France



I. Introduction&lt;br/&gt;The electric motors have been widely used in various applications such as automobiles, and home appliances. Among the various types of electric motors, the interior permanent magnet synchronous motors (IPMSM) in which permanent magnets (PM) are inserted in the rotor receive a lot of attention due to the advantage of high efficiency and high power density. Since these applications are closely related with daily life, the vibration and noise reduction of IPMSM used in these applications are important. Further, most of these applications require continuous driving under certain load condition. Thus, it is important to reduce the vibration and noise of IPMSM used for continuous driving under certain load condition [1]. To reduce the vibration of IPMSM under certain load condition, the asymmetric rotor design which changes mechanical air-gap length has been proposed in [2]. However, the average torque is decreased as mechanical air-gap length is changed. Therefore, in this paper, arrangement of the PM and flux barrier is modified to make the asymmetric rotor shape which changes magnetic air-gap length instead of mechanical air-gap length. Through this method, the vibration can be reduced maintaining average torque under certain load condition. To confirm the vibration reduction of IPMSM with asymmetric rotor shape under certain load condition, the vibration analysis of the 4-pole 24-slot IPMSM with the symmetric and asymmetric rotor shape is conducted using 2-dimensional finite element analysis (2D FEA).&lt;br/&gt;&lt;br/&gt;II. Relationship between radial force density and air-gap magnetic flux density&lt;br/&gt;The radial force density can be expressed by the Maxwell stress tensor method. The radial force density generates the stator displacement which causes the vibration of motors. The spatial harmonic order of the radial force density is called as the vibration order. The stator displacement is inversely proportional to the fourth power of the vibration order [3]. Thus, the radial force density with low vibration order should be decreased to reduce the vibration. As a result, it is necessary to make the radial air-gap magnetic flux density sinusoidal. The radial air-gap magnetic flux density can be calculated by multiplying the sum of the air-gap magnetic flux density neglecting slotting effect by the PM and armature with the relative specific permeance of the stator and rotor. Therefore, to make the radial air-gap magnetic flux density sinusoidal, the rotor permeance should be uniform. In this paper, the arrangement of the PM and flux barrier is modified to make the rotor permeance uniform.&lt;br/&gt;&lt;br/&gt;III. Vibration analysis using FEA&lt;br/&gt;The configuration of the 4-pole 24-slot IPMSM with the symmetric and the asymmetric rotor shape is shown in Fig. 1. The symmetric and asymmetric model have same geometric shapes only except for the rotor.&lt;br/&gt;Under the load condition of 1.92 Nm at 5000 rpm, the radial force density is calculated from (1) using 2D FEA. The spectrum analysis result of the radial force density using 2D fast Fourier transform is shown in Fig. 2(a). As shown in Fig. 2(a), at most time harmonic orders, the radial force density of the asymmetric model is less than that of the symmetric model. Specifically, at the 2nd time harmonic order, the radial force density with the lowest vibration order of 4 is decreased by 12.4% from 125.62 kN/m&lt;sup&gt;2&lt;/sup&gt; to 110.04 kN/m&lt;sup&gt;2&lt;/sup&gt;. Also, at the 10th time harmonic order, the radial force density with the lowest vibration order of -4 is decreased by 44.5% from 12.79 kN/m&lt;sup&gt;2&lt;/sup&gt; to 7.10 kN/m&lt;sup&gt;2&lt;/sup&gt;.&lt;br/&gt;Next, the vibration analysis is conducted to calculate the stator displacement using 2D FEA by applying the radial force density on the stator. The time harmonic analysis result of the stator displacement of the symmetric and asymmetric model is shown in Fig. 2(b). As shown in Fig. 2(b), at most time harmonic orders, the stator displacement of the asymmetric model is reduced. Particularly, at the 2nd, 10th, and 22nd time harmonic orders, the stator displacement of the asymmetric model is decreased by 16.1%, 45.0%, and 68.4%, respectively.&lt;br/&gt;According to these results, the vibration reduction of the asymmetric model compared with that of the symmetric model is confirmed under the load condition of 1.92 Nm at 5000 rpm. This is because under the load condition, rotor permeance of the asymmetric model is more uniform than that of the symmetric model due to the current phase angle.&lt;br/&gt;&lt;br/&gt;IV. Experimental verification and conclusion&lt;br/&gt;In this paper, the vibration analysis of the symmetric and asymmetric model is conducted using 2D FEA under the load condition of 1.92 Nm at 5000 rpm. As a result, the vibration reduction of the asymmetric model is confirmed. This is because the radial force density with a low vibration order is decreased as the rotor permeance becomes uniform. Therefore, it is expected that the 4-pole 24-slot IPMSM with asymmetric rotor shape is effective to reduce the vibration. To verify the vibration reduction of the asymmetric model, the vibration experiments will be conducted under the same load condition of 1.92 Nm at 5000 rpm.

**References:**

&lt;br/&gt;[1] C.-H. Lin and C.-C. Hwang, “Multiobjective optimization design for a six-phase copper rotor induction motor mounted with a scroll compressor”, &lt;i&gt;IEEE Trans. Magn.&lt;/i&gt;, vol. 52, no. 7, July 2016.&lt;br/&gt;[2] Y.-H. Jung, M.-R. Park, and M.-S. Lim, “Asymmetric rotor design of IPMSM for vibration reduction under certain load condition”, &lt;i&gt;IEEE Trans. Energy Convers.&lt;/i&gt;, vol. 35, no. 2, pp. 928-937, June 2020.&lt;br/&gt;[3] J.-F. Gieras, C. Wang, and J.-C. Lai, “Magnetic fields and radial forces in polyphase motors fed with sinusoidal currents”, in &lt;i&gt;Noise of Polyphase Electric Motors&lt;/i&gt;, 1st ed., Boca Raton: CRC Press, 2006, ch. 2, pp. 21-64.

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8bc9e324f08558d09564cb3afc523305.jpg)
Fig. 1. Configuration of the 4-pole 24-slot IPMSM with (a) the symmetric rotor shape (b) the asymmetric rotor shape

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/20b87d2c49e47fc9c0bcd788f10c19c7.jpg)
Fig. 2. Under the load condition of 1.92 Nm at 5000 rpm (a) spectrum analysis result of the radial force density (b) time harmonic analysis result of the stator displacement

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 Vibration Reduction of IPMSM with Asymmetric Rotor Shape under Certain Load Condition

