magnets used while maintaining the magnetic loading ratio of conventional high-speed motors. The reduction in motor power by reducing PM usage is complemented by the redesign process through the analytical method and finite element method (FEM). A manufacturing model based on the design results was then used to conduct the experimental verification. The model in this study is a high-speed motor with two poles, and in early design, we compare the characteristics of concentrated and distributed windings in a 6-slot stator. The electromagnetic properties were analyzed according to each winding method, and based on this, the MMF(magneto-motive fore) characteristics on a high-speed rotor were compared and analyzed. Then, comparative verification was performed by experimenting with a hollow-shaft rotor model with concentrated windings finally applied by comparing the electromagnetic and mechanical properties according to the type of rotor considering windings. Figure 1(a) shows the 3D structure of two different winding patterns, (b) shows the rotor shape 3D structure along the hollow shaft. Figure 1(c) shows the manufacturing model to which the hollow shaft and concentrated windings are applied. Fig. 2(a) shows the magnetic flux line according to the winding method of the 2 pole 6-slot model. It can be confirmed that the magnetic flux lines are different according to each model with a concentrated winding with a coil pitch of one and a distributed winding with a coil pitch of two. Accordingly, to analyze the winding method influence on the motor, an MMF analysis was first performed, and the mechanical properties were considered based on the results. The MMF analysis was performed as follows. When the air gap is uniform, the relative permeance is constant; therefore, the distribution of the magnetic flux density of the air gap has the same distribution as that of the MMF [3]. Therefore, MMF analysis was performed based on the magnetic flux density of the air gap owing to the armature reaction of the winding method. A space harmonic method, which is an analytical method, is used to derive the air gap magnetic flux density. The space harmonic method is an electromagnetic field analysis technique that obtains magnetic vector potential from the Maxwell equation, which was used to perform an MMF analysis according to the winding methods of a high-speed PM motor [4]. Fig. 2(b) shows the MMF analysis results of the analytical method and FEM. When comparing these two methods, the results obtained are found to be generally well matched, although there are slight harmonic differences. When a current of 15-Arms is applied in the distributed winding case and 25.5-Arms in the concentrated winding case, a similar MMF is observed. Fig. 2(c) shows the density distribution of electromagnetic losses. This result compares the electromagnetic losses generated in the rotor and stator when a hollow shaft is applied to the rotor. It was confirmed that the reduction in stator saturation owing to the reduction in the number of magnets decreased the core loss generated in the stator, and the current increase to match the same existing model output had a slight effect on the eddy current loss. Finally, Fig. 2(d) shows the line voltage according to the rotor shape under load conditions. As a result, it was confirmed that 3D analysis considering leakage through the hollow rotor shaft shape was most similar to the actual experimental results. This suggests the validity of the design results of a high-speed PM motor. Further discussion and results, including mechanical properties, are provided in the full paper.

**References:**

 [1] A. Damiano, A. Floris, G. Fois, I. Marongju, M. Porru, and A. Serpi, “Design of a High-Speed Ferrite-Based Brushless DC Machine for Electric Vehicles”, IEEE Trans. Ind. Appl., vol. 53, no. 5, pp. 4279-4287, Sep./Oct. 2017. [2] S. Musuroi, C. Sorandaru, M. Greconici, V.N. Olarescu, M. Weinman, “Low-cost ferrite permanent magnet assisted synchronous reluctance rotor an alternative for rare earth permanent synchronous motors”, Industrial Electronics Society, IECON 2013- 39th Annual Conference of the IEEE, 10-13 Nov. 2013, Vienna, pp. 2966-2970. [3] Huilin Kang, Libing Zhou, Jin Wang, “Harmonic winding factors and MMF analysis for five-phase fractional-slot concentrated winding PMSM”, 2013 International Conference on Electrical Machines and Systems (ICEMS), 16 January 2014 [4] P. Virtic, M. Hadziselimovic, T. Marcic, B. Stumberger, "Torque analysis of an axial flux permanent magnet synchronous machine by using analytical magnetic field calculation", IEEE Trans. Magn., vol. 45, no. 3, pp. 1036-1039, Mar. 2009.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/53e4f5f4e73feb3a9c70254c06e34acf.png)
Figure 1. 3D structure of (a) two different winding patterns, (b) two different rotors and (c) Manufacturing model of concentrated winding motor

![](https://assets.underline.io/uploads/markdown_image/1/image/a285ad692aa6179108fc21f93a86e7eb.png)
Figure 2 (a) Magnetic flux lines due to winding patterns and (b) MMF waveform comparison between analytical method and FEM, (c) The electromagnetic loss density distribution, (d) line voltage according to the rotor condition

poster

This paper presents a comparative study of the field modulation effects (FMEs) on consequent-pole permeant magnet (CPM) machines with different stator slot configurations, i.e., open-slot, semi-closed slot and close-slot. Due to the asymmetrical PM magneto-motive force (MMF) distributions and double-side slotting effect, the CPM machines exhibit more air-gap field harmonics for the torque production. In order to quantify the torque contributions of the various effective harmonics, the Maxwell stress tensor method (MSTD) is adopted. The torque proportions due to various air-gap field harmonics in the CPM machines with different stator slot configurations are subsequently investigated by finite element (FE) method, which confirms that the stator slot configurations have a great influence on FME. It can be found that the highest and the lowest torque proportion contributed by the modulated field harmonics can be observed in closed-slot and open-slot structures, respectively. Finally, some experimental measurements on a 12-slot/14-pole CPM machine prototype with a semi-closed slot configuration are carried out to validate the theoretical and FE analyses. I. Introduction In order to reduce permanent magnet (PM) consumption, consequent-pole PM (CPM) machines are widely investigated with hybrid excited [1], modular design [2] and multi-phase [3] in recent years. Besides, some interior CPM machines with different PM arrangements, i.e., V-shaped [4], U-shaped [5] and spoke-type [5]-[7] are studied. It demonstrates that the proposed designs exhibit comparable torque performance, high-efficiency region and relatively lower PM consumption than conventional counterparts. Moreover, the field modulation effect (FME) on CPM machine is comparatively studied with surfaced-mounted PM (SPM) machine, which shows that the CPM machine exhibits more pronounced FME than SPM case due to its double-side slotting effect [8] [9]. However, the influence of stator slot on FME of the CPM machines remain unexplained hitherto. Thus, this paper comparatively study of the FME on CPM machines with different stator slots, i.e., open-slot, semi-closed slot and closed-slot. II. Machine Topologies The illustrations of 12-slot stators with open-slot, semi-closed slot and closed-slot structures are given in Fig. 1(a), (b) and (c), respectively. In order to perform a fair comparison, the three CPM machines share the same 14-pole rotor, as shown in Fig. 1(d). Besides, in order to identify and compare the effective air-gap field harmonics for the torque production in a fair way, the same stator outer diameter, air-gap length, active stack length and current density are employed in the three CPM machine topologies. III. Comparison of Torque Contributons of Dominant Magnetic Field on CPM Machies The torque characteristics of the three CPM machines are illustrated in Fig. 1(e) and (f). It can be observed that the semi-closed slot structure exhibits the highest torque, as shown in Fig. 1(e), which is mainly due to its the lowest flux leakage. According to Maxwell stress tensor method, the instantaneous electromagnetic torque Te can be calculated by Τe=(lstkrg2/μ0)∫BrBtdθ=∑(πlstkrg2/μ0)BrkBtkcos[θrk(t)-θtk(t)]=∑Tk(t) (1) where rg is the air-gap radius. lstk is the active stack length. Tk is the instantaneous electromagnetic torque generated by the kth harmonics of radial and tangential air-gap flux densities, respectively. Thus, the contributions of the kth field harmonics to the total electromagnetic torque can be separated when the kth radial and tangential air-gap field harmonics are obtained, as illustrated in Figs. 1(f). It should be noted that, apart from the Zr order magnetic harmonic, various modulated field harmonics engage in the torque generation, which confirm that the pronounced FME in CPM machines. Besides, the Zr order harmonic contributes the highest and lowest torque proportion in open-slot and closed-slot, respectively. As a result, the highest and the lowest torque production contributed by the modulated field harmonics can be observed in closed-slot and open-slot structures, respectively. IV. Experimental Validation The stator and rotor assemblies of the CPM machine prototype with semi-closed slot configuration are shown in Figs. 2(a) and (b), respectively. The comparison of the FE predicted and measured back-EMF and average torque values are illustrated in Figs. 2(c) amd (d), respectively. Because the end flux leakage and mechanical tolerance are not considered in the FE analyses, the slight difference between the FE predicted and measured results can be observed in Figs. 2(c) and (d). Overall, a satisfactory agreement between the measured and FE predicted results confirms the theoretical analyses. The detailed analysis will be presented in the full paper.

