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—In order to reduce the cogging torque of the permanent magnet (PM) machine more effectively, a novel conception of the regional magnetic compensation (RMC) is introduced. An effective approach from the perspective of dynamic control for cogging torque reduction based on RMC is then proposed, by which the cogging torque could be reduced.&lt;br/&gt;&lt;i&gt;Index Terms&lt;/i&gt;—Cogging torque, permanent magnet machines, dynamic reduction method, regional magnetic compensation.&lt;br/&gt;&lt;br/&gt;I. Introduction&lt;br/&gt;The cogging torque is an significant issue of the PM machines, which is an inherent shortcoming of PM machines. It leads to mechanical vibration, noise, and deteriorate the performances of the PM machines [1]. A wide variety of design methods for minimizing the cogging torque of PM machines have been comprehensively studied [1-3]. The existing cogging torque reduction methods can be mainly divided into two types: stator design and rotor design techniques. Undoubtedly, these methods can weaken the cogging torque but may result in the degradation of other machine performances, such as the unnecessary harmonics introduction, cost increase, and efficiency reduction, etc. On the other hand, it is impossible to weaken the cogging torque of a PM machine that has already been manufactured. Therefore, weakening the cogging torque from the perspective of dynamic control is worth considering, but few scholars have carried out related research on this.&lt;br/&gt;In this paper, a novel cogging torque reduction method based on regional magnetic compensation (RMC) has been proposed. The imbalance property of the magnetic field between adjacent stator teeth has been investigated and the compensation strategy of the regional magnetic field has been researched. The case studies of interior and surface-mounted PM machines show that the proposed method could help to dynamic minimize the cogging torque.&lt;br/&gt;&lt;br/&gt;II. Finite Element Analysis Of Cogging Torque&lt;br/&gt;Cogging torque is caused by the construction of the magnetic circuit of the machine, which is the interaction between the rotor magnetic flux and variable permeance of the air gap due to the geometry of stator slots [4], and it also exists when the machine is not energized.&lt;br/&gt;By making accurate analysis and calculation of the cogging torque, the basis for its compensation of the PM machines is created. The net cogging torque at any rotor position, which produced by a surface/interior PM machine can be calculated by [5]&lt;br/&gt;T&lt;sub&gt;C&lt;/sub&gt;=∑&lt;sub&gt;k=1&lt;/sub&gt;&lt;sup&gt;Q&lt;sub&gt;S&lt;/sub&gt;&lt;/sup&gt;(L&lt;sub&gt;a&lt;/sub&gt;∫&lt;sub&gt;0&lt;/sub&gt;&lt;sup&gt;h&lt;sub&gt;s&lt;/sub&gt;&lt;/sup&gt;((B&lt;sub&gt;θb1&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;(r&lt;sub&gt;t&lt;/sub&gt;)−B&lt;sub&gt;θb2&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;(r&lt;sub&gt;t&lt;/sub&gt;))/(2μ&lt;sub&gt;0&lt;/sub&gt;)) (1)&lt;br/&gt;where &lt;i&gt;B&lt;sub&gt;θb&lt;/sub&gt;&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; and &lt;i&gt;B&lt;sub&gt;θb&lt;/sub&gt;&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; are the tangential components of flux densities near the adjacent stator teeth, respectively; &lt;i&gt;Q&lt;sub&gt;S&lt;/sub&gt;&lt;/i&gt; is the number of slots; &lt;i&gt;L&lt;sub&gt;a&lt;/sub&gt;&lt;/i&gt; is the effective length; &lt;i&gt;h&lt;sub&gt;S &lt;/sub&gt;&lt;/i&gt;is the radius of the slot opening.&lt;br/&gt;The cogging torque calculation of PM machines will be illustrated and analyzed in this part.&lt;br/&gt;&lt;br/&gt;III. Regional Magnetic Compensation Strategy&lt;br/&gt;According to the analytical formula of cogging torque, it can be known that the tangential flux density on both sides of the slot wall can be compensated by supplying current or voltage on the stator side, the magnetic close component of the cogging torque can be balanced, thus weakening the cogging torque.&lt;br/&gt;The cogging torque analytical calculation and the regional magnetic field compensation is shown in Fig. 1.&lt;br/&gt;Take a 2-pole, 12-slot surface-mounted PM machine as an example, the current injection scheme for different slots is illustrated in Fig. 2.&lt;br/&gt;Further detailed regional magnetic compensation schemes of different machine topologies and their cogging torque reduction results will be reported in the full paper.

