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 As the core component of the flywheel energy storage system (FESS), the flywheel energy storage motor requires low self-loss, high power density, and a wide working speed range. This paper proposes a hybrid excitation synchronous machine integrated with magnetic bearing (HESM-IMB), which is suitable for FESS. First, the structure and operation principle of the proposed HESM-IMB are explained. Afterward, the influence of field current on the electromagnetic performance of HESM-IMB is researched by the magnetic equivalent circuit (MEC). Then, the performance of HESM-IMB is present by finite element analysis (FEA). The results indicate that HESM-IMB has the advantages of adjustable air-gap flux density, high integration, and low idling loss. I. Introduction Permanent magnet (PM) synchronous machines are widely used in FESS. However, the PM machine suffers from large idling losses and poor field weakening ability. Besides, the FESS usually requires at least one axial magnetic bearing and two radial magnetic bearings, which causes an influence on rotor dynamics. In order to solve the above problems, this paper proposes a hybrid excitation synchronous machine integrated with magnetic bearing (HESM-IMB), with the advantage of adjustable air-gap flux density, high integration, and low idling loss. II. Structure and operation principle The structure of HESM-IMB is shown in Fig. 1(a). The machine adopts a hybrid excitation structure. The upper section of the out-rotor is a structure in which iron core poles and permanent magnet poles are alternately distributed, and the lower section is a bearing rotor, as a part of radial magnetic bearing. Field wingding, bias permanent magnet, and rotor permanent magnet provide working magnetic flux for the machine at the same time. Fig. 1(b) shows the magnetizing flux path of HESM-IMB. Since the magnetic resistance of the permanent magnet poles is much greater than that of the iron cores, the magnetic flux on the surface of the permanent magnet poles is almost unchanged. On the contrary, the magnetic permeability of the iron core pole is large, by adjusting the magnitude and direction of the field current, the air-gap flux density distribution on the surface of the iron core pole can be changed to meet the needs of the system under different working conditions flexibly. Similarly, the axial air gap magnetic flux on the rotor will also change with field current adjustment, so the axial force on the rotor will change greatly. Thus, an axial magnetic bearing winding at the bottom needs to be used to balance the axial force, keeping the total axial force on the rotor is around zero. As for radial magnetic bearing, the magnetic resistance of the bias permanent magnet is very large, so the flux generated by the permanent magnet poles and the field winding will hardly pass through the core of the radial magnetic bearing, the bias magnetic flux on the bearing rotor is almost unchanged, which provides convenience for control of rotor radial force. III. Simulation and analysis The back EMF waveform of HESM-IMB is shown in Fig. 2(a). In Fig. 2(b), as the field current increases, the RMS of the back EMF increases linearly, which proves that HESM-IMB has a high performance of adjusting air-gap magnetic density. Fig. 2(c) shows the idling loss in the state of field weakening and field increasing. It can be seen that field weakening can reduce the loss of the machine effectively and improve the efficiency of the system. Fig. 2(d) represents the change curve of the axial force on the rotor with the field current when the bottom axial magnetic bearing winding is not energized, which is consistent with the previous analysis. IV. Conclusion The HESM-IMB proposed in this paper can adjust the air-gap flux density flexibly, which increases power during charging and discharging, and reduces idling loss during energy storage standby. Besides, HESM-IMB integrates a radial magnetic bearing and an axial magnetic bearing in the magnetic circuit, with the advantages of high integration.

**References:**

[1] J. A. Tapia, F. Leonardi and T. A. Lipo, &quot;Consequent-pole permanent-magnet machine with extended field-weakening capability,&quot; in IEEE Transactions on Industry Applications, vol. 39, no. 6, pp. 1704-1709, Nov.-Dec. 2003.&lt;br/&gt;[2] T. D. Nguyen, K. Tseng, S. Zhang, &quot;A Novel Axial Flux Permanent-Magnet Machine for Flywheel Energy Storage System: Design and Analysis,&quot; in IEEE Transactions on Industrial Electronics, vol. 58, no. 9, pp. 3784-3794, Sept. 2011.&lt;br/&gt;[3] E. Severson, R. Nilssen, T. Undeland, &quot;Magnetic Equivalent Circuit Modeling of the AC Homopolar Machine for Flywheel Energy Storage,&quot; in IEEE Transactions on Energy Conversion, vol. 30, no. 4, pp. 1670-1678, Dec. 2015.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/492135431e04d2583404caf965c725ca.jpg)
(a) Topology. (b) Magnetizing flux paths.

![](https://assets.underline.io/uploads/markdown_image/1/image/303ca8289619826542cdfb217438faf4.jpg)
(a) The back-EMF waveform. (b) The RMS of back-EMF versus field current curve. (c) Comparison of idling loss before and after field weakening. (d) The axial force on rotor versus field current curve.