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I. Introduction The electric motors have been widely used in various applications such as automobiles, and home appliances. Among the various types of electric motors, the interior permanent magnet synchronous motors (IPMSM) in which permanent magnets (PM) are inserted in the rotor receive a lot of attention due to the advantage of high efficiency and high power density. Since these applications are closely related with daily life, the vibration and noise reduction of IPMSM used in these applications are important. Further, most of these applications require continuous driving under certain load condition. Thus, it is important to reduce the vibration and noise of IPMSM used for continuous driving under certain load condition [1]. To reduce the vibration of IPMSM under certain load condition, the asymmetric rotor design which changes mechanical air-gap length has been proposed in [2]. However, the average torque is decreased as mechanical air-gap length is changed. Therefore, in this paper, arrangement of the PM and flux barrier is modified to make the asymmetric rotor shape which changes magnetic air-gap length instead of mechanical air-gap length. Through this method, the vibration can be reduced maintaining average torque under certain load condition. To confirm the vibration reduction of IPMSM with asymmetric rotor shape under certain load condition, the vibration analysis of the 4-pole 24-slot IPMSM with the symmetric and asymmetric rotor shape is conducted using 2-dimensional finite element analysis (2D FEA). II. Relationship between radial force density and air-gap magnetic flux density The radial force density can be expressed by the Maxwell stress tensor method. The radial force density generates the stator displacement which causes the vibration of motors. The spatial harmonic order of the radial force density is called as the vibration order. The stator displacement is inversely proportional to the fourth power of the vibration order [3]. Thus, the radial force density with low vibration order should be decreased to reduce the vibration. As a result, it is necessary to make the radial air-gap magnetic flux density sinusoidal. The radial air-gap magnetic flux density can be calculated by multiplying the sum of the air-gap magnetic flux density neglecting slotting effect by the PM and armature with the relative specific permeance of the stator and rotor. Therefore, to make the radial air-gap magnetic flux density sinusoidal, the rotor permeance should be uniform. In this paper, the arrangement of the PM and flux barrier is modified to make the rotor permeance uniform. III. Vibration analysis using FEA The configuration of the 4-pole 24-slot IPMSM with the symmetric and the asymmetric rotor shape is shown in Fig. 1. The symmetric and asymmetric model have same geometric shapes only except for the rotor. Under the load condition of 1.92 Nm at 5000 rpm, the radial force density is calculated from (1) using 2D FEA. The spectrum analysis result of the radial force density using 2D fast Fourier transform is shown in Fig. 2(a). As shown in Fig. 2(a), at most time harmonic orders, the radial force density of the asymmetric model is less than that of the symmetric model. Specifically, at the 2nd time harmonic order, the radial force density with the lowest vibration order of 4 is decreased by 12.4% from 125.62 kN/m2 to 110.04 kN/m2. Also, at the 10th time harmonic order, the radial force density with the lowest vibration order of -4 is decreased by 44.5% from 12.79 kN/m2 to 7.10 kN/m2. Next, the vibration analysis is conducted to calculate the stator displacement using 2D FEA by applying the radial force density on the stator. The time harmonic analysis result of the stator displacement of the symmetric and asymmetric model is shown in Fig. 2(b). As shown in Fig. 2(b), at most time harmonic orders, the stator displacement of the asymmetric model is reduced. Particularly, at the 2nd, 10th, and 22nd time harmonic orders, the stator displacement of the asymmetric model is decreased by 16.1%, 45.0%, and 68.4%, respectively. According to these results, the vibration reduction of the asymmetric model compared with that of the symmetric model is confirmed under the load condition of 1.92 Nm at 5000 rpm. This is because under the load condition, rotor permeance of the asymmetric model is more uniform than that of the symmetric model due to the current phase angle. IV. Experimental verification and conclusion In this paper, the vibration analysis of the symmetric and asymmetric model is conducted using 2D FEA under the load condition of 1.92 Nm at 5000 rpm. As a result, the vibration reduction of the asymmetric model is confirmed. This is because the radial force density with a low vibration order is decreased as the rotor permeance becomes uniform. Therefore, it is expected that the 4-pole 24-slot IPMSM with asymmetric rotor shape is effective to reduce the vibration. To verify the vibration reduction of the asymmetric model, the vibration experiments will be conducted under the same load condition of 1.92 Nm at 5000 rpm.

**References:**

 [1] C.-H. Lin and C.-C. Hwang, “Multiobjective optimization design for a six-phase copper rotor induction motor mounted with a scroll compressor”, IEEE Trans. Magn., vol. 52, no. 7, July 2016. [2] Y.-H. Jung, M.-R. Park, and M.-S. Lim, “Asymmetric rotor design of IPMSM for vibration reduction under certain load condition”, IEEE Trans. Energy Convers., vol. 35, no. 2, pp. 928-937, June 2020. [3] J.-F. Gieras, C. Wang, and J.-C. Lai, “Magnetic fields and radial forces in polyphase motors fed with sinusoidal currents”, in Noise of Polyphase Electric Motors, 1st ed., Boca Raton: CRC Press, 2006, ch. 2, pp. 21-64.

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8bc9e324f08558d09564cb3afc523305.jpg)
Fig. 1. Configuration of the 4-pole 24-slot IPMSM with (a) the symmetric rotor shape (b) the asymmetric rotor shape

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/20b87d2c49e47fc9c0bcd788f10c19c7.jpg)
Fig. 2. Under the load condition of 1.92 Nm at 5000 rpm (a) spectrum analysis result of the radial force density (b) time harmonic analysis result of the stator displacement

poster

I.INTRODUCTION As one of the epoch-making technologies, the wireless power transfer (WPT) has significantly changed the power-accessing pattern owing to the distinctive merits of high convenience, reliability and security [1]. Possessing the capability to cordlessly transmit the energy via a long air gap, the emerging WPT has been widely investigated by many researchers [2]-[3]. Recently, the study objectives of WPT concentrate on efficiency enhancement, topology development, coil optimization and fresh applications such as the wireless lighting, wireless heating and wireless-powered implant [4]-[6]. In particular, the concept of wireless motor was newly conceived which can eliminate the metallic connection to facilitate the motor operation in an isolated environment [7]. By integrating the selective WPT with the motor drive, the wireless switched reluctance motor was proposed to remove the converter in the receiver side and centralize all controls in the transmitter side [8]. With the adoption of self-driving circuits and a full-bridge inverter in the receiver, the wireless shaded-pole induction motor was developed as tagged as the first wireless AC motor [9]. And the frequency-modulated wireless direct-drive motor was established for the underground in-pipe pumping application [10]. It should be noted the aforementioned wireless motor systems are universally evolved from the multifrequency selective WPT system which is designed to energize receivers by operating at different resonant frequencies. Nevertheless, it unavoidably adopts complicated switched capacitors, bulky transmitter coil and multiple independent receiver coils which in turn will result in a clumsy system and the unbalanced phase current of motor. To address concerns of previous wireless motor drives, a new wireless motor drive using decoupled bipolar coils is proposed and implemented for the coordinated operation of robotic arms. Specifically, two bipolar coils are orthogonally integrated to form a compact magnetic coupler while two magnetic couplers serve as the transmitter and receiver coils, respectively. The same-side coils are magnetically decoupled which indicates the transmitter-side bipolar coils can be independently controlled to facilitate the coordinated operation of two permanent magnet (PM) DC motors in the receiver side. Meanwhile, the series-inductor-capacitor-capacitor (S-LCC) compensation is adopted to ensure high transmission efficiency over a wide load range. Therefore, the proposed system is highly suitable for cordless robotic arms operating in an isolated or watery environment with electrocution free and high reliability. II.METHODOLOGY As depicted in Fig. 1 (a), the proposed system involves two half-bridge inverters, magnetic couplers, S-LCC compensations, diode rectifiers and PMDC motors. By independently controlling bipolar coils in coupler #1 in the transmitter, the motors can be separately excited by bipolar coils in coupler #2 in the receiver due to the magnetic decoupling characteristics of the same-side coils. Instead of adopting multiple resonant frequencies and multiple power-transfer channels, the proposed system can readily activate two motors with a single resonant frequency through the single power-transfer channel which in turn will significantly shrink the system volume and reduce the system complexity. In order to intuitively illustrate the magnetic coupling characteristics of the proposed coil, the finite element method (FEM) based simulations are conducted for better visualization as shown in Fig. 1 (b). It can be observed that two horizontal bipolar (Hb) coils and two vertical bipolar (Vb) coils are strongly coupled, respectively. However, the net amount of magnetic flux flows from the Hb coil to Vb coil is zero due to the symmetrical distribution of the magnetic flux. Consequently, the Hb and Vb coils are naturally decoupled which indicates the independent and wireless excitation of two PMDC motors can be realized by separately control the Hb and Vb coils from the transmitter side. III.EXPERIMENTAL VERIFICATION The experimental prototype and testing setup are built as shown in Fig. 2 (a) in which two gallium nitride (GaN) half-bridge inverters serve as the high-frequency AC source and two 150 W PMDC motors act as the load, respectively. All coils are made by Litz wires and all rectifiers are made by Schottky diodes to reduce the undesired power loss. Fig. 2 (b) shows the measured waveforms of three basic modes, namely, Mode I: motor A is active while motor B is idle; Mode II: motor A is idle while motor B is active; Mode III: both motor A and B are active. Meanwhile, it can be observed that no unexpected currents appear in the idle motor which well illustrates the good decoupled characteristics between Hb and Vb coils. Moreover, the ZVS can be readily achieved at the resonant frequency of 85 kHz in all modes. Finally, the measured results well confirm the feasibility and flexibility of the proposed wireless motor drive for the coordinated operation of robotic arms. This work was supported by Hong Kong Research Grants Council, Hong Kong, China under project 17207420.

