France



&lt;br/&gt;I. Introduction&lt;br/&gt;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 &lt;sup&gt;[1]&lt;/sup&gt;. 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 &lt;sup&gt;[2]&lt;/sup&gt;. 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.&lt;br/&gt;&lt;br/&gt;II. The proposed analysis method&lt;br/&gt;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.&lt;br/&gt;&lt;br/&gt;A. Determination of non-linear analysis steps&lt;br/&gt;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.&lt;br/&gt;&lt;br/&gt;B. Magnetic permeability extraction and interpolation&lt;br/&gt;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.&lt;br/&gt;&lt;br/&gt;C. Linear analysis&lt;br/&gt;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.&lt;br/&gt;&lt;br/&gt;D. Comparison with conventional method&lt;br/&gt;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.&lt;br/&gt;&lt;br/&gt;III. Conclusion&lt;br/&gt;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.&lt;br/&gt;The experimental verification will be conducted in the final paper.

**References:**

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

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/98b4e723bd35cddb3ef737d361a9da15.jpg)
Fig. 1 Combined nonlinear and linear FEA process

(a) Fundamental current &amp; PWM current&lt;br /&gt;
(b) Comparison of iron loss and computational time&lt;br /&gt;

![](https://assets.underline.io/uploads/markdown_image/1/image/a601bc51031344f8c410c5ebb0a85688.jpg)
Fig. 2 The influence of harmonics on the analysis results

INTERMAG 2021

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

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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:**

![](https://assets.underline.io/uploads/markdown_image/1/image/98b4e723bd35cddb3ef737d361a9da15.jpg)
Fig. 1 Combined nonlinear and linear FEA process

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

![](https://assets.underline.io/uploads/markdown_image/1/image/a601bc51031344f8c410c5ebb0a85688.jpg)
Fig. 2 The influence of harmonics on the analysis results

poster

This paper has proposed two bearingless axial motors (BLAM) with different combination of the number of the rotor poles and the stator slots. The proposed BLAMs are analyzed by 3D finite element analysis (FEA) when the suspension currents are imposed. The winding in the BLAM with the high number of the rotor poles is designed carefully to limited the coupling of different degree of freedoms (DOF) and the ripple of the active suspension force as well as the active restoring torque. The suspension performances are compared between the proposed BLAMs and it shows that ripple of the active suspension force and ripple of the active restoring torque of the BLAM with high number of the rotor poles has at least 33.6 times less than that of the BLAM with low number of the rotor poles. At the same time, the average of the radial suspension force of the BLAM with high number of the rotor poles is 2.65 times larger than that of the BLAM with low number of the rotor poles. I.Introduction The bearingless motor (BLM) is attractive in high speed applications, special environment applications and so on, since it has no lubricant, no pollution, less friction, long device lifetime and maintenance-free [1]-[3]. In the traditional bearingless radial motor (BLRM), the output torque is limited by the volume of the rotor which is limited by the active suspension force. The output torque of the BLAM is not limited due to the active suspension force varies directly as the square of the rotor radius. The BLAM can performed as an all DOF active suspension motor, which is difficult to achieve in the traditional BLRM [4]-[6]. To further enhance the suspension performance of the BLAM, the BLAMs with different combine of the number of the rotor poles and the number of the stator slots are proposed and compared in this paper, and the result shows a well-designed BLAM can reduce the ripple of the active suspension force and restoring torque obviously, and can limited the coupling of different DOF. II.Topologies of BLAM The topology of proposed BLAMs are shown in Fig. 1, which can be divided into two stators and a rotor. The concentrated winding is applied to simplify the manufacture and reduce the length of the end winding. The BLAM-HP has 14 rotor poles combined with 18 stator slots and the BLAM-LP has 4 rotor poles combined with 6 stator slots. Each coil is controlled independently so two kind of armature fields can be controlled. For the BLAM-HP, 12/14 armature fields are imposed and the former is used to control the radial active suspension force as well as the radial active restoring torque, the latter is used to control the output torque as well as the axial active suspension force. For the BLAM-LP, 2/4 armature fields will be imposed and used to control all DOF. The outer radius, the inner radius the gap thickness, the line current density and the axial length of the proposed BLAMs are uniform. III.Performance Comparison of BLAM Topologies The suspension performance comparison between the two BLAMs when only produces the x-axis active suspension force is shown in fig.2. As shows in fig.2, the x-axis active suspension force created by the BLAM-LP is 16.2N in average with 148.6% ripple, which is 43N and 4.4% for the BLAM-HP. It shows the BLAM-HP can enhance the radial active suspension force and reduce the ripple remarkable. From a different perspective, the max unexpected suspension force in the BLAM-LP is 12N, 74.1% of the average active suspension force. For the BLAM-HP, the max unexpected suspension force is 1.02N, 2.4% of the average active suspension force. It confirms that the BLAM-HP can restrain the coupling of different DOF effectively. IV.Conclusions Two BLAMs with different combine of number of rotor poles and stator slots are proposed in this paper. The suspension performances are analyzed by the FEA. According to the comparison of the results, it shows an impressively enhance of the active suspension force and reduce of the ripple and the coupling of the other DOF when the high number of the rotor poles and stator slots are chosen. Compare to the BLAM-LP, the average active suspension force is 2.65 times larger, the ripple is 33.6 times less and the coupling of different DOF is 31.2 times less when the BLAM-HP is applied.