**References:**

[1] J. A. Tapia, F. Leonardi and T. A. Lipo, IEEE Transactions on Industry Application, Vol. 39, p.1704-1709 (2003) [2] S. U. Chung, J. W. Kim and B. C. Woo IEEE Transactions on Magnetics, Vol. 47, p.4215-4218 (2011) [3] H. Dhulipati, E. Ghosh and S. Mukundan, IEEE Transactions on Energy Conversions, Vol. 34, p.2041-2051 (2019) [4] J. Li, K. Wang and H. Zhang, IEEE Transactions on Industrial Electronics, Vol. 67, p.3374-3385 (2020) [5] J. Li and K. Wang, IEEE/ASME T Transactions on Mechatronics, Vol. 24, p.2182-2192 (2019) [6] W. Liu and T, A. Lipo, IEEE Transactions on Industry Application, Vol. 54, p.5918-5929 (2018) [7] X. Ren, D. Li and R. Qu, IEEE Transactions on Energy Conversions, Vol. 33, p.2112-2121 (2018) [8] Y. Li, H. Yang and H. Lin, in Proc. XIII International Conference Electrical Machine (ICEM), pp. 65-71 (2018) [9] Y. Li, H. Yang and H. Lin, IEEE Transactions on Energy Conversions, accepted. (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7b6b32fc69a3721b8bce95d338aa550e.jpg)
Fig. 1. Machine Topologies of the CPM design with different stator slot configurations. (a) Open-slot. (b) Semi-closed slot. (c) Closed-slot. (d) CPM rotor. Torque characteristics of the CPM machines with different stator slot configurations. (e) Steady-state torque. (f) Torque proportion of the main working harmonics.

![](https://assets.underline.io/uploads/markdown_image/1/image/0b10a474aeab2a426720f5f07c6bab42.jpg)
 
Fig. 2. The CPM machine prototype with semi-closed slot. (a) Stator. (b) Rotor. Comparison of the measured and FE predicted back-EMF and average torque values. (c) Back-EMFs. (d) Average torque versus phase current.

 Comparative Study of Field Modulation Effects on Consequent-Pole PM Machines with Different Stator Slot Configurations

1. In order to extending the operating speed range and increasing the maximum torque, two design methodologies of variable-flux machines (VFMs) are proposed, which make full utilizing of the material properties of the low coercive force (LCF) magnet. The inner relationship between the permanent-magnet (PM) flux variation range and speed-torque curves is comprehensively analyzed. The variation boundary of the PM flux for non-salient-pole with id=0 control method is investigated by analytic method. Due to the complexity of the transcendental equations, the per unit system is utilized for other types of machine and control method. Because the hysteresis loops of the LCF magnet employed in VFMs are quite different, which makes it difficult for machine designers to select suitable magnet. Therefore, an ideal determination model of hysteresis loop is established considering the remanent flux density, permeability of the recoil line, knee point and coercive force of the LCF magnet. A custom method is proposed to obtain the hysteresis loop calculated form the determination model. By using the proposed methodologies, the material prosperities of the magnet can be fully utilized and provide guidance to the scholars in the initial design stage of the VFM. 2. Introduction: Owing to the controllability of the permanent-magnet (PM) magnetic field, the variable-flux machine (VFM) become a good candidate for wide-speed operating demanding areas. By applying instantaneous demagnetizing current pulse, the PM flux of the VFM can be changed with negligible copper loss [1]. Compared with the conventional PMSMs, the negative d-axis current control (flux-weakening control) used under high speed condition is superseded by the instantaneous current pulse, so the overall efficiency of the VFM can be improved. Moreover, since the no-load back electromotive force proportional to the PM flux is reduced, the machine can operate under higher speed. There are many VFM topologies proposed by scholars, which has demonstrated the concepts and verified the merits of the VFM in detailed. In order to improve the torque output capability, the hybrid-PM variable flux machines (HPM-VFMs) are proposed [2-5]. The low coercive force (LCF) magnet employed in the above mentioned VFMs are AlNiCo, SmCo and Ferrite. However, there are little design methodologies to improve the machine performance in terms of the full utilizing of the material properties of the LCF magnet. In order to address the issues mentioned above, the design methodologies of the VFM are studied in this paper. 3. Design methodology of the boundary of the PM flux variation range: Conventionally, in order to obtain wider speed range, the minimum PM flux is designed to be low enough. However, during the deeply studying of the relationship between the torque-speed curves and PM flux variation ratio, the curves of several flux variation ratio is always lower than other ratios, as shown in Fig. 1 (a).The result shows that it is unnecessary to pursuit wider flux variation range. In order to investigate the inner relationship between the flux variation ratio and speed-torque curves and find the boundary of the PM flux variation range, the machine performance is comprehensively analyzed considering the PM flux linkage, machine inductance, saliency ratio, bus voltage and current limit. The operation equations of the non-salient-pole VFM with id=0 control method is deduced, and then the PM flux variation boundary is obtained. For the non-salient-pole VFM, if the PM flux linkage after saturation magnetization is larger than the product of the d-axis inductance and the current limit, all machine always possesses speed extension capability by demagnetization process. The comparison of the torque-speed areas of the VFM with and without adopting the proposed methodology is shown in Fig 1 (c). The torque-speed curves after adopting the proposed in Fig 1 (c) is composed of many PM variation ratios. It can be seen form Fig 1 that machine 1 can obtain extra speed region after adopting the proposed methodology. The then boundaries of other types of machines and control methods are investigated. Due to the complexity of the transcendental equation, the per unit system is used. For the other machines, we can conclude that the minimum PM flux should be larger than the product of the d-axis inductance and the current limit. 4. Design methodology of the Optimum PM hysteresis loop: By comparing the hysteresis loops of the AlNiCo, SmCo and Ferrite, the hysteresis loops are quite different from each other, and it is necessary to find the suitable loop. An ideal determination model of hysteresis loop is established considering the remanent flux density, permeability of the recoil line, knee point and coercive force of the LCF magnet. The overall performance of the VFM are also considered, including maximum torque, re/demagnetization difficulty and anti-passive demagnetization ability, and the ideal hysteresis loop can be obtained. By connecting the LCF and the high-coercive force magnet in series and adjusting the ratio of the two magnet, we can customize the hysteresis loop. Based on the proposed model and the custom method of the hysteresis loop, a VFM with optimum PM hysteresis loop is designed. The simulation result shows that the PM torque of the VFM can be increased. By using the proposed methodologies, the material properties of the LCF magnet can be fully utilized.