**References:**

[1] G. A. Covic, and J. T. Boys, “Inductive power transfer,” Proceedings of the IEEE, vol. 101, no. 6, pp. 1276-1289, Jun. 2013. [2] Z. Zhang, H. Pang, A. Georgiadis and C. Cecati, “Wireless power transfer – an overview,” IEEE Trans. Ind. Electron., vol. 66, no. 2, pp.1044-1058, Feb. 2019. [3] S. Li and C. C. Mi, “Wireless power transfer for electric vehicle applications,” IEEE J. Emerg. Sel. Topics Power Electron., vol. 3, no. 1, pp. 4-17, March 2015. [4] W. Han, K. T. Chau, C. Jiang, W. Liu and W. H. Lam, “High-order compensated wireless power transfer for dimmable metal halide lamps,” IEEE Trans. Power Electron., vol. 35, no. 6, pp. 6269-6279, Jun. 2020. [5] W. Han, K. T. Chau, and Z. Zhang, “Flexible induction heating using magnetic resonant coupling,” IEEE Trans. Ind. Electron., vol. 64, no. 3, pp. 1982-1992, Mar. 2017. [6] C. Liu, C. Jiang, J. Song and K. T. Chau, “An effective sandwiched wireless power transfer system for charging implantable cardiac pacemaker,” IEEE Trans. Ind. Electron., vol. 66, no. 5, pp. 4108-4117, May 2019. [7] L. Wang, J. Li, H. Nie, J. Liu and S. Ke, “Coaxial nested couplers-based offset-tolerance rotary wireless power transfer systems for electric excitation motors,” IEEE Access, vol. 8, pp. 44913-44923, 2020. [8] C. Jiang, K. T. Chau, C. Liu, and W. Han, “Design and analysis of wireless switched reluctance motor drives,” IEEE Trans. Ind. Electron., vol. 66, no. 1, pp. 245-254, Jan. 2019. [9] H. Wang, K. T. Chau, C. H. T. Lee, L. Cao and W. H. Lam, “Design, analysis and implementation of wireless shaded-pole induction motors,” IEEE Trans. Ind. Electron., doi: 10.1109/TIE.2020.3007116. [10] W. Liu, K. T. Chau, C. H. T. Lee, L. Cao and C. Jiang, “Frequency-modulated wireless direct-drive motor control,” IEEE Trans. Magn., doi: 10.1109/TMAG.2020.3021708.

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/1049ee4681cae363c70b8ba26c367283.jpg)
Fig.1 Proposed wireless motor drive. (a) Configuration. (b) Magnetic field distributions of bipolar coils.

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/46c8226acabb0fe004625c1e59a36396.jpg)
Fig.2 Experimental verification. (a) Prototype. (b) Measured waveforms.

 Compact Wireless Motor Drive Using Decoupled Bipolar Coils for Coordinated Operation of Robotic Arms

I. Introduction Nowadays, electric vehicles (EVs) have developed rapidly for reducing environmental pollution and alleviating the scarcity of resources. With the driving environment of EVs becoming increasingly complex, the performance requirements of traction motor are more and more strict, such as the high efficiency and high torque density. As is known, interior permanent magnet (PM) motors have been the popular machine type for EV applications, however, the air gap magnetic field of conventional PM motors keeps constant, which leads to the disadvantages of the limited speed range and low efficiency in flux-weakening control region. So, to realize the flux regulation in PM motors, a variable leakage flux permanent magnet (VLF-PM) motor has aroused widespread attention due to the characteristics of variable flux leakage [1]. This kind of motor can control the flux leakage by regulating the q-axis current, then the magnetic flux leakage region can be effectively adjusted and wide speed range can be realized [2]. Moreover, the different saturation degrees under various operation conditions may cause the variation of magnetic density fluctuation. Based on above analysis, VLF-PM motor uses different magnetic flux leakage and saturation degrees under different operation conditions to improve the performance of the motor. At the same time, the magnetic density fluctuation caused by different saturation degrees will have a great impact on the fluctuation of iron loss. Thus, to VLF-PM motors, exploring the magnetic flux leakage characteristics to reduce the average and fluctuation of iron loss and ensure the stability of efficiency is extremely meaningful. In this paper, the key of research is to solve the problem of high iron loss and fluctuation, which caused by the distinctly various magnetic density of the rotor flux leakage region in VLF-PM motor under different operation conditions. For further research, this paper proposes a method that the magnetic flux leakage region is divided from the perspective of magnetic circuit change and each region selects the representative point, which has contributed to evaluating the fluctuation of magnetic density and iron loss. Finally, by optimizing the size of motor, the iron loss and its fluctuation can be reduced. II. Motor topology and analysis of the performance Fig. 1(a) shows the configuration of the proposed VLF-PM motor. Fig. 1(b) shows urban operation conditions. It can be found that low-speed operation condition of the motor accounts for 86% and it is worthy to be focused. Fig. 1(c) shows magnetic circuit under different loads. Based on Fig. 1(c), Fig. 1(d) shows the selections of typical magnetic density region. In Fig. 1(e), through the analysis of flux leakage regions under different operation conditions, different points are selected for the analysis of magnetic density, it can be seen that the magnitude and amplitude of the magnetic density of the selected points change because of the variation of saturation degree, which explains the phenomenon that the iron loss of VLF-PM motor fluctuates greatly after reaching a stable level. Fig. 2(a), Fig. 2(b) and Fig. 2(c) optimize parameters Rfw and Rsw from perspectives of the average of core loss, the fluctuation of core loss and the torque. Fig. 2(d) and Fig. 2(e) shows comparison of iron loss between initial motor and optimal motor. It can be seen that the average and fluctuation of optimal motor both decrease through optimizing. III. Conclusion In this paper, the iron loss characteristics are studied and improved based on VLF-PM motor under multiple operation conditions. The average and fluctuation of iron loss are reduced by optimizing the size of the motor. The results provide a new orientation for studying the iron loss characteristics of VLF-PM motor. More detailed electromagnetic performance analysis and experimental results will be presented in the full paper.

**References:**

[1] M. Minowa, H. Hijikata, K. Akatsu and T. Kato, in Proc. IEEE ECCE, 2014, pp. 3828-3833. [2] W. Wu, Q. Chen and X. Zhu, IEEE Trans. Magn., doi: 10. 1109, Aug. 2020, Art no. 3015784.

**Images:**
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d53d8d5dba649d979c465f249102d187.jpg)

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/0b46567e1fcb594d28161877f6615f94.jpg)

 Research on iron loss characteristics of a variable-leakage-flux permanent magnet motor considering multiple operation conditions