**References:**

&lt;br/&gt;[1] W. Fei and Z. Q. Zhu, “Comparison of cogging torque reduction in permanent magnet Brushless machines by conventional and herringbone skewing techniques,” &lt;i&gt;IEEE Trans. Energy Convers.&lt;/i&gt;, vol. 28, no. 3, pp. 664–674, Mar. 2013.&lt;br/&gt;[2] J. Gao, G. Wang, X. Liu, W. J. Zhang, S. D. Huang, and H. M. Li, “Cogging Torque Reduction by Elementary-Cogging-Unit Shift for Permanent Magnet Machines,” &lt;i&gt;IEEE Trans. Magn.&lt;/i&gt;, vol. 53, no. 11, p. 8208705, Nov. 2017.&lt;br/&gt;[3] L. Zhu, S. Z. Jiang, Z. Q. Zhu, and C. C. Chan, “Analytical methods for minimizing cogging torque in permanent-magnet machines,” &lt;i&gt;IEEE Trans. &lt;/i&gt;Magn., vol. 45, no. 4, pp. 2023–2031, Apr. 2009.&lt;br/&gt;[4] E. H. Abd-Elhameed and M. Iwasaki, &quot;Pulsating torque modeling and compensation for high precision positioning control,&quot; 2009 IEEE International Conference on Mechatronics, Malaga, 2009, pp. 1-5.&lt;br/&gt;Z. Q. Zhu and D. Howe, “Analytical Prediction of the Cogging Torque in Radial-field Permanent Magnet brushless motors,” &lt;i&gt;IEEE Trans. Magn&lt;/i&gt;., vol. 28, no. 2, pp. 1371–1374, Mar. 2009.

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 Cogging Torque Dynamic Reduction Based on Regional Magnetic Compensation

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—In order to reduce the cogging torque of the permanent magnet (PM) machine more effectively, a novel conception of the regional magnetic compensation (RMC) is introduced. An effective approach from the perspective of dynamic control for cogging torque reduction based on RMC is then proposed, by which the cogging torque could be reduced. Index Terms—Cogging torque, permanent magnet machines, dynamic reduction method, regional magnetic compensation. I. Introduction The cogging torque is an significant issue of the PM machines, which is an inherent shortcoming of PM machines. It leads to mechanical vibration, noise, and deteriorate the performances of the PM machines [1]. A wide variety of design methods for minimizing the cogging torque of PM machines have been comprehensively studied [1-3]. The existing cogging torque reduction methods can be mainly divided into two types: stator design and rotor design techniques. Undoubtedly, these methods can weaken the cogging torque but may result in the degradation of other machine performances, such as the unnecessary harmonics introduction, cost increase, and efficiency reduction, etc. On the other hand, it is impossible to weaken the cogging torque of a PM machine that has already been manufactured. Therefore, weakening the cogging torque from the perspective of dynamic control is worth considering, but few scholars have carried out related research on this. In this paper, a novel cogging torque reduction method based on regional magnetic compensation (RMC) has been proposed. The imbalance property of the magnetic field between adjacent stator teeth has been investigated and the compensation strategy of the regional magnetic field has been researched. The case studies of interior and surface-mounted PM machines show that the proposed method could help to dynamic minimize the cogging torque. II. Finite Element Analysis Of Cogging Torque Cogging torque is caused by the construction of the magnetic circuit of the machine, which is the interaction between the rotor magnetic flux and variable permeance of the air gap due to the geometry of stator slots [4], and it also exists when the machine is not energized. By making accurate analysis and calculation of the cogging torque, the basis for its compensation of the PM machines is created. The net cogging torque at any rotor position, which produced by a surface/interior PM machine can be calculated by [5] TC=∑k=1QS(La∫0hs((Bθb12(rt)−Bθb22(rt))/(2μ0)) (1) where Bθb1 and Bθb2 are the tangential components of flux densities near the adjacent stator teeth, respectively; QS is the number of slots; La is the effective length; hS is the radius of the slot opening. The cogging torque calculation of PM machines will be illustrated and analyzed in this part. III. Regional Magnetic Compensation Strategy According to the analytical formula of cogging torque, it can be known that the tangential flux density on both sides of the slot wall can be compensated by supplying current or voltage on the stator side, the magnetic close component of the cogging torque can be balanced, thus weakening the cogging torque. The cogging torque analytical calculation and the regional magnetic field compensation is shown in Fig. 1. Take a 2-pole, 12-slot surface-mounted PM machine as an example, the current injection scheme for different slots is illustrated in Fig. 2. Further detailed regional magnetic compensation schemes of different machine topologies and their cogging torque reduction results will be reported in the full paper.