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 Research of a hybrid excitation synchronous machine integrated with magnetic bearings

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As the core component of the flywheel energy storage system (FESS), the flywheel energy storage motor requires low self-loss, high power density, and a wide working speed range. This paper proposes a hybrid excitation synchronous machine integrated with magnetic bearing (HESM-IMB), which is suitable for FESS. First, the structure and operation principle of the proposed HESM-IMB are explained. Afterward, the influence of field current on the electromagnetic performance of HESM-IMB is researched by the magnetic equivalent circuit (MEC). Then, the performance of HESM-IMB is present by finite element analysis (FEA). The results indicate that HESM-IMB has the advantages of adjustable air-gap flux density, high integration, and low idling loss. I. Introduction Permanent magnet (PM) synchronous machines are widely used in FESS. However, the PM machine suffers from large idling losses and poor field weakening ability. Besides, the FESS usually requires at least one axial magnetic bearing and two radial magnetic bearings, which causes an influence on rotor dynamics. In order to solve the above problems, this paper proposes a hybrid excitation synchronous machine integrated with magnetic bearing (HESM-IMB), with the advantage of adjustable air-gap flux density, high integration, and low idling loss. II. Structure and operation principle The structure of HESM-IMB is shown in Fig. 1(a). The machine adopts a hybrid excitation structure. The upper section of the out-rotor is a structure in which iron core poles and permanent magnet poles are alternately distributed, and the lower section is a bearing rotor, as a part of radial magnetic bearing. Field wingding, bias permanent magnet, and rotor permanent magnet provide working magnetic flux for the machine at the same time. Fig. 1(b) shows the magnetizing flux path of HESM-IMB. Since the magnetic resistance of the permanent magnet poles is much greater than that of the iron cores, the magnetic flux on the surface of the permanent magnet poles is almost unchanged. On the contrary, the magnetic permeability of the iron core pole is large, by adjusting the magnitude and direction of the field current, the air-gap flux density distribution on the surface of the iron core pole can be changed to meet the needs of the system under different working conditions flexibly. Similarly, the axial air gap magnetic flux on the rotor will also change with field current adjustment, so the axial force on the rotor will change greatly. Thus, an axial magnetic bearing winding at the bottom needs to be used to balance the axial force, keeping the total axial force on the rotor is around zero. As for radial magnetic bearing, the magnetic resistance of the bias permanent magnet is very large, so the flux generated by the permanent magnet poles and the field winding will hardly pass through the core of the radial magnetic bearing, the bias magnetic flux on the bearing rotor is almost unchanged, which provides convenience for control of rotor radial force. III. Simulation and analysis The back EMF waveform of HESM-IMB is shown in Fig. 2(a). In Fig. 2(b), as the field current increases, the RMS of the back EMF increases linearly, which proves that HESM-IMB has a high performance of adjusting air-gap magnetic density. Fig. 2(c) shows the idling loss in the state of field weakening and field increasing. It can be seen that field weakening can reduce the loss of the machine effectively and improve the efficiency of the system. Fig. 2(d) represents the change curve of the axial force on the rotor with the field current when the bottom axial magnetic bearing winding is not energized, which is consistent with the previous analysis. IV. Conclusion The HESM-IMB proposed in this paper can adjust the air-gap flux density flexibly, which increases power during charging and discharging, and reduces idling loss during energy storage standby. Besides, HESM-IMB integrates a radial magnetic bearing and an axial magnetic bearing in the magnetic circuit, with the advantages of high integration.

**References:**

[1] J. A. Tapia, F. Leonardi and T. A. Lipo, "Consequent-pole permanent-magnet machine with extended field-weakening capability," in IEEE Transactions on Industry Applications, vol. 39, no. 6, pp. 1704-1709, Nov.-Dec. 2003. [2] T. D. Nguyen, K. Tseng, S. Zhang, "A Novel Axial Flux Permanent-Magnet Machine for Flywheel Energy Storage System: Design and Analysis," in IEEE Transactions on Industrial Electronics, vol. 58, no. 9, pp. 3784-3794, Sept. 2011. [3] E. Severson, R. Nilssen, T. Undeland, "Magnetic Equivalent Circuit Modeling of the AC Homopolar Machine for Flywheel Energy Storage," in IEEE Transactions on Energy Conversion, vol. 30, no. 4, pp. 1670-1678, Dec. 2015.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/492135431e04d2583404caf965c725ca.jpg)
(a) Topology. (b) Magnetizing flux paths.

![](https://assets.underline.io/uploads/markdown_image/1/image/303ca8289619826542cdfb217438faf4.jpg)
(a) The back-EMF waveform. (b) The RMS of back-EMF versus field current curve. (c) Comparison of idling loss before and after field weakening. (d) The axial force on rotor versus field current curve.

poster

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)

![](https://assets.underline.io/uploads/markdown_image/1/image/6c78447899fe9fc221d44bbc7606e6a9.jpg)