I.Background Transmission line (TL) is a fundamental structure that can easily be identified in an electric system by various forms, for instance, the external incoming/outgoing line and internal windings of an electrical machine, etc. [1]–[4]. These TLs represent dominant propagation paths for radiated noises coupling into an apparatus, resulting in potential susceptibility effects like over-voltage breakdown, insulation failure. As a result, with the objective to ensuring safety operation of system in complex electromagnetic environment and assessing its radiated immunity, it is of great interest to predict the voltage/current responses of TL under the illumination of external electromagnetic interferences. In this connection, the TL model based on solving telegrapher's equation receives undoubtedly the most attention. To incorporate the impinging field contribution into TL model, pioneer works by Taylor et al. [5], Agrawal et al. [6] and Rachidi et al. [7] argued three different but equivalent approaches to cast the field contributions as a set of equivalent circuit sources. Besides, researches started to look outside of classic FC models for alternatives approaches, the motivation includes interpreting Taylor's, Agrawal's and Rachidi's approach in a unified theory [8], predicting transient field responses [9], analyzing the worst-case load responses [10]–[12], etc. Lorentz reciprocity theorem, which was exploited in [8]–[12], demonstrated great potentials in modeling the FC problem. However, a simple concise FC model in parallel to Agrawal's model was still missing in the literature. In this study, we re-consider the FC problem by taking advantage of the reciprocity theorem, specifically, through solving the TL in transmitting mode, analytical solution of far-field radiation pattern and input impedance are obtained, which leads to closed-form expressions of equivalent voltage sources accounting for the field contributions. The sources are then incorporated into a passive TL model, resulting in a solvable two-port network with active feeding sources and terminal impedances connecting to the terminals. II.The Proposed FC Approach As shown in Fig.1, a lossless single conductor transmission line of length l and radius rw is placed parallel above the ground plane at height h. The system can be regarded as a two-port system under the assumption h&lt;&lt;c0/f, where c0 is speed of light in free space, f is frequency. The TL is illuminated by a linearly polarized uniform plane wave of electrical field E, magnetic field H, and propagates vector k. Incidence angles (θ, Φ) and polarization angle (η), are defined in the spherical coordinates. In this regard, the TL under study can be treated as a two-port network with two voltage sources connected to two ports, representing the contribution of external field, resorting to the generic multi-port reciprocity theorem discuss in [13], the sources can be cast as function of radiation pattern and input impedance, which needs to be solved by considering TL in transmitting mode, namely, a dummy voltage source is connected to the port whereas the opposite terminal is left open. According to passive TL model and solution in [14], [15], the far-field radiation field can be solved analytically, which finally leads to the proposed closed-form TL model. The proposed method is verified by comparing to the classic FC model [16]. Without the loss of generality, we consider a TL of l=1 m, h=1 cm, rw=1 mm and impedances ZL=10 Ω, ZR=50 Ω. Let |E|=1 V/m. Different impinging waves are considered, namely, wave #1 (θ=138.6o, Φ=40.9o, η=184.1o), wave #2 (θ=90o, Φ=73o, η=180), wave #3 (θ=90o, Φ=73o, η=270o). The magnitude of the induced voltage across the left load |VL| predicted by both proposed reciprocity model and classic TL model from 1 MHz to 1 GHz, the results are summarized in Fig. 2. The predicted load voltages by two methods agree perfectly with each other for all three cases. Therefore, it can be concluded that the proposed model could offer trustworthy predictions to the FC problems. III.Conclusions An algorithm for computing the field-to-wire coupling problem is proposed based on the reciprocity theorem. The contributions due to the external field are modeled as equivalent voltage sources, whose expressions are obtained in closed-form. Owing to the non-conventional definitions of incidence and polarization angles, the proposed method offers a more concise and physical interpretation for the field-to-wire coupling phenomena, the effects of incidence and polarization angles are conveniently decoupled in the closed-form solution. In this connection, the proposed method is more advantageous in addressing the wave angles associating to maximal/minimal coupling efficiency.

**References:**

[1] Y. Ryu, B. Park, and K. J. Han, “Estimation of High-Frequency Parameters of AC Machine From Transmission Line Model,” IEEE Transactions on Magnetics, vol. 51, no. 3, pp. 1–4, Mar. 2015, doi: 10.1109/TMAG.2014.2355718. [2] Y. Huangfu, L. D. Rienzo, and S. Wang, “FDTD Formulation Based on High-Order Surface Impedance Boundary Conditions for Frequency-Dependent Lossy Multi-Conductor Transmission Lines,” IEEE Transactions on Magnetics, vol. 56, no. 1, pp. 1–4, Jan. 2020, doi: 10.1109/TMAG.2019.2950603. [3] Q. Zhang et al., “Application of an Improved Multi-Conductor Transmission Line Model in Power Transformer,” IEEE Transactions on Magnetics, vol. 49, no. 5, pp. 2029–2032, May 2013, doi: 10.1109/TMAG.2013.2245874. [4] H. D. Gersem and A. Muetze, “Finite-Element Supported Transmission-Line Models for Calculating High-Frequency Effects in Machine Windings,” IEEE Transactions on Magnetics, vol. 48, no. 2, pp. 787–790, Feb. 2012, doi: 10.1109/TMAG.2011.2172197. [5] C. D. Taylor, R. S. Satterwhite, and C. W. Harrison, “The response of a terminated two-wire transmission line excited by a nonuniform electromagnetic field,” IEEE Transactions on Antennas and Propagation, vol. 13, no. 6, pp. 987–989, 1965, doi: 10.1109/TAP.1965.1138574. [6] A. K. Agrawal, H. J. Price, and S. H. Gurbaxani, “Transient response of multiconductor transmission lines excited by a nonuniform electromagnetic field,” IEEE Transactions on Electromagnetic Compatibility, vol. EMC-22, no. 2, pp. 119–129, 1980, doi: 10.1109/TEMC.1980.303824. [7] F. Rachidi, “Formulation of the field-to-transmission line coupling equations in terms of magnetic excitation field,” IEEE Transactions on Electromagnetic Compatibility, vol. 35, no. 3, pp. 404–407, 1993, doi: 10.1109/15.277316. [8] M. Stumpf and G. Antonini, “Electromagnetic Field Coupling to a Transmission Line—A Reciprocity-Based Approach,” IEEE Transactions on Electromagnetic Compatibility, pp. 1–9, 2018, doi: 10.1109/TEMC.2018.2884038. [9] R. G. Olsen and A. G. Tarditi, “EMP Coupling to a Straight Conductor Above Ground: Transmission Line Formulation Based on Electromagnetic Reciprocity,” IEEE Transactions on Electromagnetic Compatibility, pp. 1–9, 2018, doi: 10.1109/TEMC.2018.2838080. [10] F. Vanhee, D. Pissoort, J. Catrysse, G. A. E. Vandenbosch, and G. G. E. Gielen, “Efficient Reciprocity-Based Algorithm to Predict Worst Case Induced Disturbances on Multiconductor Transmission Lines due to Incoming Plane Waves,” IEEE Transactions on Electromagnetic Compatibility, vol. 55, no. 1, pp. 208–216, Feb. 2013, doi: 10.1109/TEMC.2012.2208754. [11] T. Liang and Y.-Z. Xie, “Determining Incidence and Polarization of Electromagnetic Field for Maximal/Minimal Coupling to Transmission Line System,” IEEE Microwave and Wireless Components Letters, vol. 30, no. 11, pp. 1021–1024, Nov. 2020, doi: 10.1109/LMWC.2020.3021695. [12] T. Liang, G. Spadacini, F. Grassi, and S. A. Pignari, “Coupling of wideband radiated IEMI to cables above ground,” IEEE Transactions on Electromagnetic Compatibility, vol. 61, no. 6, pp. 1–9, 2018, doi: 10.1109/TEMC.2018.2877508. [13] T. Liang, G. Spadacini, F. Grassi, and S. A. Pignari, “Worst-Case Scenarios of Radiated-Susceptibility Effects in a Multiport System Subject to Intentional Electromagnetic Interference,” IEEE Access, vol. 7, pp. 76500–76512, 2019, doi: 10.1109/ACCESS.2019.2921117. [14] R. Ianconescu and V. Vulfin, “Radiation from transmission lines PART I: free space transmission lines,” arXiv preprint arXiv:1701.04878, vol. 2, no. 1, pp. 1–9, 2017, [Online]. Available: http://arxiv.org/abs/1701.04878. [15] R. Ianconescu and V. Vulfin, “Radiation from free space TEM transmission lines,” IET Microwaves, Antennas & Propagation, Jun. 2019, doi: 10.1049/iet-map.2018.6061. [16] C. R. Paul, Analysis of multiconductor transmission lines. New York: IEEE, 2007.

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 Closed-Form Electromagnetic Field Coupling to Transmission Line Model Exploiting the Reciprocity Theorem