**References:**

 [1] W. Fei and Z. Q. Zhu, “Comparison of cogging torque reduction in permanent magnet Brushless machines by conventional and herringbone skewing techniques,” IEEE Trans. Energy Convers., vol. 28, no. 3, pp. 664–674, Mar. 2013. [2] J. Gao, G. Wang, X. Liu, W. J. Zhang, S. D. Huang, and H. M. Li, “Cogging Torque Reduction by Elementary-Cogging-Unit Shift for Permanent Magnet Machines,” IEEE Trans. Magn., vol. 53, no. 11, p. 8208705, Nov. 2017. [3] L. Zhu, S. Z. Jiang, Z. Q. Zhu, and C. C. Chan, “Analytical methods for minimizing cogging torque in permanent-magnet machines,” IEEE Trans. Magn., vol. 45, no. 4, pp. 2023–2031, Apr. 2009. [4] E. H. Abd-Elhameed and M. Iwasaki, "Pulsating torque modeling and compensation for high precision positioning control," 2009 IEEE International Conference on Mechatronics, Malaga, 2009, pp. 1-5. Z. Q. Zhu and D. Howe, “Analytical Prediction of the Cogging Torque in Radial-field Permanent Magnet brushless motors,” IEEE Trans. Magn., vol. 28, no. 2, pp. 1371–1374, Mar. 2009.

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/9e00f76d4a91dc15460041f836e5411e.jpg)

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poster

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

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.

 Research of a hybrid excitation synchronous machine integrated with magnetic bearings

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

 Structure and Control of Modular Frequency-Multiplying Inverter with Low-Carrier-Ratio for High Speed Machine

1) Introduction As the use of high-efficiency and high-performance motors as motors for drones and home appliances increases, the use of PMSM (Permanent Magnet Synchronous Motor) type motors is increasing. To this end, many studies are being conducted on speed control in high-speed areas, and studies on sensorless control are also actively being conducted to reduce space constraints and weight and cost. [1][2] However, as the high-speed range increases, the position estimation signal of the sensor becomes unstable due to harmonics and inductance components, and it is greatly affected when small noise and disturbance occur. These errors degrade the performance of the high-speed control algorithm and the reliability of the motor. In this paper, to solve the sensorless error problem from low speed to high speed range, we use the signal output method of line drive method. The line drive output method generates signals that are complementary to each other, and through calculation, it can have strong characteristics against electrical noise and disturbance. Based on this, sensorless control in the high-speed region with high reliability was performed through detection and correction of signal distortion and disturbance in the signal generated at high speed due to inductance and harmonics. The PMSM simulation was configured to compare before and after application of the algorithm and verified its validity. 2) Methodology The sensorless control algorithm of the PMSM method generally includes current-based sensorless control and back EMF-based sensorless control. The current model-based sensorless control is used to estimate the speed and initial position using information of voltage and current, and the back EMF-based sensorless control estimates the position information through the estimated value of the back EMF. For current-based sensorless control, a lambda gamma-axis voltage equation that estimates the position from the existing dq-axis voltage equation is required, and the magnitude of the current is converted into an equation for the change of inductance to detect the position of the rotor. However, as the high-speed region increases, the delay of the current due to the inductance component and the positional error due to harmonics increase, so in the high-speed region, a sensorless control method using a back EMF model is used. Back EMF sensorless control includes a back EMF term as shown in Equation (1), and it is possible to establish voltage equations for lambda and gamma that estimate the position as a difference by θ. Through this, the back EMF equation can be expressed as Equation (2). Using this, you can estimate the position for θ as in Equation (3). Vγ=(R+pLd)iγ-(ωrLq)iδ+eγ, Vδ=(ωrLd)iγ+(R+pLq)iδ+eδ (1) êγ=Eex(-sinΔθ), êδ=Eex(-cosΔθ) (2) Δθ=tan-1(êγ/êδ) (3) However, when the motor reaches the high speed range, the distortion of the waveform becomes severe and it is more affected by disturbances such as vibration. Through this, the accuracy of sensorless control based on back EMF is deteriorated. In order to improve this, there is a harmonic injection method or an extended back EMF method, but the calculation is complicated and the system configuration cost increases due to an increase in the amount of operation. To improve this, we propose a signal correction method of the line drive method applied to the encoder. The basic concept of the line drive method is that the sum of the two signals must always be 1 by calculating the normal signal and the reverse signal at the same time. Therefore, even if an incorrect signal comes into one signal due to interference or disturbance, if a value other than 1 is output through the calculation of the normal component and the reverse component, the instantaneous count is not performed. By applying the method, the A-phase normal signal is processed using the existing signal for the A, B, and C-phase signals, and the reverse-phase signal is made based on the result obtained through the back EMF estimation method. Therefore, even if the A-phase normal signal is changed through disturbance and distortion of the signal, an error of the signal can be detected through comparison of the reverse-phase signal. Fig. 1 briefly shows the disturbed A-phase normal component and reverse phase component, and the resulting error values. As shown in Fig. 1, the position and magnitude of the error value can be detected by calculating the normal and inverse components. Based on this, the accuracy of the sensorless control algorithm can be improved by applying the compensation signal generated with the magnitude of the phase opposite to the error value to the signal generated by the disturbance. 3) Conclusion In order to verify the sensorless control algorithm in the high-speed region using the line drive method, the simulation was conducted after artificially adding noise using Matlab Simulink. In the case of using only the existing sensorless method, control was broken by noise and it was not able to operate properly. On the other hand, when the compensation of the line drive method was performed, the initial error was gradually compensated as shown in Fig 2, and it was confirmed that the motor operates stably after 0.4 seconds. Through this, we verified the validity of the algorithm proposed in this paper.