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

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

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

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

I. INTRODUCTION Recently, high-speed electrical machines have attracted much attention in the application of gas compressors [1], which have the advantages of high power density, small volume, small moment of inertia and fast response speed. In addition, the gearbox could be eliminated, because the gas compressor could be directly driven by a high-speed electrical machine. So that the maintenance costs and noise can be reduced [2]. Moreover, compared with the squirrel cage induction machine and the switched reluctance machine, the permanent magnet synchronous machine (PMSM) has higher efficiency and has been widely used in high speed applications [3-4]. Therefore, a high speed PMSM, which is rated at 15kW, 120krpm for a gas compressor, has been designed and analyzed in this paper. The performance of the proposed machine is verified by finite element method (FEM). Furthermore, the proposed machine has been optimized to reduce wind friction loss and increase power density. II. TOPOLOGY AND OPERATION PRINCIPLE OF THE FRPM MACHINE According to the design specifications given in the left column of TABLE I, the main dimensions of the machine are designed and listed in the right column of TABLE I. Fig.1 shows the prototype of the proposed machine. The structural strength and thermal constraints are the two main design constraints of high speed PMSM [2]. Therefore, various measures are used to ensure the strength of the rotor and reduce the losses of the proposed machine. Firstly, since the permanent magnet (PM) is weak in tension, a glass fiber sleeve is applied to protect the PM in high speed operation condition. Secondly, silicon steel sheets with a smaller core loss coefficient are used for stator to reduce core loss. Moreover, the toroidal windings are applied for easy installation and reducing the end length of the wire caused by one pole pair design, thereby reducing copper loss. FEM model of the proposed machine is established to obtain the output performances, e.g., output torque, core loss. The air gap computational fluid dynamics (CFD) model of the proposed machine is established to calculate the wind friction loss of the machine. The results show that the performance of the proposed machine can meet the design specifications, with a wind friction loss of 64.22W, an efficiency of 97.85% and a power density of 6.398kW/kg. Considering the sensitivity of different parameters to the objective function, the motor optimization is divided into two steps. Considering that the wind friction loss has a significant effect on the temperature rise of the rotor, the slot width b0 and the slot height h0 are optimized and the reduced wind friction loss is selected as one optimal object function in step 1. The relationship between them is shown in Fig.2. The stator tooth width b1, stator slot depth h1 and PM thickness hPM are optimized to maximize the power density in step 2. The optimization process of each step is as follows. Firstly, the output characteristics of the proposed machine under different design parameters are obtained as sample data through FEM/CFD. After that, a total of 50 sample data has been taken for analysis and an interpolation model has been established by Kriging interpolation. The interpolation model can be used to obtain the objective function value under different design parameters. Finally, the optimal values of the design parameters are obtained by using genetic algorithm. III. RESULTS AND DISCUSSION Through FEM analysis, the electromagnetic performance of the proposed machine is verified to be satisfactory. Further, the proposed machine has been optimized. As shown in Fig.3, the wind friction loss of the optimized machine is 57.28W, the power density is 6.865kW/kg. The main output characteristics of the proposed machine and the optimized machine are compared in TABLE II. The maximum relative error between the interpolation model and the CFD/FEM is less than 1.2%, which indicates that the interpolation model is accurate. Compared with the proposed machine, the wind friction loss of the optimized machine is reduced by 9.72%, and the power density is increased by 7.25%. Note that the efficiency of two machines is almost the same, while the efficiency of the optimized machine is 97.84%. Detailed characteristics and comparison results will be discussed in the future full paper.

**References:**

[1] F. Zhang, G. Du, T. Wang, F. Wang, W. Cao, and J. L. Kirtley, “Electromagnetic Design and Loss Calculations of a 1.12-MW High-Speed Permanent-Magnet Motor for Compressor Applications,” IEEE Transactions on Energy Conversion, vol. 31, pp. 132-140, Jan. 2016. [2] D. K. Hong, B. C. Woo, Y. H. Jeong, D. H. Koo, and C. W. Ahn, “Development of an ultra high speed permanent magnet synchronous motor,” International Journal of Precision Engineering & Manufacturing, vol. 14, pp. 493-499, 2013. [3] D. Gonzalez, “Performance validation of a high-speed permanent-magnet motor for centrifugal compressors,” in 2016 XXII International Conference on Electrical Machines (ICEM), 2016, pp. 545-549. [4] Z. Huang and J. Fang, “Multiphysics Design and Optimization of High-Speed Permanent-Magnet Electrical Machines for Air Blower Applications,” IEEE Transactions on Industrial Electronics, vol. 63, pp. 2766-2774, 2016.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/84e2d1d48d0cfa071cc0559649bb87c8.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/dcac46f623c12157f584d44cb500b030.jpg)

 Design and optimization of a high-speed permanent magnet synchronous machine for gas compressors