**References:**

[1] V. Ostovic, IEEE Ind. Appl. Mag. , Vol. 9, p. 52 (2003) [2] M. Ge, J. Li and R. Qu, IEEE Trans. on Appl. Sup. Vol.28(3), p. 1-5 (2018) [3] H. Yang, Z. Q. Zhu and H. Lin, IEEE Trans. on Mag. Vol.53(5), p. 1-4 (2017) [4] A. Athavale, K. Sasaki, and R. D. Lorenz, IEEE Trans. on Ind. Appl. Vol.53, p.4318-4326 (2017) [5] Z. Q. Zhu, H. Hua, A. Pride, IEEE Trans. on Mag. Vol.53(11), p. 1-4 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/12801efde0326c8f2103714289521f41.jpg)
Comparison of the torque-speed areas of the VFM with and without adopting the proposed methodology

 Design Methodologies for Variable-Flux Machines for Fully Utilizing the Material Properties of the Magnet

Recently, new energy electrical vehicles have a great development. To achieve longer driving range and higher acceleration performance at defined battery capacity and driving conditions, there is a demand of high efficiency and high torque-speed characteristics for electrical drive machines [1-2]. One of solutions is to use rectangular conductors, e.g. hair-pin winding. It can enhance the slot filling ratio to simultaneously decrease resistance and increase heat transfer ability. Furthermore, the tooth can be kept enough width and benefits for peak performance. The peak performance in new energy electrical vehicles generally require short duration (10-60 seconds) at each speed within an allowable temperature rise (Depend on the insulation level of winding and starting temperature). However, due to the strong skin effect, the current distribution in conductors become more and more uneven with speed rising. This will bring overheat risks at high speed because the temperature rising rate in short duration is closely related to the copper loss density. In this paper, a new peak torque-speed characteristics estimation method for these machines is proposed. Not only supplied maximal voltage and current limitation are considered, but also the skin effect of conductors and transient thermal issues are investigated. The copper loss density in the last conductor which has severest skin effect can be theoretically kept constant from some speed. Firstly, the supplied maximum voltage (Um) and current (Im) are defined according to the capability of battery and power electronic unit (PEU). The electromagnetic torque (Te), d-axis voltage (Ud), q-axis voltage (Uq) and terminal voltage (Us) are calculated under specified lead angle and current intervals. By scanning all points and based on MTPA and MTPV, the conventional peak torque-speed curve is acquired. Secondly, to apply the temperature rising limitation, an analytical equation on basis of the conductor size, position and frequency is used and the AC resistance of active parts of conductors is calculated [3]. rN/rdc=φ(ξ)+N(N-1)ψ(ξ) rN represents the AC resistance at some speed due to the skin effect and rdc represents the DC resistance. Both are only related to the conductors in stator lamination core. The functions φ(ξ) and ψ(ξ) are related to the frequency and conductor size because ξ is expressed by the ratio of conductor height and skin depth. To keep the highest copper loss density constant with speed rising, the current limitation Im shall be decreased with speed rising according to below question. Im=Ib/√(φ(ξ)+N(N-1)ψ(ξ)) where Ib is the current limitation at the base speed nb. At this base speed, the copper loss density reaches the maximum allowable value. It can be defined through thermal simulation or measurement. N represents the ID of conductors in stator slot which starts counting from slot bottom. φ(ξ)=ξ(sh(2ξ)+sin(2ξ))/(ch(2ξ)-cos(2ξ)) ψ(ξ)=2ξ(sh(ξ)-sin(ξ))/(ch(ξ)+cos(ξ)) In the end, the maximum torque at each speed with similar temperature rising level in short duration will be found out and improved peak torque and power curves are finally outputted. A typical PMSM with 8 poles and 48 slots are investigated. Figure 1 and 2 show the comparison results between the conventional and proposed methods. Based on CFD simulation or measurements, the maximum copper loss density can be defined under specified S2 work condition. The special prototype with 20 thermal couples in the stator is built. The simulated torque-speed curve and measured hotspots are compared. It verifies the good effectiveness of the proposed method.

**References:**

[1] Z.Q.Zhu and D. Howe, Proceedings of the IEEE, Vol:95, 2007. [2] L. Sepulchre, M. Fadel, IEEE Transactions on Industry Application, p6081-6089, Vol:54, 2018. [3] D. Lin and P. Zhou, ICEMS, p3810-3814. Nov. 2008. [4] J. Brauer, IEEE Transactions on Magnetics, Vol: 18, Mar 1982

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/06c8a22958201169c3cffedcfe1bea96.jpg)
Comparison of peak torque and power performance between conventional and proposed methods

![](https://assets.underline.io/uploads/markdown_image/1/image/e3d42ed2af385d786bd3ed8faff91a1e.jpg)
Comparison of copper loss densities in the last conductor of stator slot between conventional (dash line) and proposed (solid line) methods

 Torque-Speed Characteristics Evaluation for Permanent Magnet Synchronous Motors with Rectangular Conductors