**References:**

[1] X. Song, J. Fang, B. Han, and S. Zheng, “Adaptive compensation method for high-speed surface PMSM sensorless drives of EMF-based position estimation error,” IEEE Trans. Power Electron., Vol. 31, No. 2, pp. 1438-1449, Feb. 2016. [2] G. Wang, H. Zhan, G. Zhang, X. Gui, and D. Xu, “Adaptive compensation method of position estimation harmonic error for emf-based observer in sensorless IPMSM drives,” IEEE Trans. Power Electron., Vol. 29, No. 6, pp. 3055-3064, Jun. 2014.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/76f075f49ab706ea99c61b8f10ce32c1.jpg)
Fig. 1 A,A-,Err graph using line drive method

![](https://assets.underline.io/uploads/markdown_image/1/image/2607ae6609735773963af48240233c1c.jpg)
Fig. 2 Actual angle and angle of line drive method

 A Study on High Reliability Sensorless Control of High Speed Permanent Magnet Synchronous Motor Using Line Drive Method

—Electrically excited homopolar inductor machine (EE-HIM) has good application in the field of flywheel energy storage system (FESS) due to its merits of simple structure, brushless exciting and little idling electromagnetic losses. However, the copper loss of field winding in the charge/discharge operation state would decrease the efficiency of energy conversion. To improve the efficiency of charge/discharge and inherit the merit of little idling electromagnetic losses, a novel HIM with flux memory (HIM-FM) is proposed. Firstly, the structure and operation principle of HIM-FM are illustrated. Then, the key structure parameters, including the rotor tooth width and slots depth are optimized. Finally, the electromagnetic performance, including the air-gap flux density, flux linkage, back-EMF and output torque and losses of HIM-FM are analyzed by finite element method. The result indicates that the proposed HIM-FM has the merit of little idling electromagnetic losses and no copper loss, which can be help to improve the energy conversion efficiency. I. Introduction An electrical machine is the key component of flywheel energy storage system (FESS), whose performance would directly affect the ration of energy conversion of FESS. Among the various electrical machine topologies, an electrically excited homopolar inductor machine (EE-HIM) has attracted much attention in the FESS due to its merits of robust rotor structure, brushless exciting. Moreover, the idling electromagnetic loss of EE-HIM can be eliminated by cutting off the field current [1]. However, the copper loss of field winding would decrease the charge/discharge efficiency of EE-HIM. Addressing this issue, a NdFeB permanent magnet (PM) HIM is proposed in [2]. While the idling loss would be caused due to the no-load high frequency magnetic field generated by PM. To improve the efficiency of charge/discharge and inherit the merit of little idling electromagnetic losses, a novel HIM with flux memory (HIM-FM) is proposed in this paper. II.Topology and operation principle The topology of proposed HIM-FM is shown in Fig. 1. As shown, the rotor is made of solid steel and has teeth on its both ends. The left and right teeth axes are differed by 180o electrical degree. Two stator cores are made of laminated steels and sandwich a magnetizing coil, which is used to demagnetize and magnetize the circular Al-Ni-Co permeant magnet (PM). Two segment shells are placed on both sides of Al-Ni-Co PM and provide the flux path for fluxes generated by the PM or the magnetizing coil. The PM would be magnetized when the HIM-FM works at charge/discharge state and demagnetized when the HIM-FM works at idling state. III.Performance evaluation Fig. 2(a) shows the air-gap flux density distribution of HIM-FM when the Al-Ni-Co PM has different remanence. It can be found that the maximum and minimum air-gap flux density is 0.848 and 0.021T. Fig. 2(b) gives the phase back electromotive force (EMF) of HIM-FM under different demagnetization. The amplitude of back-EMF can be regulated by 97.2% compared with the zero demagnetization. The stator core loss of HIM-FM are respectively 13.3 W and 0.0284W and the rotor eddy current loss of HIM-FM are respectively 0.85 W and 0.00197W under zero and severe demagnetization. Compared with the zero demagnetization, the stator core loss and eddy current loss can be reduced by 99.91% and 99.77%, which indicates that the proposed HIM-FM can be greatly reduced the idling electromagnetic loss. IV.Conclusion This paper proposed a novel HIM with flux memory (HIM-FM) for the application of flywheel energy storage system. The performance of HIM-FM is evaluated, which indicates that the proposed HIM-FM helps to reduce the idling electromagnetic loss and improve the efficiency of charge/discharge. The other electromagnetic performance of HIM-FM, such as the flux linkage, output torque and losses, would be presented in full paper.