I. Introduction When a short-circuit fault occurs on the DC side of the ship DC system, the peak short-circuit current on the DC side can reache 100kA, and the current rise rate can reach 20kA/ms, which is difficult for the existing DC circuit breaker (DCCB) to remove the fault circuit [1], [2]. The coordination of superconducting fault current limiter (SFCL) and DCCB is a good current limiting and breaking scheme. However, there is a lack of feasibility experimental studies of SFCL in short-circuit faults of ships. The topology of DC superconducting current-limiting switch (SCLS) is shown in Fig. 1(a). The structure of SCLS is designed, then the prototype is manufactured and its principle experimental tests are conducted. II. Principle and Structure of SCLS Superconducting flux-coupling coil is one of core component of SCLS, its principle mainly includes two aspects. The first is the principle of branch current sharing, in which reverse-coupled coils can maintain the same current in two branches. The second is the principle of current limiting, which uses the quench characteristics of R-SFCL to increase the line impedance and reduce the short-circuit current level [3]. Due to R-SFCL usually use non-inductive coils and the two branches of SCLS are connected in series with a DCCB, there are mainly two coil winding methods for SCLS: pancake-winding (PW) and layer-winding (LW) both made of 4 mm wide 2G YBCO tape [4], [5]. These two coils are manufactured and the structure diagram are shown in Fig. 1(b). By calculating the distribution of the leakage magnetic field of the two coils in COMSOL, it is found that the gap between each cake in PW coil makes the magnetic field distribution uneven and there is a larger leakage magnetic field than LW coil. It can also be calculated from Formula (1) and (2) that the LW coil has a higher m by measuring the inductance of the two coils with the LCR instrument. Therefore, the following principle verification experiment uses LW coil. Leq=M+(L1-M)//(L2-M)=M+(L-M)/2=(L+M)/2 (1) m=-M/L (2) (where L1 and L2 are the branch inductance, L1 = L2=L, M is the mutual inductance, Leq is the actually measured coupling inductance, and m is the coupling degree.) III. Experimental results and discussion The current sharing test is completed. Put SCLS into DC source circuit, and the currents of the two branches i1=i2=8A. With or without LW coil, the branch current sharing effects of DCCB breaking at different times are compared. At t1, t3, the DCCB of branch 1 is opened, and at t2, t4 the DCCB of branch 2 is opened. The experimental results are shown in Fig. 2(a), (b). Before t1, from Fig. 2(a), the two branch currents are different due to the minor difference in branch impedance; However, before t3 in Fig. 2(b), i1=i2 due to the existence of the LW coil. During t1~ t2 in Fig. 2(a), all current in branch 1 is gradually transferred to branch 2; However, during t3~ t4 in Fig. 2(b), the current of branch 2 can basically remain unchanged. Therefore, SCLS has a good current sharing effect, which verifies the effectiveness of the current sharing principle. The current limiting effect of the LW coil of SCLS is tested experimentally. Since this huge surge in the fault current is caused by the discharge of the DC-link capacitor [6], an RLC DC impact platform is built to simulate the fault current waveform. Set the main paraments of the circuit are R=0.2Ω, L=0.1mH, C=6mF so that the rise time of the fault current is within 1ms. And the current peak value can be gained by adjusting the capacitor charging voltage. The comparison of current limiting effect before and after installation of LW coil is shown in Fig. 2(c). The current limiting effect of the LW coil is obvious, the peak value of impulse current is limited from 3.0kA to 1.3kA, and current limiting ratio can reach 56.67%. In addition, the time of the peak is also delayed from the original t5=0.83ms to t6=0.97ms. It can also be seen from Fig. 2(d), the quench resistance of each branch can increase from 0Ω to 0.7Ω in 1ms, which has a fast current limiting response speed. Therefore, the LW coil of SCLS has a good current limiting effect, which verifies the efficiency of the current limiting principle. IV. Conclusion In this research, the structures of PW coil and LW coil are designed and compared, and the principles of SCLS are experimentally studied. The experimental results are as follows: (1) Compared with PW coil, the LW coil has a more uniform magnetic field distribution and a higher m. (2) Due to the existence of the coupling coil, SCLS can ensure that the currents of the two branches are equal and can also reduce the current deviation caused by the two switches not being opened at the same time. (3) The superconducting coil plays a key role in restraining short-circuit current level and absorbing DCCB breaking capacity, which is conducive to the smooth removal of the fault.

**References:**

 [1] "IEEE Recommended Practice for 1 kV to 35 kV Medium-Voltage DC Power Systems on Ships," in IEEE Std 1709-2018 (Revision of IEEE Std 1709-2010) , vol., no., pp.1-54, 7 Dec. 2018. [2] K. Satpathi, A. Ukil. “Modeling and real-time scheduling of DC platform supply vessel for fuel efficient operation,” IEEE Transactions on Transportation Electrification, vol. 3, no. 3, pp. 762–778, 2017. [3] Z. Cai and L. Ren, "Design and Analysis of Superconducting Current-Limiting Switch in Ship MVDC System," 2020 IEEE International Conference on Applied Superconductivity and Electromagnetic Devices (ASEMD), pp. 1-2, Tianjin, 2020. [4] S. Yan, Y. Tang, L. Ren and Z. Wang, "AC loss analysis of a flux-coupling type superconducting fault current limiter," 2018 IEEE International Magnetics Conference (INTERMAG), pp. 1-2, Singapore, 2018. [5] L. Chen, "Current limiting characteristics of a novel flux-coupling type superconducting fault current limiter", IEEE Trans. Appl. Superconduct., vol. 20, no. 3, pp. 1143-1146, Jun. 2010. [6] Satpathi, Kuntal, Abhisek Ukil. Short-circuit fault management in DC electric ship propulsion system: protection requirements, review of existing technologies and future research trends [J]. IEEE Transactions on Transportation Electrification, 4 (1): 272-291, 2017.

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/06821fcef7bbfa2f172f74f81ab3fc7e.jpg)
Figure 1: (a) The topology of SCLS; (b) The structure and physical diagram of PW coil and LW coil.

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Figure 2: Current sharing experiment: (a) without superconducting coupling coil; (b) with superconducting coupling coil; Current limiting experiment: (c),(d) Current limiting result.

 Design and Experimental Verification of DC Superconducting Current-Limiting Switch

Interior permanent magnet synchronous motors (IPMSMs) are used for applications that require high torque and an extended operational speed range. In IPMSMs, both magnetic torque and reluctance torque are generated due to the difference of inductance between the d- and q-axis. Therefore, torque utilization is high. Moreover, IPMSMs have a wide operating range because of flux-weakening control, which increases the d-axis flux in the negative direction [1, 2]. In general, current source analysis based on sinusoidal current is employed for the design of IPMSMs. This process can simplify the design, and the obtained values of the overall electromagnetic characteristics are almost identical to experimentally measured values. In the IPMSM drive system, the space vector pulse width modulation (SVPWM) technique is widely used due to high voltage utilization rate. SVPWM generates current harmonics through switching processes. These harmonic components increase torque ripple and loss, as well as vibration and noise. Therefore, current source analysis considering current harmonics provides highly accurate predictions of the electromagnetic characteristics of IPMSMs, because it enables more accurate loss prediction than sinusoidal current source analysis does [3]. Moreover, by comparing the mechanical analysis of IPMSMs considering sinusoidal and harmonic currents, the influence of current harmonics on mechanical noise can be determined. In this study, mechanical analysis of IPMSM based on SVPWM control is performed to analyze the influence of current harmonics on mechanical noise. Harmonic current can be obtained via experiment and simulation, as shown in Figure 1. (a) and (b). Figure 1. (a) shows the back-to-back experimental setup used for the IPMSMs. Current is applied to the motor through the SVPWM inverter and contains harmonics due to the switching in the SVPWM inverter. The load torque to the motor is generated by the generator on the other side of the motor through the torque sensor. The torque of the generator can be adjusted using the DC load machine. The analysis model used in this study, as shown in Figure 1. (a), is a V-shape IPMSM with 6 poles, 9 slots, and a concentrated winding. The experiment is performed at the rated speed of the analysis model, and the current applied to the motor is measured and used in the mechanical noise analysis. Figure 1. (b) shows the SVPWM control block of the IPMSMs in simulation. Moreover, the current-generating technique of the SVPWM inverter identified. SVPWM inverter contains proportional and integral (PI) controllers for adjusting the current and speed. To improve the control performance, dq-axis coordinate transformation is used. Park’s transformation converts the stationary dq-axis coordinates to rotating dq-axis coordinates. Clark’s transformation converts the Cartesian coordinates to stationary dq-axis coordinates. Feedback of speed and position information is obtained from the motor to ensure that the motor can follow the reference speed and current closely. Figure 2. (a) shows the measured current waveform obtained through the experiment, and harmonic component can be seen in this figure. Figure 2. (b) presents the harmonic spectrum of the measured current. We can confirm that the 3rd, 5th, 7th, 11th, and 13th harmonics have a significant influence on the harmonic current. Figure 2. (c) and (d) present the mechanical vibration analysis results for the sinusoidal and measured current, respectively. The noise from the current containing harmonics is greater than that from the sinusoidal current; the majority of the noise is generated by the 6th, 12th, 18th, 21st, and 24th harmonics. From Figure 2, it can be seen that multiples of 6th order component of the current harmonic affects the mechanical noise although the harmonic magnitude is small. In finalized of version of this paper, the current harmonic in the SVPWM control simulation will be discussed, and its mechanical analysis will be presented. In addition, a more detailed discussion and more results will be provided.