Most mathematical torque models for the permanent magnet synchronous machines (PMSMs) are established based on neglecting the core reluctance. In order to analyze the torque of high power density PMSMs more effectively in the saturated state, this paper has considered the core reluctance in the torque analysis and a novel torque model is proposed to adapt magnetic saturation condition. It is demonstrated by simulation and experiment that the proposed torque model is closer to the actual torque. Index TermsTorque, permanent magnet synchronous machines (PMSMs), core reluctance, high power density. I. Introduction Various torque analysis studies have been presented for permanent magnet synchronous machines (PMSMs). For instance, when the machine is gradually saturated, it is considered with the variation of dq-axis self-inductances depending on operating conditions [1] and the cross-magnetization phenomenon in the electrical machine has been subjected to detailed scrutiny [2]. In order to deal with saturation and cross-saturation, an extension of the d-q model is proposed in [3]. However, those studies have not analyzed the effect of core reluctance on magnet torque. With the saturation level in PMSMs is getting severer, this will cause the magnetic conductivity of the core to decrease rapidly, in this case, the core reluctance cannot be ignored. Although some literatures have analyzed the influence of core reluctance on the magnetic circuit, there is no specific analysis of the influence on magnet torque [4]. This paper has considered the core reluctance on the magnetic circuit and analyzed the influence of the core magnetic motive force (mmf) generated by the core reluctance on the magnet torque, then a novel magnet torque model is proposed to adapt magnetic saturation condition. Finally, the validity of the proposed torque model is verified by experiment and simulation. II. Analysis of Magnet Torque A. Neglecting the Core Reluctance In the conventional analysis of magnet torque, core reluctance can often be made much smaller than that of the air gap, in this case, the reluctance of the core can be neglected, the dominant reluctance is that of the air gap. Therefore, the stator mmf Fs is equal to the air gap mmf Fsg provided by the stator and the rotor mmf Fr is equal to the air gap mmf Frg provided by the rotor. It can be known from the literature [5], the general expression for the magnet torque for the multi-pole non-salient-pole machines could be expressed as Te=-p(μ0πDl/2g)FsFrsinδsr (1) Where μ0 is the permeability of free space, p is the number of pole-pairs and g is the length of the air gap. D is the average diameter of the air gap; l is the axial length of the air gap and δsr is the angle between the mmf of the stator and the rotor. B. Considering the Core Reluctance When the machine is in the saturated state, this will cause the magnetic conductivity of the core to decrease rapidly, the core reluctance should be considered. In this case, the mmf includes the air gap mmf and the core mmf, the expression (1) could be rewritten as Te′=-p(μ0πDl/2g)(Fs-Fst)(Fr-Frt)sinδsr (2) Then, through a series of simplification, (2) could be expressed as Te′=Te(Fgd/(Fgd+Ftd))2 (3) Where Fg is the resultant air gap mmf and Ft is the resultant core mmf. Fgd and Ftd are the d-axis components of the Fg and Ft respectively. Further detailed derivation formula and calculation method will be reported in the full paper. III. Simulation and Experiment In order to verify the analysis, a 350kW high power density interior PMSM is studied as an example. The conventional id=0 control strategy is applied to eliminate the influence of reluctance torque. The air gap magnetic field intensity Hgd and the magnetic field intensity of stator teeth Htd in the d-axis direction are obtained by finite element software. The magnetic field intensity of the machine is illustrated in Fig. 1. Because most of the core mmf is in the stator teeth, the yoke mmf is ignored. Fgd=Hgd*g, Ftd=Htd*lt and lt is the calculated length of the magnetic circuit of the stator teeth. Then a 350kW high power density interior PMSM has been prototyped and tested for validation. As shown in Fig. 2, through comparison, the magnet torque Te obtained by conventional calculation has large error. The magnet torque Te` obtained by the modified torque model is very close to the actual torque and simulation torque, which verifies the validity of the torque analysis proposed in this paper.

**References:**

 [1] G. H. Kang, J. P. Hong, G. T. Kim, and J. W. Park, “Improved parameter modeling of interior permanent magnet synchronous motor based on finite element analysis,” IEEE Trans. Mag., vol. 36, pp. 1867–1870, July 2000. [2] E. Levi and V. A. Levi, “Impact of dynamic cross-saturation on accuracy of saturated synchronous machine models,” IEEE Trans. Energy Conversion, vol. 15, pp. 224–230, June 2000. [3] Stumberger, B.; Stumberger, G.; Dolinar, D.; Hamler, A.; Trlep, M.; “Evaluation of saturation and cross-magnetization effects in interior permanent-magnet synchronous motor,” IEEE Transactions on Industry Applications, vol.39, no.5, pp. 1264- 1271, Sept.-Oct. 2003 [4] Gabriel Forstner, Andreas Kugi, Wolfgang Kemmetmüller, “A Magnetic Equivalent Circuit Based Modeling Framework for Electric Motors Applied to a PMSM With Winding Short Circuit,” IEEE Transactions on Power Electronics, vol. 35, no. 11, pp. 12285–12295, Nov. 2020. [5] S. D. Umans, Fitzgeral & Kingslye’s Electric Machinery. New York, NY, USA: McGraw-Hill, Jan. 2013.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f74ac5e1ba446481d7b22ba84c9cfaa7.jpg)
Fig. 1. The machine model and magnetic field intensity distribution.

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Fig. 2. Comparison of the torque.

 Torque Analysis of High Power Density Permanent Magnet Synchronous Machines by Considering Core Reluctance