**References:**

 [1] P. Tsao, M. Senesky, and S. Sanders, “An integrated flywheel energy storage system with homopolar inductor motor/generator and high-frequency drive,” IEEE Trans. Ind. Appl., vol. 39, no. 6, pp. 1710–1725, Nov./Dec.2003. [2] Z. Q. Liu, K. Wang and F. Li, "Design and Analysis of Permanent Magnet Homopolar Machine for Flywheel Energy Storage System," IEEE Trans. on Magn., vol. 55, no. 7, pp. 1-6, Jul. 2019.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3382740e74094ea148be468a3449ecde.jpg)

 Investigation of a Novel Homopolar Inductor Machine with Flux Memory for the Flywheel Energy Storage System

I Introduction Owing to high efficiency, high power density and inhererly high fault-tolerant capacity, multiphase permanent magnet synchronous machines (PMSMs) equipped with the fractional-slot concentrated windings (FSCWs) have been drawing much attention [1]. Unfortunately, they are still limited by the excessive armature magnetomtive force (MMF) harmonics which will produce high eddy current loss in the PMs. To improve this situation, some new stator and winding arrangements, which can reduce the content of armature MMF harmonics, are proposed. But, it should be noted that the amplitude of the winding short-circuit current of these new topologies will increase due to the reduction of the harmonic leakage inductance. In this paper, the winding short-circuit faults of three six-phase PMSMs with different stator configurations whose contents of armature MMF harmonics are different are compared. II Six-Phase PMSMs with Different Armature MMF Distributions The well-known six-phase 12-slot/14-pole PMSM with traditional single-layer FSCW is shown in Fig. 1(a). The MMF distribution produced by the troditional single-layer FSCW contains a large content of harmonics as shown in Fig. 1(d). The two harmonics of order υ=1 and υ=5 are the main components, which are both the main contributors to PM eddy loss and harmonic leakage inductance. To improve the quality of armature MMF distribution produced by the traditional single-layer FSCW, two low armature MMF harmonic topologies are proposed, as shown in Fig.1 (b) and (c). By employing modular stator as shown in Fig. 1(b), the amplitude of the harmonic of order υ=1 can be significantly reduced. By using the concept of stator shifting [5], a double-layer 2-pitch 24-slot/14-pole six-phase PMSM can be obtained, as shown in Fig. 1(c). It can be seen that the main harmonic components, i.e. harmonics of order υ=1 and υ=5, are significantly reduced in the 24-slot/14-pole six-phase PMSM. In this way, three six-phase PMSMs with different contents of armature MMF harmonics are obtained for the comparison studies. III Winding Short-Circuit Currents and Demagnetization Analyses The winding short current will contain a transient component and a steaty component when the winding short current occurs in a PM machine. In orde to compare the surface-mounted PM demagnetization withstand ability of the three six-phase PMSM, the peak negative d-axis current during the whole short-circuit fault should be firstly obtained. The transit short current trajectories are shown in Fig. 2. It can be found that for the three six-phase PMSMs, the peak d-axis components of the winding short currents are -29.8 A, -39.5 A and -74.8 A, respectively. The amplitudes of the peak d-axis currents are increase with the decrease of the content of the armature MMF harmonics. A high winding short-circuit current will destroy the balance thermal distribution, which is the main drawback of the low armuture MMF harmonic designs. Futunately, owing to more even armature MMF distributions, even with higher negative d-axis current, the minimum flux densities of the PMs of the low armature MMF harmonics designs will be lower than the traditional one, as shown in Fig. 3.