This paper proposes a novel axial dual-stator flux-switching permanent magnet (FSPM) machine for high-speed (HS) applications. The machine adopts a fractional slot distributed winding, which has a higher winding factor, power and torque density. Firstly, the HSFSPM machine topology and operating principle are introduced. By using the principle of winding complementarity, the HSFSPM machine can counteract the even harmonics of a single stator and generate the standard sinusoidal waveform flux linkage. Besides, it can effectively reduce the cogging torque and torque ripple. Secondly, based on the three-dimensional (3D) finite element method (FEM), the no-load and load performance of the machine is obtained. Finally, a HSFSPM prototype is manufactured, and a test platform is built to test the no-load and load performance of the machine, which verified the correctness of the theoretical analysis. I． Introduction High-speed (HS) machines are widely used in many civil and industrial applications, such as flywheel energy storage transportation electrification, air compressor, etc. The rotor permanent magnet (PM) machines are used in most applications. However, the PMs in the rotor are exposed to strong centrifugal forces particularly at high speed. They are easy to be damaged due to their vulnerability even if they are protected by a retaining sleeve or the iron core [1]. The stator PM machine has neither windings nor PMs on the rotor. It has a simple structure and is suitable for high-speed operation. The PMs and the armature winding are located in the stator, which makes the PMs easy to cool [2]. The HSFSPM machine is more promising and widely studied due to its higher torque density. II．Topology and operation principle The topology of a three-phase HSFSPM machine with six stator-slots and four rotor-poles is shown in Fig. 1. There are two stators in the axial direction, named Stator_A and Stator_B. The magnetization directions of PMs in different stators are opposite. The two rotor poles differ from each other by 45° in mechanical angles. Six distributed armature winding coils are wound around 12 stator teeth. Fig. 2 shows the flux-linkage and back electromotive force (EMF) for phase winding. It can be seen that the flux linkage and back EMF generated in a single stator contain a large number of second harmonics. With the dual stator structure proposed in this paper, the axial complementarity of the windings can be used to generate a flux linkage and back EMF close to the sinusoidal waveform. The detailed motor design process and performance analysis of no-load and load conditions will be given in the full text. Fig. 1 Proposed dual-stator HSFSPM machine Topology Fig. 2 Flux-linkage and EMF for phase windings III．Experimental verification To verify the HSFSPM machine operating principle, no-load and load performance, a HSFSPM machine is manufactured, and a prototype test platform is built as shown in Fig. 3(a). Figs. 3 (b), (c) and (d) show the waveform and harmonic content of the measured results compared with the predicted values. Fig. 3 The HSFSPM machine experimental platform and test results. V. Conclusion In this paper, a novel axial dual-stator HSFSPM machine for high-speed (HS) applications is proposed. The operating principle, no-load and load performance of the machine is studied, and the correctness of the theoretical analysis is verified through experiments.

**References:**

Reference [1]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, doi: 10.1109/TIE.2013.2286777. [2]M. Liu, W. Sixel, and B. Sarlioglu, “Comparative Study of 6/4 FSPM and SPM Machine for High-Speed Applications,” IEEE Transportation Electrification Conference and Expo (ITEC), Jun. 2019, pp. 1–7, doi: 10.1109/ITEC.2019.8790622.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/58016aa02ae6123b0c0f5757d25e90a0.jpg)
Fig. 1 Proposed dual-stator HSFSPM machine Topology and Flux-linkage and EMF for phase windings

![](https://assets.underline.io/uploads/markdown_image/1/image/884780de65bba42c8740da475e2acdf0.jpg)
Fig. 3 The HSFSPM machine experimental platform and test results.

 A Novel High-Speed Dual-Stator Flux Switching Permanent Magnet Machine

Recently, permanent magnet machines have been widely used in various industrial fields, such as devices using permanent magnets having high coercive force and residual magnetic flux density due to the development of manufacturing technology. Machines rotating at high speed have the advantage of miniaturization and cost reduction through the application of a direct-drive system connected directly to the shaft of an electric device without using a gear system [1],[2]. In addition, it has the advantage of high device output and efficiency according to the power conversion device development. Owing to these advantages, they are used in various fields such as turbine generators, machine tools, and electric vehicle propulsion motors [3]. However, because the high-speed machine rotates at such high speed, the problem of damage and loss of the rotor caused by centrifugal force still exists. To prevent damage to the rotor owing to this problem, the scattering of permanent magnets is prevented through the sleeve, and the shaft uses materials with excellent mechanical rigidity [4]. However, depending on the shaft material, it has a significant influence on the electromagnetic and mechanical properties of high-speed devices. In this study, the design of high-speed permanent magnet synchronous generator with two different shaft Materials considering overhang effect and mechanical characteristics was performed. As for the shaft material, two materials were used: STS420J2, which has lower stiffness(740Mpa) than Inconel 718, but is cheaper and has paramagnetic properties, and Inconel 718, which is expensive but has excellent stiffness(1100Mpa) characteristics and is non-magnetic. Fig. 1 (a) shows the result of leakage magnetic flux analysis according to each shaft material. In the case of Inconel 718 material, the leakage magnetic flux hardly occurs due to the non-magnetic material. However, although STS420J2 has paramagnetic properties, it is deformed into ferromagnetic properties through heat treatment during rotor assembly, resulting in a large leakage magnetic flux. The leakage inductance increases due to the effect of the leakage magnetic flux, and the increase in reactance becomes a factor of the voltage drop as shown in Fig. 1 (b). Therefore, the result was obtained that the output of the generator decreased due to the voltage drop. It is important for high-speed machines to accurately predict the natural frequency mode of the rotating body during high-speed rotation. The critical speed is a phenomenon where the vacuum space rapidly increases because of resonance. This phenomenon is a direct cause of rotor damage, stator collision, noise, and bearing damage. Therefore, it is essential to analyze the critical rotor speed of a high-speed machine. The rotating body can be divided into rigid body and bending modes according to its shape, and the design should be accomplished while avoiding the bending mode frequency as much as possible. Therefore, in this study, the critical speed characteristics of the rotor were analyzed to check the resonant frequency range when the rotor designed for each material rotates at the rated speed (36,000 rpm). Resonant generation of critical speed is generally analyzed through Campbell diagram. The Campbell diagram shows the natural frequency change related to rotational speed with the rotational axis speed as the horizontal axis and the structure frequency as the vertical axis. Fig. 1 (c) is the result of the STS420J2 material, and Fig. 1 (d) is the Campbell diagram characteristics of the Inconel718 material. As a result of the characteristic analysis, the critical speed mode closest to the rated speed is the 3rd mode, and deformation occurs at approximately 41 873 rpm for STS420J2 and 52 106 rpm for Inconel 718. It was confirmed that there was no problem in the rotor design because both materials had no intersection of critical speed and bending mode when rotating at the rated speed. It can be seen that the critical speed of the rotor is formed higher as the rigidity of the Inconel 718 material is stronger. The rotor was manufactured using two materials, STS420J2 and Inconel 718, as shown in Fig. 2(b), based on the shape used for critical speed analysis, as shown in Fig. 2(a). In general, performance verification of electric machines are performed using a dynamo system or a Back-to-Back system. However, the generator designed and manufactured in this study has high rated speed and output power. Therefore, as shown in Fig. 2(c), the back-to-back system was configured using a high-speed motor, and the generator was evaluated through commercial inverter control. The design, analysis results, and measurements of the high-speed synchronous generators will be presented in more detail in the final paper.