This paper proposes a rotor design method suitable for double-layer interior permanent magnet synchronous motor (BIPMSM), which can reduce electromagnetic torque ripple and at the same time reduce the electromagnetic noise of the motor. In previous studies, the inverse cosine function (ICF) has been used for torque ripple reduction by making the air gap flux density distribution sinusoidal under a no-load condition. However, ICF can only be used in a single-layer interior rotor structure. Therefore, this article proposes a piecewise inverse cosine function (PICF) based on ICF, which can be applied to BIPMSM. To verify the validity of the proposed design method, the characteristics of 8-pole, 36-slot motors that have different rotor shapes are analyzed using finite element analysis. 1.INTRODUCTION there are a number of advantages of shaping the salient pole shoes of interior permanent magnet (IPM) synchronous machines to produce a sinusoidal air-gap flux density distribution [1]. Firstly, the phase electromotive force (EMF) will be more sinusoidal which will reduce the electromagnetic torque ripple from the machine when using sinusoidal phase currents. Secondly, cogging torque will also be reduced. Thirdly, the magnitude of the radial force in the air-gap is proportional to the square of the radial component of the air-gap flux density. Therefore, the radial force space distribution in the air-gap will contain much reduced number of space harmonics which will lower the probability of exciting stator core resonances. All of these aspects will have a positive effect on the noise and vibration behavior of the machine. In [1], the application method of inverse cosine function in single-layer interior permanent magnet synchronous motor is demonstrated in detail. After optimizing the rotor structure through the inverse cosine function, a more sinusoidal air gap flux density can be obtained under no-load conditions. In [2], the author, through finite element analysis, found that ICF can reduce the torque ripple of the motor, but at the same time it can also cause the torque to drop. In this article, PICF makes the air gap magnetic density of BIPMSM more sinusoidal, thereby reducing torque ripple and electromagnetic noise, and improving the performance of the motor. 2.PRINCIPLES OF BICF The traditional ICF can be expressed by the following formula: Bmaxcosθ=μ0Fg/Ig(θ). where Bmax is the maximum value of the air gap flux density，Ig(θ) is the air gap length using，μ0 is the permeability of vacuum and Fg is the air gap magnetic potential by PM. In the traditional ICF, the magnetic potential generated by the permanent magnet can be regarded as a fixed value, but the magnetic potential generated by the permanent magnet in BIPMSM is not a fixed value, as shown in Fig.1. Therefore, it is necessary to calculate the magnetic potential in sections according to θ1 and θ2 , so that the air gap flux density generated by each section meets the same sinusoidal distribution. 3.FINITE ELEMENT SIMULATION VERIFICATION In order to verify that based on PICF, the rotor structure designed in this paper can reduce the torque ripple and electromagnetic noise of the motor, and the finite element simulation of the designed motor rotor is carried out. It can be seen from Fig.2(a) that after the use of PICF to improve the motor rotor structure, the electromagnetic torque ripple is well suppressed, but the torque amplitude is slightly reduced, which is consistent with the conclusion in [2]. Fig.2(b) shows the two-dimensional Fourier decomposition results of the radial force before and after the optimization. PICF greatly weakens the amplitude of most electromagnetic force components, which will effectively reduce the electromagnetic noise of the motor under different operating conditions. 4.DISCUSSION Through PICF, the torque ripple of BIPMSM can be significantly reduced and the motor control accuracy can be improved. As the air gap distance increases, the electromagnetic torque of the motor will inevitably be reduced. However, PICF can greatly reduce the electromagnetic noise of the motor, and it can effectively attenuate the noise of the motor at different operating speeds.

**References:**

[1] S. A. Evans, "Salient pole shoe shapes of interior permanent magnet synchronous machines," The XIX International Conference on Electrical Machines - ICEM 2010, Rome, 2010, pp. 1-6. [2] K. Wang, Z. Q. Zhu, G. Ombach and W. Chlebosz, "Optimal rotor shape with third harmonic for maximizing torque and minimizing torque ripple in IPM motors," 2012 XXth International Conference on Electrical Machines, Marseille, 2012, pp. 397-403.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/451f4fe7202c192a822ac896e7f41f42.jpg)
Fig.1

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Fig.2

 Optimized Rotor Shape for Reducing Torque Ripple and Electromagnetic Noise

1. Introduction Ultra-high-speed (UHS) surface-mounted permanent magnet synchronous motor (SPMSM) is widely used for driving air compressor [1]. The electromagnetic losses generated by the UHS SPMSM inculde iron loss, copper loss, rotor eddy current loss, and etc. Especially, the UHS SPMSM can be have large stator iron loss and rotor eddy current loss due to its high rotational speed [2]. The stator iron loss is related to the magnetic properties of the stator iron core, and the rotor eddy current loss is related to the electrical properties of the rotor sleeve and permanent magnet (PM). In addition, the magnitude of these losses can be influenced by the armature magnetomotive force (MMF), which is the product of the number of turns and current. Accordingly, in order to determine the armature MMF, it is necessary to determine the appropriate number of turns and current magnitude in the motor design process. Since the magnetic flux density of stator iron core is different according to the armature MMF, the nonlinearity of the stator iron core must be considered in the motor design process. The contribution of this research is to propose the kriging surrogate model-based design process of UHS SPMSM considering stator iron loss and rotor eddy current loss. In the proposed design process, the nonlinearity of the stator iron loss and rotor eddy current loss according to the magnetic saturation is considered through the kriging surrogate model. The kriging surrogate model is suitable for use in electric motor design because it has high predicitive ability for reponses with nonlinear charateristics [3]. For the verification, a prototype is fabricated and the experiments wiil be conducted. 2. Kriging surrogate model-based design process Using the constructed kriging surrogate models, the motor is designed through the motor design process shown in Fig. 1. The kriging surrogate model-based design process is divided into two stages: size determination and loss minimization. In both stages, optimization techniques are applied. First, the optimization problem is defined to minimize the objective function while satisfying the constraints. Next, the design of experiments for the selected design variables is performed, and a kriging surrogate model is created. Finally, the kriging surrogate models are used to determine the optimal model that satisfies the objective function and constraints. As a result, the model designed using the kriging surrogate model improves as follow compared to the model designed using the conventional design methodology: 1.4% reduction in stator outer diameter, 11.8% reduction in stack length, and 6.4% reduction in total losses. A. Size Determination The radial dimension of the rotor is determined in consideration of the mechanical stiffness and air gap magnetic flux density. Optimization technique is applied in the size determination. The objective function is set to minimize the stack length, and the constraints are defined considering the electrical specificatons. The tooth width, yoke thickness, and the number of turns are selected as design variables. Then, the respones to be predicted by the kriging surrogate models are the stator outer diameter, stack length and line to line voltage. When kriging surrogate models are used in the motor design process, the tendency according to design variables and the nonlinearity of the core can be considered. In particular, when the current is the same, the change in the armature MMF according to the number of turns affects the magnetic flux density of the stator core. Since saturation of core is an important parameter in determining the motor size, it is considered by using the kriging surrogate model. B. Loss Minimization In this paragraph, the loss of the motor is minimized by changing the stator shape. The considered losses are iron loss, rotor eddy current loss, alternation current (AC) copper loss, and windage loss. As mentioned in section 2. A, optimization technique is applied to minimize motor losses. UHS SPMSM is designed through the kriging surrogate model for losses because the ratio of the stator core loss and the rotor eddy current loss due to the high rotational speed is large. Another major loss to consider in UHS SPMSMs is AC copper loss. As mentioned in section 1, since the frequency of the input current is large in the UHS SPMSM, the AC copper loss is also large, which is considered through kriging surrogate model. The windage loss generated in the air gap and increases with increasing rotational speed. The windage loss is also considered through the kriging surrogate model. The constraints for motor loss minimization are electrical specifications and target torque. Design variables are selected as tooth tip and slot open. Using the kriging surrogate model, the optimal model is obtained that minimizes motor loss while satisfying the constraints. 3. Result and Conclusion In this paper, a kriging surrogate model-based design process is proposed. Through the process, a motor that satisfies the required motor size and specifications is determined. As a result, the model designed using the kriging surrogate model reduced the stator iron loss by 7.6% and the rotor eddy current loss by 24.9% compared to the model designed using the conventional design methodology. As shown in Fig. 2, a prototype of the designed model is fabricated. Through the test, the validity of the designed model will be verified.