**References:**

[1] K. H. Shin, J. Y. Choi, and H.W. Cho, “Characteristic Analysis of Interior Permanent-Magnet Synchronous Machine With Fractional-Slot Concentrated Winding Considering Nonlinear Magnetic Saturation,” IEEE Trans. Appl. Supercond., vol. 26, no. 4, June. 2016, ID 5200404. [2] S. H. Lee, Y. J. Kim, and S.Y. Jung, “Numerical Investigation on Torque Harmonics Reduction of Interior PM Synchronous Motor With Concentrated Winding,” IEEE Trans. Magn., vol. 48, no. 2, pp. 927-930, Feb. 2012. [3] T. C. Jung, W. H. Kim, M. J. Kim, K. D. Lee, J. J. Lee, J. H. Han, T. H. Sung, H. J. Kim, and J. Lee, “Current Harmonics Loss Analysis of 150-kW Traction Interior Permanent Magnet Synchronous Motor Through Co-Analysis of d-q Axis Current Control and Finite Element Method,” IEEE Trans. Magn., vol. 49, no. 5, pp. 2243-2246, May. 2013.

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Figure 1. (a) Back-to-back experimental setup for IPMSMs. (b) SVPWM control block of IPMSMs.

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Figure 2. (a) Measured current waveform. (b) Harmonic spectrum of measured current waveform. Results of mechanical noise analysis for (c) sinusoidal current and (d) measured current.

 Influence of Current Harmonics on Mechanical Noise of Interior Permanent Magnet Synchronous Motor Driven by SVPWM Control

Induction motors are widely used in production due to their simple structure, no-winding rotor, low cost, and convenient maintenance. In order to further improve the electromagnetic performance, some researchers have proposed a new topology structure of the double skewed rotor, which has the advantages of low noise and low vibration [1], and solved the problem that the single skewed rotor induction motor is prone to axial movement and the shortcomings of synchronous additional torque cannot be completely eliminated [2]. In recent years, researchers have optimized the main rotor parameters, but only briefly introduced the intermediate ring (IR) parameters in this type of center ring rotor [3]. In addition, the lack of design strategies for thermal simulation can lead to potential motor failures. This article puts forward a point of view, due to the difference in the electrical density of the middle ring (IR) and the conductive bar will cause greater thermal stress at the junction. Taking into account that under certain operating conditions, when the instantaneous load is huge, the thermal stress at the start time is likely to cause broken bars and broken shafts. Therefore, this article believes that the thermal stress at the moment of startup is considered the main cause of IR electrical failure. Figure 1 a is an electromagnetic model, b is a thermal simulation model and c is the experimental prototype. Compared with the electromagnetic model, thermal simulation model it considers parts such as the casing and wind blades that cannot be ignored. Fig. 2 a is the steady-state thermal analysis of the squirrel cage rotor and shaft in case of locked rotor, and b is the thermal stress analysis of the squirrel cage rotor and shaft. It can be seen from the figure that due to the temperature difference between the guide bar and the middle ring, the maximum thermal stress of the squirrel cage appears at the junction of the guide bar and the middle ring, while the maximum temperature of the rotating shaft is at the location of the middle ring. The simulation situation is roughly consistent with that of the prototype. Detailed results and discussion will be given in the full text.

**References:**

[1] L. Wang, X. Bao, C. Di and J. Li, "Effects of novel skewed rotor in squirrel-cage induction motor on electromagnetic force and vibration characteristics," 2015 IEEE International Magnetics Conference (INTERMAG), Beijing, 2015, pp. 1-1, doi: 10.1109/INTMAG.2015.7157420. [2] L. Wang, X. Bao, C. Di, et al. Analysis of synchronous parasitic torque in dual skew cage rotor induction motors with equivalent slot number[J]. Iet Electric Power Applications, 2017, 11(8):1357-1365. [3] W. Xu, X. Bao, C. Di, L. Wang and Y. Chen, "Optimal Angle Combination for Improving Electromagnetic Torque in Induction Motor With Double-Skewed Rotor," in IEEE Transactions on Magnetics, vol. 53, no. 11, pp. 1-5, Nov. 2017, Art no. 8206405, doi: 10.1109/TMAG.2017.2707239.

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 Analysis and Calculation of Magneto-Thermal-Structure Coupling of Double-skewed Induction Motor based on Multiphysics field

I. Introduction Motor characteristics are calculated considering sinusoidal current in a conventional design stage. However, pulse width modulation(PWM) is used to generate alternating current(AC), which will lead to a current distortion. The harmonics in the PWM current cause considerable losses on the iron core [1]. For this reason, considering fundamental current for analysis leads to the decrease of the accuracy of the prediction results. Therefore, it is essential to predict motor characteristic considering harmonic current for electromagnetic design [2]. However, Conventional method considering PWM current needs to put all the large number of analysis step of PWM current into nonlinear finite element analysis(FEA), which leads to the increase of analysis steps and computational time. Therefore, this paper proposes a combined nonlinear and linear FEA method to reduce computational time. In order to reduce the number of analysis step, fundamental current is used to calculated permeability of each element through nonlinear FEA. Then the permeability at each step is interpolated and PWM current is used to predict the motor characteristic through linear FEA. The proposed method is applied to a 130kW IPMSM for traction to calculate iron loss. Comparing with a conventional method that considered PWM current, the proposed method has a high accuracy with a low computational time. II. The proposed analysis method The proposed analysis method is shown in Fig.1. Since the difference between fundamental current and PWM current is small enough not to affect the saturation in iron core as shown in Fig.2 (a), the saturation considering fundamental and PWM current are assumed to be the same. Therefore, the fundamental current can be used to calculate the saturation of the core, and the number of nonlinear analysis step can be reduced. Then, the permeability of each element can be calculated by nonlinear FEA. In order to perform the linear FEA by PWM current which has a lot of data, permeability is interpolated to satisfy all the linear analysis points. Finally, the iron loss can be calculated by linear FEA. A. Determination of non-linear analysis steps First of all, since the PWM current has a large number of data, the number of nonlinear analysis step needs to be large enough, which leads to an increase in computational time. In order to reduce the computational time and maintain the correctness of the analysis, the fundamental current is used to perform a nonlinear FEA. Secondly, gradually reduce the number of step while ensuring the magnetic flux waveform is almost constant. Then, by comparing with the magnetic flux waveform at different positions, it can be known that rib has the highest correlation between the magnetic flux density and step number. And 91 steps are the minimum analysis steps that can describe the original waveform best. Therefore, 91 steps are selected as the minimum analysis steps in this paper. B. Magnetic permeability extraction and interpolation After selecting 91 steps as the minimum analysis steps, the permeability of each element of nonlinear analysis is extracted. And then, considering that the PWM current has a lot of steps, the permeability is interpolated, in order to well describe the PWM current. C. Linear analysis After interpolating the permeability, the number of linear analysis step is increased in order to well describe the PWM current. Then put the interpolated permeability into each element to perform the linear analysis. D. Comparison with conventional method From the analysis results, as shown in the Fig.2 (b), the iron loss calculated by the conventional PWM current method, conventional fundamental current method and the proposed PWM current method can be obtained. Comparing the above three, it can be seen that the iron loss calculated by conventional fundamental current method is quite different from conventional PWM current method, with a difference of 29.7%. However, iron loss calculated by proposed PWM current method is similar with conventional PWM current method, only with a 1% difference. At the same time, computational time is reduced by 88.5% compared with conventional PWM current method. III. Conclusion In this paper, a combined nonlinear and linear analysis method based on PWM current is proposed, which can greatly shorten the analysis time on the premise of ensuring the accuracy of analysis. Compared with the conventional nonlinear analysis which considering the PWM current, this method has high accuracy with only 1% difference. And the computational time is also dramatically reduced. The method proposed in this paper is reliable and feasible. The experimental verification will be conducted in the final paper.

**References:**

[1] Y. Miyama, M. Hazeyama, S. Hanioka, "PWM Carrier Harmonic Iron Loss Reduction Technique of Permanent-Magnet Motors for Electric Vehicles," in IEEE Transactions on Industry Applications, vol. 52, no. 4, pp. 2865-2871, July-Aug. 2016. [2] R. Mayuri., N. R. Sinnou and K. Ilango, "Eddy current loss modelling in transformer iron losses operated by PWM inverter," 2010 Joint International Conference on Power Electronics, Drives and Energy Systems & 2010 Power India, New Delhi, 2010, pp. 1-5.