**References:**

 [1] F. Barrero and M. J. Duran, “Recent advances in the design, modeling, and control of multiphase machines—Part I,” IEEE Trans. Ind. Electron., vol. 63, no. 1, pp. 449–458, Jan. 2016. [2] P. B. Reddy, K.-K. Huh, and A. M. El-Refaie, “Generalized approach of stator shifting in interior permanent-magnet machines equipped with fractional-slot concentrated windings,” IEEE Trans. Ind. Electron., vol. 61, no. 9, pp. 5035–5046, Sep. 2014.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/03b46be4fba1176ff03595252310aead.jpg)
Fig. 1 Three six-phase PMSMs and MMF distributions

![](https://assets.underline.io/uploads/markdown_image/1/image/0b7fb4f0b8a5714732e48873f62e01e1.jpg)

 Comparative Studies of Winding Short-Circuit Currents of Six-Phase PMSMs with Different Armature Magnetomovtive Force Distributions

1. Introduction In recent wind power generation systems, a permanent magnet synchronous generator(PMSG) using rare earth magnets has been widely used for high power density and miniaturization per unit volume[1]. However, rare earth magnets have the disadvantage of high prices and high instability in supply and demand due to the characteristics of resources produced mostly in specific countries[2]. On the other hand, ferrite magnets have the advantage of stable material supply and demand and low cost compared to rare earth magnets. However, ferrite magnets have a low magnetic flux density, about 1/3 of that of rare earth magnets, and a spoke-type structure was developed to compensate for this. The spoke-type is a structure in which magnetic flux is concentrated by arranging two magnets in a radial direction on the rotor. By combining the magnetic fluxes of two magnets facing each other, the magnetic flux can be increased to obtain a high airgap magnetic flux density[3]-[4]. Currently, various research and development of spoke-type are carried out and used in the motor field, but application cases, research and development are still insufficient in generators. In this paper, a 10-pole 36-slot spoke-type PMSG was designed using a 3kW class wind turbine as a model, and a hybrid magnetic flux intensive PMSG with improved performance of the conventional spoke-type was proposed. 2. Conventional spoke-type shape and features A spoke-type rotor structure typically has two feature types, as shown in Figure 1 (a) and (b). There are types of non-conductors, such as (a), that are designed to prevent magnetic flux from flowing into the inside of the rotor, and (b), such as the inside of the rotor is designed extremely small, to rapidly saturate the inner core of the rotor to reduce the leakage magnetic flux. For the first method, high output density can be expected because it essentially removes passes from the leakage magnetic flux, but it has the disadvantage of high manufacturing difficulty and production costs due to the need for another material component inside the rotor. Additional structures are also needed for binding to non-elastic bodies and cores to support the release of the pole piece. The second method is advantageous in terms of manufacturability and production cost, but even though the rotor shape has an extremely small inner side, leakage magnetic flux occurs and the output density decreases. If the inner side is too shortened, there is a limit to reducing the inner side because it is disadvantageous in terms of rigidity.[5]-[6]. 3. Hybrid spoke-type permanent magnet synchronous generator design and characteristic analysis In this paper, the shape of a hybrid spoke-type permanent magnet synchronous generator for wind power generation system is proposed. The hybrid spoke-type PMSG is a shape in which the inner and outer bridges of the rotor are arranged in zigzag as shown in Fig. 1(c), and they are intersected when stacked. Since it does not require additional components, it has better fabrication than the (a) type, and the inner leakage magnetic flux is reduced by using only half of the inner bridge, and the stiffness is supplemented by adding an outer bridge. Cogging torque related to the starting performance of wind turbines, efficiency during load operation, and voltage fluctuation rate are compared and analyzed for each model using finite element analysis(FEA). The cogging torque was 3.6, 3.5, and 2.3[Nm], respectively, and the proposed model had the best cogging torque performance. During load operation, the efficiency was 96.2, 95.7, and 95.6[%], respectively, and there was a difference of about 0.6%P between the (a) model and the proposed model, in which the internal leakage was blocked. As a result of the 3D analysis, the voltage fluctuation rate during load operation occurred above the target specification value of 15% for each model[7]. As the voltage fluctuation rate increases, the target output and efficiency cannot be satisfied. The voltage decrease during load operation is due to the armature reaction, so the number of turns and the voltage drop are proportional. Therefore, the number of turns was reduced by applying the overhang model, and as a result, the voltage fluctuation rate was reduced, and the final model was designed that satisfies the target specifications of cogging torque, voltage fluctuation rate, efficiency, and output. 4. Performance test and Conclusion To confirm the validity, a prototype was produced based on the final design model and a performance test was performed. The comparison of the test values with the FEA analysis results is shown in Table 1 and shows that the test values are similar to the analysis results. In this paper, a hybrid spoke-type PMSG for wind turbines was designed. By comparing the performance with the existing spoke-type models, it was confirmed that the cogging torque, an important performance specification of the wind turbine, was reduced, and the final model with overhang was designed to reduce the voltage drop that occurs during load operation. The performance was reviewed through 2D and 3D FEA, and a prototype was produced to verify the validity of the analysis results. Acknowledgments This work was supported in part by Technology Innovation Program (No. 20000401) funded By the Ministry of Trade, Industry & Energy(MOTIE), Korea and in part by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2020R1A2C1013724).