**References:**

[1] H. Qiu, B. Tang, W. Yu, S. Yuan, J. Wu, C. Yang, and G. Cui, “Analysis of the super high-speed permanent magnet generator under unbalanced load condition”, IET Electr. Power Appl., vol. 11, no. 8, pp. 1492-1498, 2017. [2] Y. Zhang, S. McLoone, W. Cao, F. Qiu and C. Gerada, “Power Loss and Thermal Analysis of a MW High-Speed Permanent Magnet Synchronous Machine”, IEEE Trans. Energy Convers., vol. 32, no. 4, pp. 1468-1478, 2017. [3] X. Jannot, J. C. Vannier, C. Marchand, M. Gabsi, J. S. Michel, and D. Sadarnac, “Multiphysic Modeling of a High-Speed Interior PermanentMagnet Synchronous Machine for a Multiobjective Optimal Design”, IEEE Trans. Energy Convers., vol. 26, no. 2, pp. 457-467, Jun. 2011. [4] K. H. Shin, T. K. Bang, H. W. Cho, J. Y. Choi, “Design and Analysis of High-Speed Permanent Magnet Synchronous Generator With Rotor Structure Considering Electromechanical Characteristics”, IEEE Trans. Appl. Supercond., vol. 30, no. 4, Art. no. 5204305, 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/24b6eadd6d0f7ec1f90a2870f683033b.jpg)
Fig. 1. (a) Leakage flux according to shaft material (b) Voltage characteristics at load according to shaft material (c) Campbell diagram: STS420J2 (d) Campbell diagram: Inconel 718.

![](https://assets.underline.io/uploads/markdown_image/1/image/204d5d832cf3ce4e44d2187710234783.jpg)
Fig. 2. (a) Rotor shape of designed (b) rotor assembly (c) Test bed of high-speed permanent magnet synchronous generator.

 Design of High-Speed Permanent Magnet Synchronous Generator with Two Different Shaft Materials Considering Overhang Effect and Mechanical Characteristics

High-speed permanent magnet synchronous motors (PMSMs) are developed in direct-drive applications such as centrifugal compressors and vacuum pumps because of the advantages of compact size and high efficiency [1]. However, due to the small size, it has a high loss density and a limited heat dissipation surface, which causes difficulties in cooling [2]. Therefore, the accurate prediction of electromagnetic losses is very important in the design stage of high-speed PMSM. Particularly, in the case of a high-speed PMSM, it includes many harmonic components in the current applied to the machine due to pulse width modulation (PWM) inverter. Although the amplitude of harmonic components is small, they produce additional losses over and above the fundamental component. In this study, electromagnetic analysis considering PWM inverter and effective three-dimensional (3D) electromagnetic structure is proposed for predicting accurate electromagnetic losses of high-speed PMSM. Fig. 1 shows the 3D structure and side view of the high-speed PMSM and the evaluation system of the prototype. To accurately predict the applied current, it is necessary to derive the back EMF constant, resistance, and inductance using the 3D finite element method (FEM). Using the dynamic model based on the derived machine constants, it is possible to predict the applied PWM current similar to the experimental results as shown in Figs. 2(a) and (b). As shown in Fig.2(c), mechanical losses according to speed can be calculated by subtracting the core losses calculated from FEM from the measured no-load losses. Using the proposed effective 3D model, accurate electromagnetic losses such as AC and DC copper losses, core loss, and rotor loss can be predicted. Considering mechanical losses, the error between the proposed electromagnetic loss analysis and the experiment is within 3% according to the operating condition as shown in Fig. 2 (d). The analysis, discussions, and measurements of high-speed PMSM will be explained in more detail in the full paper.