**Images:**

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Fig. 1 Combined nonlinear and linear FEA process

(a) Fundamental current & PWM current 
(b) Comparison of iron loss and computational time 

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Fig. 2 The influence of harmonics on the analysis results

 Prediction of Iron Loss with Combined Nonlinear and Linear Finite Element Analysis Considering Current Harmonics by PWM

Ι. Introduction The anode saturable reactor is a critical element in the thyristor converter vavle of HVDC (high voltage direct current) transmission system, which is designed for limiting the current rise of the thyristor so as to protect it. However, the non-uniform distribution of core loss of anode saturable reactor can cause overheating and thermal aging of the insulating material, eventually lead to the failure of the reactor [1-2]. It is difficult to measure the local core loss of reactor directly so we have to monitor real-time temperatures with the infrared thermocamera [3]. Because of the complex working current waveform of saturable reactor, Bertotti core loss separation model suitable to sinusoidal excitation is no longer available [4]. Therefore, the dynamic core loss calculation method is used to calculate core loss of the reactor [5-6]. In this paper, the model of saturable reactor is established, and the core loss is analyzed by electro-magnetic finite element method (FEM). To couple the data from magnetic field to temperature field accurately, core loss is mapped between heterogeneous meshing. Meanwhile, the thermal network model of the saturable reactor is built up. Based on the calculation results of computing fluid dynamics (CFD) software, the convective heat transfer coefficients on the reactor surfaces are extracted for thermal resistances calculation. Finally, the steady-state temperature distribution is obtained. The validity of the FEM and thermal network is verified by the temperature rise experiment. ΙΙ. Anode saturable reactor model The model of the saturable reactor is shown in Fig.1(a). Located inside the reactor, the hollow aluminum winding consists of 5 turns, which is wrapped by epoxy resin and cooled by circulated water in the aluminum tubes. The 9 pairs of cores, epoxy resin and winding are encapsulated into the reactor fiberglass enclosure with polyurethane elastomer. The outside surfaces of the reactor dissipate heat by natural convection, while the inside surfaces of the reactor can transfer the heat through the circulation aluminum tubes due to highly efficient forced water cooling. In addition, because of the geometric symmetry of the reactor, a one-ninth model of saturable reactor is established for temperature simulation, as shown in Fig.1(b). Other boundary conditions of the model are shown in Fig.1(c). ΙΙΙ. Magnetic-thermal- fluid coupling analysis A. Magnetic field calculation In order to reduce eddy loss, the core is made of ultra-thin silicon steel sheets with 0.1mm thickness. The leakage magnetic flux penetrates into the silicon steel normally, so the outermost layers silicon steel sheets have significant eddy current. The exact laminated model of sheet-by-sheet reactor is difficult to computed. In order to simulate the surface local eddy current, the homogenous numerical technique is adopted for FEM modelling. The distribution of magnetic flux density is shown as Fig.2(a). Under the impact of air gap, winding structure and leakage magnetic field, the eddy loss is concentrated in the core surfaces and the air gap as shown in Fig.2(b). B. Calculation of temperature field and fluid field In traditional magneto-thermal coupling method, the loss from magnetic field is obtained by integrating over the whole region and then distributed evenly to each element. This coupling mode with equally distributed loss density underestimates the highest hot-spot so as not to be accurate enough for the reactor model. Consequently, the node-to-node mapping method can predict the loss distribution inside the saturable reactor more precisely. The triangulation element in magnetic field calculation is tetrahedron, while the element in the solid region of CFD is hexahedron. Namely, the meshes of the two physical fields are heterogeneous, so the data cannot be delivered directly. The method of interpolation between the adjacent nodes is proposed in the paper to map the core loss to CFD. The heat sources of saturable reactor are consisted of core loss and hollow aluminum winding loss. Since the temperature in aluminum winding is lower than that in epoxy resin and core, and the cooling water inside winding is a fluid with stable flow rate, the convection heat transfer coefficient is constant. So the winding can be regarded as an internal convective heat transfer boundary condition, which convection heat transfer coefficient on the interface of the winding is 6 W/(m2●K) by experiment [7]. Contacting with air, the exterior surfaces of reactor dissipate heat by natural convection. By solving energy conservation, momentum conservation and mass conservation equations, the distributions of reactor temperature and air velocity are shown in Fig.2(c) and Fig.2(d). ΙV. Experimental results and discussion The current of the reactor under actual operating conditions is excited into the winding. When the overall temperature is stable, the infrared thermograph is used to record the temperature distribution on the reactor housing. The experimental results show that the highest temperature on the shell is located in the inner toroidal surface, which is 317.15K and in good agreement with CFD simulation results. V. Conclusion The average surface temperature of the saturable reactor is 315.15K, and the highest temperature is 317.15K at the top of the inner ring surface. Affected by the buoyancy and the uneven distribution of loss, the hottest spot of core is located at the inner and upper position with 354.15K.

**References:**

[1] C. Peng, S. Baokui, and J. Feng, High Voltage Engineering., Vol.42, p.2612-2617 (2016) [2] Z. Yang, 2019 IEEE 10th International Symposium on Power Electronics for Distributed Generation Systems., p.294-298, (2019) [3] J. Cao, F. Ji, and J. Liu, IET Science, Measurement & Technology., Vol.10, p.77-83 (2016) [4] G. Wenjun, H. Shaogang, and Y. Yuwen, Motor and Control Application., Vol.43, p.82-85 (2016) [5] S. Barg, K. Ammous and H. Mejbri, IEEE Transactions on Power Electronics., Vol.32, p.2146-2154 (2017) [6] D. Lin, P. Zhou, and W. N. Fu, IEEE Transactions on Magnetics., Vol.40, p.1318-1321 (2004) [7] M. Yan, D. Shengchu, and G. Lu, High Voltage Engineering., Vol.44, p.3359-3367 (2018)

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/9cf6e1206600c2719dceffe99c377d82.jpg)
Fig.1 Establishment of anodic saturation reactor model

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/9753a737299e46d235b4eec5a0573616.jpg)
Fig.2 Simulation results of one-ninth model