**References:**

[1] Zaijun Wu, Xiaobo Dou, Jiawei Chu and Minqiang Hu, “Operation and Control of a Direct-Driven PMSG-Based Wind Turbine System with an Auxiliary Parallel Grid-Side Converter”, Energies 2013, pp. 3405-3421, 12. July. 2013. [2] J. Seaman, “Rare Earths and Clean Energy: Analyzing China’s Upper Hand,”2010. [3] W. Zhao, T. A. Lipo, and B. I. Kwon, “Torque pulsation minimization in spoke-type interior permanent magnet motors with skewing and sinusoidal permanent magnet configurations,” IEEE Trans. Magn., vol. 51, no. 11, Nov. 2015 [4] S. I. Kim, S. Park, T. Park, J. Cho, W. Kim, and S. Lim, “Investigation and experimental verification of a novel spoke-type ferrite-magnet motor for electric-vehicle traction drive applications,” IEEE Trans. Ind. Electron., vol. 61, no. 10, pp. 5763–5770, Oct. 2014. [5] Sandra M. Castano;Ehab Sayed;James Weisheng Jiang;Jianbin Liang, " Design of a Spoke-Type Ferrite Magnet Generator for a Hybrid Electric Vehicle Application," 2019 IEEE Transportation Electrification Conference and Expo (ITEC), 08 August 2019 [6] Mohammad Kimiabeigi; James D. Widmer; Raymond Long; Yi Gao; James Goss, On Selection of Rotor Support Material for a Ferrite Magnet Spoke-Type Traction Motor," IEEE Transactions on Industry Applications Volume: 52, Issue: 3, May-June 2016 [7] Sung Gu Lee;Jaenam Bae;Myungchin Kim;Won-Ho Kim, ” Study on the Improvement of the Correction Coefficient Considering the 3-D Effect of Spoke-Type Permanent-Magnet Synchronous Motor “ IEEE Transactions on Magnetics, Volume: 56, Issue: 3, March 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4c46d14717a099bee2f8b8c899a7f2ba.jpg)
Fig.1 Shape cross section for each rotor type

![](https://assets.underline.io/uploads/markdown_image/1/image/f373b2142d465bd6377247713506e6f2.jpg)
Table.1 Comparison of FEA and Test results

Cogging Torque Dynamic Reduction Based on Regional Magnetic Compensation

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