**References:**

[1] 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. [2] D.-K. Hong, B.-C. Woo, and D.-H. Koo, “Ultra High Speed Motor Supported by Air Foil Bearings for Air Blower Cooling Fuel Cells,” IEEE Trans. Magn., Vol. 48, No. 2, pp. 871–874, 2012.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/49e65a54b9f9184c7473a643d76a949e.jpg)
Fig. 1. (a) Structure of HPMSM with concentrated winding and (b) performance evaluation system.

![](https://assets.underline.io/uploads/markdown_image/1/image/d6999679273e0606e88eeed21bba2afd.jpg)
Fig. 2. Comparison with analysis and experimental results: (a) estimated, (b) measured phase current, (c) measured mechanical loss, and (d) electromagnetic losses.

 Characteristic Analysis and Experimental Study for Accurate Prediction of Electromagnetic Losses considering Current Harmonics in High-Speed Permanent Magnet Synchronous Motors

In this paper, a 40kW, 36000rpm high-speed permanent magnet synchronous generator（HSPMSG） with the ambient temperature of 350 Celsius is taken as an example to study the accurate calculation of iron loss. Considering the influence of high temperature and high frequency on the loss and electromagnetic performance of electromagnetic materials, the corresponding iron loss coefficient is fitted according to the variable coefficient iron loss separation model. Then, based on the field-circuit co-simulation method, the influence of switching frequencies and modulation ratios on the iron loss characteristics of the HSPMSG under the conditions of SVPWM modulation is studied. The calculation accuracy of the iron loss is improved. Finally, the effectiveness of the proposed method is verified by the experimental results, which provides a reference for the precise analysis of iron loss of the same type of HSPMSG. I. Introduction High-speed permanent magnet synchronous generators have drawn more and more attention due to the advantages of high-power density and high efficiency in the fields of aerospace applications. However, due to the poor heat dissipation conditions, it may lead to the excessive temperature of the PMs and increase the risk of irreversible demagnetization. A method combining 2-D nonlinear finite element analysis with 3-D frequency-domain harmonic analysis is proposed in [1], the motor loss under the influence of the harmonic field generated by the inverter is calculated. The iron loss analysis of HSPMSM considering the influence of multi-physical factors is proposed in [2], but the influence of harmonic current under inverter PWM modulation is not considered. The total loss value of a 100kW, 32000rpm HSPMSM is calculated by numerical analysis and verified by test results in [3], but it did not separate the calculation of each loss. The novelty of this paper is as follows. Considering the influence of temperature and frequency on the iron loss. The influence of switching frequencies and modulation ratios on the iron-loss characteristics of high-temperature HSPMSG under the conditions of SVPWM modulation is studied based on the method of field-circuit coupling co-simulation, which improves the calculation accuracy of the iron-loss of the HSPMSGs. II. Loss Performance Test The magnetization and loss characteristics of electromagnetic materials are not only related to temperature, but also related to frequency. Therefore, it is necessary to evaluate the temperature-frequency-magnetization characteristics and temperature-frequency-loss characteristics of electromagnetic materials. The loss characteristics of 1J22 soft magnetic alloy materials at the frequency of 1000Hz is shown as Fig.1. III. Variable Coefficient Iron Loss Separation Model In this paper, based on the orthogonal decomposition model, an improved variable coefficient orthogonal decomposition model is used to study the iron core loss, which takes into account the magnetization mode and the skin effect, and the variable coefficient orthogonal decomposition model suitable for calculating the iron loss of the HSPMSG is obtained. IV. Iron Loss Calculation and Analysis Based on the field-circuit co-simulation method, the influence of switching frequencies and modulation ratios on the iron loss characteristics of the HSPMSG under the conditions of SVPWM modulation is studied. The calculation accuracy of the iron loss is improved. V. Experimental Verification The HSPMSG test platform was built as shown in Fig.2.And the iron loss of the HSPMSG was tested. The test results are in good agreement with the calculated results, which verifies the accuracy of the previous calculation results. VI. Conclusion In this paper, the loss characteristics and electromagnetic performance of electromagnetic materials under high temperature and high frequency are tested, and the corresponding iron loss coefficients are fitted according to the variable coefficient iron loss separation model. Based on the field-circuit co-simulation method, the influence of switching frequencies and modulation ratios on the iron loss characteristics of the HSPMSG under the conditions of SVPWM modulation is studied, and the accuracy of the calculation method is verified by comparison with the test results, which is of great significance for the accurate analysis of the iron loss of the HSPMSGs.