**References:**

[1] Z.Zhang, Z. Deng,and Q. Sun, IEEE Transactions on Magnetics., Vol. 55, p.1-11 (2019) [2] F. Zhou, J. Shen, and W. Fei, IEEE Transactions on Magnetics., Vol. 42, p. 3398-3400 (2006) [3] S. Kim, S.-Y. Lee, and J.-M. Kim, IEEE Transactions on Energy Conversion., Vol. 35, p.2056-2065 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e8038cd4fa9f73262d8420feee425528.jpg)
Fig. 1 Proposed kriging surrogate model-based design process

![](https://assets.underline.io/uploads/markdown_image/1/image/5df0db304ff9b96b9765d9cb3af52f65.jpg)
Fig. 2. Experimental setup for no-load test of prototype

 Kriging Surrogate Model-Based Design of Ultra-High-Speed Surface-mounted Permanent Magnet Synchronous Motor Considering Stator Iron Loss and Rotor Eddy Current Loss

Comparing with the radial flux permanent magnet (RFPM) motor, axial flux permanent magnet (AFPM) motor has higher power density, higher torque density. Especially, if the AFPM motor is designed to work at a high speed, its size will be further reduced, leading to a more compact size and a significant volume saving. In addition, the AFPM motor has a superior cooling structure. The above features will boost the application of the high speed AFPM in many potential fields, such as flywheel energy storage system, man-portable power platforms, turbo-compressors, and machining spindles, and so forth [1-3]. A 3,2000r/min, 200W AFPM generator with a slotless stator core and toroidal coils was reported in literature [4]. Literature [5] designed a single-sided AFPM machine with 100W shaft output power at 50,000r/min, and stator core is slotless and made of powder composite material. Literature [6] developed a 15kW, 25,000 r/min AFPM motor, the stator core is slotted and used amorphous alloy. A 30kW, 16,000 r/min AFPM motor has been developed for the flywheel in which a slotted stator core and distributed winding are applied [7]. A 30kW, 30,000 r/min AFPM generator having 2 stators and 3 rotors was propounded [8]. It can be found that, in low power field such as hundreds of watts, high speed AFPM machines generally apply the slotless stator. Because the stator windings occupy the air gap, which leads to a wider air gap, then the air gap flux density is low, whereupon, the power can not be designed very large. However, for kilowatt power level field, a slotted stator is necessary. Moreover, the power can be further increased by the combination of multi-layer stator and rotor. It is well known that the slotless stator core also can eliminate the cogging torque. However, slotted stator will increase ripple torque. Relative to the AFPM motor with slotless stator, how much the motor power and the torque ripple can increase for the one with the slotted stator. It is an interesting, challenging question. However, rare researches about this are reported. Therefore, first, the paper will solve the electromagnetic field of the AFPM motor analytically. Then, electromagnetic torque will be obtained by Maxwell stress tensor method (MSTM). Thirdly, an example will be carried out for the cases in which both slotless and slotted stators are considered. Finally, results of torque comparison will be given and discussed. The analytical solution is verified by 3D finite element method (FEM) and experiment data.

**References:**

[1]S. Neethu, S. P. Nikam and S. Pal, et al. IEEE T Ind Electron.,vol. 67, no. 7, pp. 5269-5277 (2020) [2]M. G. Kesgin, P Han and N. Taran, et al. in Proc. Conf. (ICRERA), pp. 1026-1031 (2019). [3]WJ Cheng, ZK Deng and L Xiao, et al. Journal of Electrical and Computer Engineering, vol. 2019, pp. 1469637 (2019) [4]S. Kumar, T. A. Lipo and B. I. Kwon, et al. IEEE Trans. Magn.,vol. 52, no. 7, pp. 8205004 (2016) [5]L Zheng, TX Wu, K. B. Sundaram, et al. IEEE International Conference on Electric Machines and Drives (2005) [6]WM Tong, YP Ci. Electric Machines and Control, vol. 20, no. 6, pp. 68-76 (2016) [7]F. Sahin, A. M. Tuckey, and A. Vandenput. IEEE Industry Applications Conference (2001) [8]M. Sadeghierad, H. Lesani, and H. Monsef, et al. Journal of Applied Sciences, vol. 9, no. 10, pp. 1915-1921 (2009)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fe375fb5c114165cee876cb4fa8e68a2.jpg)
Models of AFPM motor with slotless/slotted stator

![](https://assets.underline.io/uploads/markdown_image/1/image/17da96cf6decd8e991766ea2e804eb58.jpg)
Comparsion of results from analytical model and FE model

 Torque Comparison between Slotless and Slotted Ultra-high Speed AFPM Motors

I. Introduction The electro-hydrostatic actuators (EHA) are very attractive for the More-Electric Aircraft (MEA) due to its excellent performance such as safety, reliability, weight and cost [1]. Because of the advantages of high torque density, high efficiency, the permanent magnet synchronous machine (PMSM) can be used for the EHA [2]. When the PMSM is running at high speed, the torque ripple will cause the vibration and noise of the EHA, and the machine magnetic field will produce a lot of eddy current loss in the rotor [3]. Excessive eddy current loss of permanent magnet will lead to irreversible demagnetization at high temperature. Therefore, it is of great significance to study the torque ripple and rotor eddy current loss of high-speed PMSM for EHA applications. II. Main Body The high-speed PMSM consists of the stator, rotor, and enclosure. The structural diagram of the high-speed PMSM is shown in Fig. 1. The stator has the iron core and three phase windings, and the rotor has the stainless steel retaining sleeve, magnets, and the shaft. The rated power of the high-speed PMSM is 4 kW, and the rated speed is 18000 r/min. Fig. 2 shows the stator core losses and rotor eddy current losses density distribution at different stator slot openings of the high-speed PMSM, where the Bs0 is the width of stator slot openings.. The current I is 15.5 A, and the frequency is 600 Hz. The stator core losses of the closed slot are 118.35 W, Bs0 = 2 mm are 116.54 W. It can be found that the rotor eddy current losses are focus on the retaining sleeve and magnets. The rotor eddy current losses of the closed slot are 2.43 W, Bs0 = 2 mm are 18.64 W. The rotor eddy current losses are the minimum when the stator slot openings selected as the close slot. The cause is the larger the slot opening is, the severer the permeance variation, and the more significant the rotor eddy current losses. The torque waveforms of different stator slot openings are studied. It shows that the average torque of the Bs0 = 2 mm is 2.5 Nm, and the closed slots is 2.494 Nm, which is almost the same. The torque ripple of the Bs0 = 2 mm is 15.38%, the Bs0 = 0 is 6.56%. The torque ripple of the closed slots is almost decreasing 60% than that of the stator slot openings is 2 mm. The EMF waveforms also measured and compared with the FEA, which agrees well with the results of the FEA. The torque ripple are measured by a digital torque meter, the measured results are also agrees well with the results of the FEA. III. Conclusion This paper has analyzed the stator slot openings width for the reduction of torque ripple and rotor eddy current losses in a high-speed PMSM for the electro-hydrostatic actuator applications. It is demonstrated that when the stator slot openings selected as the closed slot, the torque ripple and rotor eddy current losses can be extremely reduced. Finally, the prototype machine with the closed slots is fabricated and experimented.