 Magnetic-Thermal Coupling Analysis of Anode Saturable Reactor

1. This research aims to study the edge computing devices with a faster processing and signal connecting function based on development of the physical layer and magnetic sensing devices. It is important matter for smart robot in multi-axis motor control. Based on the variable robot properties, it includes humanoid robots, wheeled machines, and fixed robots, respectively, are contented. This research is constructed as follows: to establishing an edge computing device system, the image vision system with neural-network learning theory to control robot arm path, multiple magnetic sensors in physical layer to analyze the signals of the motor, voltage, current, temperature, etc., are transmitted signal to the edge computing device and IoTs computing server system. 2. Introduction The Industry 4.0 concept represents the trend of data exchange and automation in the manufacturing industry. It is defined by cloud computing, cyber-physical systems and the IoTs. In Industry 4.0, computers and automation technologies are integrated with robots and their components [1,2]. These robots and other components are remotely connected to a computer system, and the computer system is equipped with algorithms that can control and learning robots with minimal human intervention. For the motor device, the robot composes the control of the DC motor and relate to the accessories vital role. However, there are many factors that can misguide the controller's work, to make an unable to accurately control and/or have the desired dynamic behavior. For example, the resistance (Ohmic) of the coil winding of the motor is changed due to the temperature is different. If the vibration level is high and the wear of the rotor ball bearing becomes larger, the friction coefficient will also be affected. Therefore, the cloud computing environment of industrial factories, a continuous processing is required to re-evaluate the precise values of motor parameters and update the corresponding controller settings. In addition, it should be noted that the torque and speed sensors of the motor must have the correct selection to assist for achieving the correctness of the program. 3. Theory and methods: multi-axis motor sensing and visual images of robotic arms Collaborative robots focus on intelligent motor control. Based on this construction, multiple sensor component signals are added. The physical information such as voltage, current, vibration, electric heating, magnetic flux sensing, and motor position is diagnosed through integrated control. This study, the artificial intelligent motor with the sensing signals, is used to control motor speed, positioning, constant horsepower, constant torque, force feedback, vibration resistance, overheating, overload, and instantaneous short circuit, as shown in Figure 1. The electromagnetic control of this paper is as follows: A. Single robotic arm function automation: Directly control the robot motor, at the same time, it has higher precision and speed to perform specific tasks repeatedly, but most of them cannot clearly actuate without an electromagnetic sensor. B. Part of the arm automation: It assists decision-making through environmental sensing input signals. In this study, robots use vision and sensors to determine the decision-making process, which is not easy to deal with accidental arm interference. C. Conditional autonomous robot: Control the arm according to the environmental monitoring behavior, but the external server can operate in real time. D. Highly autonomous robot: an environment that needs to be defined in an area or any situation without human operation. 4. Experimental results and discussion Based on the motor control of intelligent robots, this research proposes a better and faster algorithm structure, which is a neural network-like combined with particle swarm method, which is used to calculate the convergence result of a lower loss function, which can accurately control the motor parameters and combine the IoTs, as shown in Figure 2. First, the robotic arm establishes multi-input sensing values, using the above algorithm to evaluate the robotic arm motor parameters, the prevention of interference from peripheral physical sensing, and the signal processing of external visual images. The issues raised based on past research experience include:(1) Establish edge and fog calculations to control the voltage and current of the motor, (2) establish neural network algorithm to calculate motor parameter, (3) construct the image vision system, (4) establish a smart robot platform, including wheel-shaped and human-shaped robots as experiments, which uses the above-mentioned deep learning theory to construct the test of the robot's motor motion and signal transmission response, (5) to use the multiple sensors, motor electromagnetic signals, piezoelectric sensors, and load signals, as the force feedback of the robot to calculate and judge. Finally, (6) to integrate the edge computing of the sensing layer, the fog computing of the signal processing layer, and faster computing layer through the IoTs cloud server. The IoTs chip is to use the dual-core Linkit-7697 (Taiwan’s MediaTek Inc). The chip can perform as a cloud computing and remote device, which indeed meet the requires of providing multi-sensing force feedback for cooperative robot handling objects.

**References:**

[1]. Chang-Hung Hsu*, et. al., “Effect of Magnetostriction on the Core Loss, Noise, and Vibration of Fluxgate Sensor Composed of Amorphous Materials,” IEEE Trans. on Magnetics, vol. 49, no. 9, pp: 3862-3865, 2013. [2]. Chang-Hung Hsu*, “Fractional Order PID Control for Reduction of Vibration and Noise on Induction Motor, IEEE Transactions on Magnetics, vol. 55, no. 11, pp. 6700507-1-7, Nov. 2019.

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/25aedc186791a6c6ab6b9b1e787bf147.jpg)
Figure 1 The artificial intelligent motor with the sensing signals including as motor speed, positioning, horsepower, torque, force feedback signals.

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/4f2f81175e1c787ad9280be42610481b.jpg)
Figure 2 The smart motor of the robot performance testing results and AI vision detection.

 Research on Electromagnetic Control of Robot Arm using Smart Motor Combined with Internet of Things

The renewable energy is introduced because of global environmental problems. The vibration energy generated by the electric vehicle and the buildings is considered. Using the linear synchronous generator, this energy is converted to electric energy. The charging circuit with the EDLC (Electric Double-Layer Capacitor) for the linear synchronous generator is introduced. The linear synchronous generator extends the cruising distance of the electric vehicle and lighting of the buildings. In addition, it also suppresses vibration. Thus it is used as the damping device such as the mechanical damper [1]. Fig.1 shows the linear synchronous generator. The electric energy is generated by using the linear synchronous generator. The linear synchronous generator consists of the stator part and the vibration part. The permanent magnet and the iron yoke are set on the stator part. The coil for the generation is set on the vibration part. The vibration is generated by giving the initial energy (the elastic energy by the mechanical spring) to the vibration part. When the coil moves in the x-axis direction on the permanent magnet, the linkage flux from the permanent magnet is changed. The electromotive force in the coil is generated by the linkage flux is changed [2]. In this paper, the charging characteristics and the damping characteristics of the linear synchronous generator are studied. The charging characteristics are determined by the charging energy of the EDLC. The vibration waveform is damped by the charging energy of the EDLC, the power consumption in the wire-wound resistance of the coil and the internal resistance of the EDLC, the mechanical loss. The mechanical loss is calculated as the loss proportional to the velocity using the viscosity coefficient c = 2.0 derived from the vibration waveform of the linear synchronous generator. Their characteristics are examined by changing the initial energy given to the vibration part and the frequency of the vibration waveform. The initial energy is changed by the initial displacement of the vibration part. The frequency is changed by the spring constant [3]. In this study, MATLAB/Simulink and PSIM (the electronic circuit simulation software) are used for analysis. The generated voltage Vin is converted to DC voltage by the rectifier. The analysis conditions are as follows; the coil inductance L = 1.4 mH and the wire-wound resistance of the coil RL = 3.0 Ω, the EDLC capacitance C = 0.141 F and the internal resistance of the EDLC RC = 6.67 Ω. The charging characteristics and the damping characteristics are studied by changing the initial energy (0.073 ~ 7.3 J). The initial displacement of the vibration part is changed (10 ~ 100 mm) and the spring constant is 1465 N/m. The frequency is 5 Hz. From the result, the charging energy of the EDLC is increased proportionally as the initial energy increases. This is because the electromotive force in the coil is increased as the initial energy increases. And charging efficiency of the EDLC is increased as the initial energy increases. The linear synchronous generator can be charged with high efficiency as the initial energy increases. The stop time of the vibration part compared to the case that the charging circuit is not connected is the fastest and the vibration part is stopped 38.6% faster when the initial energy is 7.3 J. But the power consumption in the wire-wound resistance and in the internal resistance of the EDLC, and the mechanical loss are increased. The charging characteristics and the damping characteristics are studied by changing the frequency (1 ~ 10 Hz). The initial energy is fixed at 0.36 J. Figs.2(a) shows the vibration waveform (1, 5, and 10Hz), and Figs.2(b) shows the charging energy of the EDLC by changing the frequency (1 ~ 10 Hz). From the result, the charging energy of the EDLC is decreased as the frequency increases. This is because the current in the circuit and the velocity of the vibration part is increased as the frequency increases, and the power consumption in the wire-wound resistance and in the internal resistance of the EDLC, and the mechanical loss is increased. The stop time of the vibration part is shortened as the frequency increases. To improve the charging characteristics, the circuit switching the EDLC is created. Switching uses two EDLCs. The charging characteristics are improved. This is because a low voltage that isn't charged can be charged. And the damping characteristics are improved because the kinetic energy of the vibrating part is consumed faster. In conclusion, the charging characteristics are improved when the initial energy is large and the frequency is low. The damping characteristics are improved when the initial energy is large and the frequency is high. When using as the power generator, the vibration with the large energy amount and low frequency is effective. And when using as the vibration damping device, the vibration with the large energy amount and high frequency is effective. The circuit that switching the EDLC is effective for both the charging characteristics and the damping characteristics.

**References:**

[1] M. Mueller, P. Brooking and J. Xiang, “Low Speed Linear Electrical Generators for Renewable Energy Applications,” Proc. of Int. Symposium on Linear Drives for Industry Applications, pp.29 -32 (2003) [2] K. Ishida, J. Muranishi, T. Aoki, S. Ohashi, “The Generation Characteristics of the Improved Configuration of the Stator and the Mover in the Linear Generator Using Vibration Energy,” IEEE Region 10 Conference (TENCON), pp.2634-2637 (2016) [3] S. Ohashi, T. Matsuzuka, “Basic Characteristics of the Linear Synchronous Generator Using Mechanical Vibration,” IEEE Trans. Magnetics, vol.41, No.10, pp.3829-3831 (2005)

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/a9f91f4198fd736a3b8444300cac1f0c.jpg)
Fig.1 The linear synchronous generator

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/a2e1256195b4fcdf29ac95773ca348b4.jpg)
Fig.2 The charging characteristics and the damping characteristics by changing the frequency

Vibration Reduction of IPMSM with Asymmetric Rotor Shape under Certain Load Condition

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