**References:**

[1] K. Yamazaki and S. Watari, "Loss analysis of permanent-magnet motor considering carrier harmonics of PWM inverter using combination of 2-D and 3-D finite-element method," IEEE Trans Magn, vol. 41, no. 5, pp. 1980-1983, May 2005. [2] G. Liu, M. Liu and Y. Zhang，"High-speed permanent magnet synchronous motor iron loss calculation method considering multi-physics factors, " IEEE Trans. Ind. Electron., vol. 67, no. 12, pp. 10109–10120, Dec. 2020. [3] Z. Huang, Fang. J and Liu. X, "Loss calculation and thermal analysis of rotors supported by active magnetic bearings for high-speed permanent-magnet electrical machines," IEEE Trans. Ind. Electron.,vol. 63, no. 4, pp. 2027-2035, Apr. 2016.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/10719caf61cd41d320a186c9d5decd07.jpg)
Fig.1. The loss characteristics of 1J22 at the frequency of 1000Hz

![](https://assets.underline.io/uploads/markdown_image/1/image/7dac747d1f6a146b243fddb8fa08e4ef.jpg)
Fig.2. The HSPMSG test platform

 Accurate Calculation of Iron Loss of High Temperature and High Speed Permanent Magnet Synchronous Generator Under the Conditions of SVPWM Modulation

I. Introduction At present, high-speed switched reluctance motors (SRM) have been widely used in different applications, such as electric vehicle, aircraft, turbine and compressor, due to low manufacturing cost, high reliability, robustness, possible operation at high temperature, and high rotational speed [1]. However, stator loss will reduce the reliability of high-speed motor, and low loss material has been attractive candidates in motor design. In addition, the acoustic noise of high-speed SRM is relatively higher than that of induction machines and permanent magnet synchronous machines (PMSMs). It has limited the widespread development of high-speed SRM, especially for noise-sensitive applications [2]. It is widely recognized that radial force is caused by motor excitation, and radial vibration is transmitted through the stator structure and emitted from motor surface [3]. Vibration and acoustic noise will be especially intensified when excitation or its harmonic frequency is close to any natural frequencies of the motor. Therefore, it is meaningful to analyze the natural frequency and mode shapes of high-speed SRM. In addition, the effect of different control strategies on current waveform is also very obvious, which will lead to the difference of radial force and vibration. Therefore, the current optimization has been attractive research for high-speed SRM. This paper focused on modal frequency calculation and vibration analysis of high-speed SRM with amorphous alloy core. Firstly, this paper compared different current waveforms and analyzed the effect of current waveforms on radial force. Radial force calculation method was improved to adapt to amorphous alloy material. Secondly, natural frequency of high-speed SRM was calculated with properties of amorphous alloy core considered. Modal shapes of stator system were analyzed and compared. Then, the modal frequency experiment was carried out to verify the calculation method. Finally, magnetostriction of amorphous alloy core was introduced to the vibration analysis of high-speed SRM. II. Radial force of high-speed SRM A. Theoretical analysis of radial force Considering the magnetic flux density and permeability of amorphous alloy core, this paper proposed the calculation method of radial force. In addition, the harmonic distribution of stator magnetomotive force of switched reluctance motor is related to phase current and control strategy. B. Effect of current waveforms on radial force Through theoretical model, radial force could be calculated. And radial force produced by different current waveforms were compared in this paper, the comparison result was shown in Fig. 1. For angle position control (APC), current chopper can increase the fundamental wave component and reduce the dc component. From the comparison of radial force density, dc component will produce more severe radial force. III. Natural frequency calculation and experiment A. Analytical model of amorphous alloy core Different motor components, such as stator core, housing, bearings and end plates, have great effect on modal frequency and dynamic performance at high speed. All of them are related to the reliability and output performance of high-speed SRM indirectly. Based on traditional natural frequency calculation method, the effect of axial mode on high-speed motor and the properties of amorphous alloy is considered in this paper. B. Experiment and verification With axial mode considered, the natural frequency was calculated and compared with the experimental result. Mode shapes and experiment platform were shown in Fig. 2. IV. Vibration analysis of high-speed SRM with amorphous alloy core The vibration characteristics of amorphous alloy core are different from those of silicon steel core. Amorphous alloy materials have high magnetostrictive coefficient and magnetostrictive strain is related to magnetic field distribution. Through theoretical model, the relationship between magnetostrictive stress and magnetic field in the core was analyzed, and the vibration performance of amorphous alloy core can be more accurately predicted. A 20kW high-speed SRM with amorphous alloy core was manufactured and vibration experiment has been carried out, see the Fig. 1. V. Conclusion In this paper, effect of current waveform on radial force and vibration was analyzed. Through improved natural frequency calculation method, natural frequency and mode shapes of amorphous alloy core were calculated more accurately with axial mode considered. The experimental results verify that high-speed SRM with amorphous alloy core shows more severe vibration. From analysis of current harmonic distribution and radial force component, high harmonics of phase current will cause more severe radial force, which will produce high frequency vibration. By using the current chopper of the controller, certain harmonic could be effectively removed.