**References:**

[1] A. Trentin, P. Zanchetta, P. Wheeler, J. Clare, “Power flow analysis in electro-mechanical actuators for civil aircraft,” IET Electr Power Appl., vol. 5, no. 1, pp. 48-58, 2011. [2] Wenping Cao, Barrie C. Mecrow, et al. “Overview of Electric Motor Technologies Used for More Electric Aircraft (MEA),” IEEE Trans. Ind. Electron, vol. 59, no. 9, pp. 3523-3531, Sep. 2012. [3] D. Gerada, A. Mebarki, N. L. Brown, C. Gerada, A. Cavagnino, and A. Boglietti, “High-speed electrical machines: Technologies, trends, and developments,” IEEE Trans. Ind. Electron, vol. 61, no. 6, pp. 2946-2959, Jun. 2014.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/89ce574a6607a23ca7f3b5a72c11a071.jpg)

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 Reduction of Torque Ripple and Rotor Eddy Current Losses by Closed Slots Design in a High-speed PMSM for EHA Applications

1 Introduction Compared with ordinary motors, high-speed permanent-magnet synchronous motors (HPMSMs)[1] have obvious advantages [2]. However, under the collective influence of temperature, armature reaction and other factors, a serious temperature rise in the inner components of the motor will cause demagnetization of the permanent magnet [3]. The problems of achieving the global optimization of the motor structure parameters include the selection of a global optimization algorithm and the establishment of a fast calculation model. The bat algorithm [4] is a new heuristic algorithm. Quantum evolutionary computation [5] makes full use of the theory of quantum bits and superposition states in quantum computation. At present, the combination of quantum theory and intelligent algorithms has become a popular research method [6]. The quantum bat algorithm (QBA) [7] introduces the idea of quantum evolutionary computation into the bat algorithm and gives full play to its advantages. This algorithm is a very effective global optimization algorithm. In this paper, a regression modeling method based on a deep neural network (DNN) [8] for HPMSM structure optimization is employed. Through the network structure of the DNN multi hidden layer, the model accuracy is improved by learning the parameters layer by layer, and the calculation model of the HPMSM is established to provide high-precision and high-efficiency model support for global optimization. Based on the QBA with the DNN model, the structure parameters of the HPMSM are optimized to obtain the optimal combination to minimize the loss of the motor. The performance of the optimized HPMSM is verified by finite element simulation analysis and prototype experiments. 2 Quantum Bat Algorithm In the QBA, the probability amplitude of a qubit is directly used as the code of the current position of the bat. Considering the randomness of coding during population initialization, the coding scheme in Fig. 1(a) is adopted. The position of the bat changes according to a quantum revolving gate. Therefore, the update of the bat movement speed in the ordinary bat algorithm (BA) is converted to the update of the quantum revolving gate angle, and the update of the bat position is converted to the update of the qubit probability amplitude for the bat. Suppose that the optimal position searched by the whole population is Pg, then, the bat status update rules are as Fig. 1(b). 3 Deep Neural Network Model The DNN model is composed of multilayer adaptive nonlinear elements [16], and it continuously reduces the model prediction error by learning layer by layer. The structure of the DNN algorithm can be divided into a visual layer and hidden layer. The visual layer includes the input layer and the output layer. Its basic structure is shown in Fig. 1(c). The DNN adopted in this paper is a fully connected neural network, where each layer can be expressed as a weight W multiplied by a vector x and is composed of neurons, and the deviation quantity b is added. 4 Design Optimization of the HPMSM Fig. 1 (d) shows an HPMSM that has 18 slots and 2 inner rotor pole pairs. With the initial main design parameters, which take into account the limitation of the current density of the conductors in the stator slots, the magnitude of the ampere conductors of the total electric loading are obtained based on magnetic circuit computations; they are shown in Fig. 2(a). According to the constraint conditions of the structural parameters, a 5-factor 4-level variable scale is given, as shown in Fig. 2(b), and there are 1024 orthogonal combination modes in total. Since the temperature rise of the HPMSM is directly related to the loss of the motor, the loss under different structural parameters is used to build the sample library. To verify the accuracy of the DNN rapid calculation model established in this paper, sample points are randomly selected in the solution domain. The total loss and the output torque of the test samples simulated by the FEM and DNN model are predicted and compared. The difference between the DNN model and FEM simulation is calculated by η. The accuracy verification of the DNN model is shown in Fig. 2(c). To achieve better overall performance, the HPMSM is optimized through a single-objective problem. The output torque and total loss for different iteration numbers are shown in Fig. 2(d). The final design parameters after optimization are given in Fig. 2(e). When the HPMSM is working at the rated working point, as shown in Fig. 8, in which the rated speed is 100 krpm, and the output torque is 1.026 Nm, the efficiency can reach 96%. Within the speed range of 20 krpm to 120 krpm, the efficiency can be maintained at higher than 93%. 4 Conclusion This paper systematically studies the QBA optimization method combined with a DNN model for the structure optimization problem of HPMSMs. The DNN models for the objective functions of the loss and torque are proven to be accurate enough to replace the FEM simulation. Instead of calculating a FEM simulation for each particle, applying DNN models can shorten the working time of the optimization process. The QBA optimization algorithm has a faster convergence speed than the traditional PSO algorithm.

**References:**

[1] J. Ahn, C. Han, C. Kim, and J. Choi, "Rotor Design of High-Speed Permanent Magnet Synchronous Motors Considering Rotor Magnet and Sleeve Materials," IEEE Transactions on Applied Superconductivity, vol. 28, no. 3, pp. 1-4, 2018. [2] H. L. Shuhua Fang, Haitao Wang, Hui Yang, Heyun Lin, "High Power Density PMSM With Lightweight Structure and High-Performance Soft Magnetic Alloy Core," IEEE Transactions on Applied Superconductivity vol. 29, no. 2, pp. 1-5, 2019. [3]Y. C. J. Z. Y. F. Y. G. Y. Xia, "Multi-field coupling finite-element analysis of the temperature rise in permanent magnet synchronous motor applied for high speed train," presented at the 2016 19th International Conference on Electrical Machines and Systems (ICEMS), Chiba, Japan, 13-16 November, 2016, 16650589. [4]H. L. Y. L. Y. S. F. L. Y. Man, "A Hybrid Bat Algorithm for Economic Dispatch With Random Wind Power," IEEE Transactions on Power Systems, vol. 33, no. 5, pp. 5052 - 5061, 2018. [5]S. L. H. S. Y. P. N. J. Huang, "A Quantum-Inspired Evolutionary Algorithm for Multi-Objective Design," IEEE Transactions on Magnetics vol. 49, no. 5, pp. 1609 - 1612, 2013. [6]Y. L. S. Y. Z. Ren, "A Methodology Based on Quantum Evolutionary Algorithm for Topology Optimization of Electromagnetic Devices," IEEE Transactions on Magnetics vol. 55, no. 6, p. 7204004, 2019. [7]H. T. u. H. M. U. A. M. Z. Z. H. M. A. Faiz, "Economic load dispatch using novel bat algorithm with quantum and mechanical behaviour," presented at the 2017 International Symposium on Wireless Systems and Networks (ISWSN), Lahore, Pakistan, 19-22 November 2017, 2017. [8]Z. L. L. Bai, "Evaluating the supplier cooperative design ability using a novel support vector machine algorithm," presented at the 2008 12th International Conference on Computer Supported Cooperative Work in Design, Xi'an, China, 16-18 April 2008, 2008.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/530f2a0e8f322bb38900f7705db033a1.jpg)
(a) Quantum Bat Algorithm. (b) The flow chart of the QBA. (c) Basic structure of the DNN. (d) Configuration and mechanical structure of the proposed machine.

![](https://assets.underline.io/uploads/markdown_image/1/image/e9bb3518c740c68e8bc3479544bde2a0.jpg)
(a) Main Design Parameters (b) Structure Parameter Levels of the HPMSM (c)Accuracy verification of the model. (d)Output torque and total loss for different iteration numbers. (e) The optimized HPMSM

 Optimization of a High-Speed PMSM Based on the Quantum Evolutionary Bat Algorithm and Deep Neural Network

This study deals with the electromagnetic loss analysis through the coupling analysis of the controller motor considering the SVPWM control of a high-speed permanent magnet motor for driving a centrifugal pump. High-speed mechanical systems are suitable for applications such as compressors, vacuum pumps, turbine generators, flywheel energy storage systems, drilling machine tools, and electric vehicle propulsion motors in various industries such as transportation, defense, energy, aviation, and general industry. They are being developed for many industrial applications. It is not an exaggeration to say that the proportion of high-speed motors in the modern industry is on the rise. High-speed motors are operated by a power conversion device and a controller, and owing to the development of power conversion elements, high-speed and high-power motors are becoming possible [1]. In addition, there is a growing interest in the analysis of the loss and heat of high-speed motors in industry and academia. In the existing studies, the loss analysis of the motor is primarily performed through the current source analysis, which has the disadvantage of not considering the current harmonics caused by the switching of the controller. Therefore, it is difficult to predict the electromagnetic loss caused by current harmonics. In addition, few researchers have published a study on the characteristic analysis of the motor considering the current harmonics, but it is difficult to obtain accurate analysis results in all operating areas because only a single parameter of the motor is considered [2]. In addition, there is significant interest in reducing the loss and heat generation of high-speed permanent magnet motors. There are certain motor problems because of reduced efficiency and increased calorific value owing to electromagnetic losses that were not considered in the design stage. In particular, the heat generated in the rotating body of high-speed motors using sleeves in the industry is transferred to both bearings along the shaft. It also causes serious problems such as failure of bearings and shortening of life [3]. Hence, the electromagnetic loss analysis of the motor based on the controller and motor co-simulation analysis are important. Therefore, this study deals with the electromagnetic loss and dynamic characteristics analysis considering the inverter drive of a high-speed permanent magnet synchronous motor for a centrifugal pump. The motor and the SVPWM inverter were modeled, and the environment for the co-simulation analysis of the controller and the motor was established. The designed motor was manufactured, and the motor performance was evaluated. As illustrated in Fig. 1(a), a co-simulation analysis system was constructed using the analyzed motor model and the controller conceptual diagram. Results such as current applied to the motor according to the speed command and load torque, speed response characteristics, torque characteristics, and torque ripple were obtained. Fig. 1(b) depicts an experimental setup for the evaluation of a high-speed permanent magnet motor. The high-speed permanent magnet motor was combined with a centrifugal pump and a torque sensor and was operated through a controller. Fig. 1(c) presents the voltage and current waveforms of the motor measured in the rated speed and rated output range. It could be verified that the rated current was applied to the motor within the range not exceeding the voltage limit. Fig. 2(a) presents a comparison of the sinusoidal current and the incoming current waveforms of the motor during the coupling analysis. It could be verified that harmonics were included in the current waveform by the SVPWM switching frequency and were introduced into the motor. Fig. 2(b) shows the order and magnitude of the harmonic components included in the current waveform. Figs. 2(c) and (d) depict the analysis results of the loss of iron and permanent magnet rotors that occur during general sinusoidal current analysis and coupling analysis. Notably, the iron loss and eddy current loss increased owing to the harmonic components included in the current. Therefore, coupling analysis is important for detailed electromagnetic loss analysis. Based on the results presented here, it is judged that this study will contribute to the related industries by designing, developing, and evaluating the performance of a motor that can be used for industrial 12,500 rpm and 100 hp class centrifugal pumps. In addition, the co-simulation analysis method used in this dissertation is considered to be useful in the design of high-speed motors that can be applied to various industrial applications.

**References:**

[1] D.-K. Hong, D. Joo, Y.-H. Jeong, and D.-H. Koo, IEEE Transactions on Magnetics, vol.49, no.7, p. 4072, 2013. [2] Yunkai Huang , Jianning Dong , Long Jin , Jianguo Zhu , and Youguang Guo, IEEE Trans. Magnetics, Vol.47, No.10, October 2011. [3] Ziyuan Huang, Jiancheng Fang, Member, IEEE, Xiquan Liu, and Bangcheng Han, IEEE Trans. on Industrial Electronics, Vol.63, No.4, APRIL 2016.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c832222bcfe2429056186ddf507e509b.jpg)
Fig. 1. (a) Concept diagram of the co-simulation analysis of motor including speed controller and current controller. (b) Motor performance test bed combined with centrifugal pump. (c) Motor voltage and current measurement results at rated speed and rated output.

![](https://assets.underline.io/uploads/markdown_image/1/image/9b1ae76ed958d99138172dea6058e43a.jpg)
Fig. 2. (a) Comparison of sinusoidal current and PWM current waveforms using co-simulation method. (b) Harmonic analysis result of motor current using co-simulation analysis. (c) Core loss analysis result according to current waveform. (d) Rotor loss analysis result according to current waveform.

 Electromagnetic Loss Analysis of High-Speed Permanent Magnet Motors for High-speed and High-head Centrifugal Pump using Co-Simulation Method with Controller

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