**References:**

[1] J. Furqani, M. Kawa, K. Kiyota, "Current Waveform for Noise Reduction of a Switched Reluctance Motor Under Magnetically Saturated Condition," in IEEE Transactions on Industry Applications, vol. 54, pp. 213-222(2018). [2] X. Guo, R. Zhong, M. Zhang, "Fast Computation of Radial Vibration in Switched Reluctance Motors," in IEEE Transactions on Industrial Electronics, vol. 65, pp. 4588-4598(2018). [3] A. H. Isfahani and B. Fahimi, "Comparison of Mechanical Vibration Between a Double-Stator Switched Reluctance Machine and a Conventional Switched Reluctance Machine," in IEEE Transactions on Magnetics, vol. 50, no. 2, pp. 293-296, Feb. 2014.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4a5785968cf4ea9aec5cb2debb0b60b6.png)
Fig. 1. Vibration analysis and experiment verification, (a) radial force analysis with ideal square-wave current, (b) radial force analysis with angle position control(APC), (c) Vibration experiment platform of high-speed SRM, (d) Experimental results of stator surface.

![](https://assets.underline.io/uploads/markdown_image/1/image/08ac5295a531e9b152999fee187a1b36.png)
Fig. 2. Analytical model, corresponding FEA result and Experiment platform.

 Current waveform for vibration analysis of high-speed switched reluctance motor with amorphous alloy core

I. Introduction In recent years, with the gradual development of wind power technology from land to sea, the unit capacity of its generating units has developed from low voltage (690V) and medium power (2-3MW) to medium voltage (3.3kV) and high power (5-10MW). For the medium-voltage high-power wind power converters with power level of 5-10MW, the switching frequency of the equipment is usually required to be within 1kHz, which brings many difficulties to the control of the converter [1]. In particular, for semi-direct drive wind power system, the operating frequency of the generator is relatively high, while the switching frequency of the converter is relatively low, which results in the problem of low sampling rate. This further increases the control difficulty of the medium voltage high power converter [2-3]. In addition, in the permanent magnet semi-direct drive wind power generation system, the operating frequency of the generator is usually greater than 100Hz, so the sampling rate is low. It also deteriorates the dynamic and steady-state performance of the traditional model predictive control with low switching frequency, and affects its stability. In order to realize the low switching frequency control of medium-voltage high-power permanent magnet synchronous generator with low sampling ratio, this paper proposes a structure and a control method of a modular frequency-multiplying inverter with low-carrier-ratio. II. System Topology and Principle The modular frequency-multiplying inverter adopts a nested H-Bridge structure. For example, a modular frequency-tripling inverter includes an inner layer, a middle layer and an outer layer. A1-A4 constitute the outer layer module, B1-B4 constitute the middle layer module, and C1-C4 constitute the inner layer module. The outer module uses independent IGBTs, and the middle and inner modules employ bidirectional switches composed of two anti-parallel IGBTs. The two anti-parallel IGBTs share a gate switch signal. The input voltage of the inverter is Vin. The output of the upper module is used as the input of the next module, and so on. The final output voltage of the inverter is Vo. The specific structure is shown in Fig. 1(a). A control signal is applied to each IGBT, where the switch at the diagonal position in the H bridge is turned on and off at the same time, the upper and lower switches on the same arm are turned on complementary, and the phase shift between each layer of modules is 120° electric angle. It can be seen from Fig. 1(b) that the frequency of the inner output voltage Vo of the inverter is three times the frequency of the outer output voltage V1. That is, a triple frequency output voltage is obtained at the fundamental switching frequency. III. Simulation According to Fig. 1(a), a simulation model is established, and the IGBT is controlled by SPWM. The input voltage Vin is 20V, and the fundamental frequency is 50Hz. Assuming that the carrier ratio of the outer switching tube is M, since the switching frequency of the three layer modules is the same, and the output frequency of the inner layer is three times the fundamental wave, the carrier ratio of the entire inverter is reduced to one third of the outer layer, i.e. M/3. The simulation results verify the proposed method. Under the condition that the fundamental frequency is 50Hz and the switching frequency of tube is not increased, an output voltage frequency of 150Hz is achieved. Analyzing the output voltage through FFT, the result shows that the third harmonic component is the highest, which is consistent with the desired result. The output voltage FFT analysis result is shown as in Fig. 2. IV. Discussion and Conclusion The structure and control method of the low-carrier-ratio frequency-multiplying inverter proposed in this paper can output voltages of several times the fundamental frequency without increasing the switching frequency. Simulations and experiments verify the method. The inverter system is simple in structure and easy to implement, and can solve the low carrier ratio control of medium-voltage high-power permanent magnet synchronous generators at low sampling rates. The inverter system can also be expanded to a more layered structure to achieve higher frequency output. The detailed analysis process and experimental results will be provided in the full manuscript.

**References:**

[1] H. Bizhani, R. Noroozian and S. M. Muyeen, IEEE Trans. on Power Electronics., Vol. 34, p. 3407-3417 (2019). [2] X. Zhao, S. Niu and W. Fu, IEEE Trans. on Magnetics., Vol. 56, p. 1-5 (2020). [3] W. Xu, R.D. Lorenz, IEEE Trans. on Industry Applications., Vol. 51, p. 3932-3942 (2015).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9d6629a6189646490cf1d18c718f1b23.jpg)
Fig. 1 (a) Low carrier ratio modular frequency-multiplying inverter structure; 
(b) Output of V1 and Vo 

![](https://assets.underline.io/uploads/markdown_image/1/image/f43b1024813a658d4714a6370e017930.jpg)
Fig. 2 Spectrum of load voltage

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