**References:**

[1] X. Sun, L. Chen, Z. Yang. “Overview of Bearingless Permanent-Magnet Synchronous Motors，” TIE, vol. 60, no. 2, pp. 5528-5538, Dec. 2013. [2] T. Nussbaumer, P. Karutz, F. Zurcher, J. W. Kolar. “Magnetically Levitated Slice Motor – An Overview，” TIA, vol. 47, no. 2, pp. 754-766, Mar. 2011. [3] B. Warberger, R. Kaelin, T. Nussbaumer, J. W. Kolar, “50-Nm/2500-W Bearingless Motor for High-Purity Pharmaceutical Mixing” TIE, vol. 59, no. 5, pp. 2236-2247, May. 2012. [4] M. Takemoto, S. Iwasaki, H. Miyazaki, A. Chiba, and T. Fukao, "Experimental evaluation of magnetic suspension characteristics in a 5-axis active control type bearingless motor without a thrust disk for wide-gap condition," in 2009 IEEE Energy Conversion Congress and Exposition, pp. 2362-2367, 2009. [5] S. Ueno, K. Nakazawa and C. Jiang, "Improvement of Stability of an Tilt-Controlling Axial Gap Self-bearing Motor with Single Stator," in 2019 12th Asian Control Conference (ASCC), pp. 1216-1221, 2019. [6] M. Osa, T. Masuzawa, R. Orihara, and E. Tatsumi, "Compact maglev motor with full DOF active control for miniaturized rotary blood pumps," in 2017 11th International Symposium on Linear Drives for Industry Applications (LDIA), pp. 1-6, 2017.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ae2f84d3e4552a49ced6b79519e9540c.jpg)
Fig.1 The topology of the proposed BLAM. a) shows the BLAM with high number of rotor poles and b) shows the BLAMwith low number of rotor poles.

![](https://assets.underline.io/uploads/markdown_image/1/image/13d1bc476ea33d1a0792cf554c3db4b4.jpg)
Fig.2 The suspension performance comparison when only the x-axis active suspension force is produced.

 A suspension performance comparison of the bearingless axial motor with different number of the rotor poles and stator slots

I.Introduction Because the hybrid magnetic bearing (HMB) has the advantages of long life, high precision and low loss, the high-speed rotor supported by HMBs instead of traditional bearings can obtain higher speed and higher power. It is widely used in life science, flywheel energy storage, aerospace and other occasions [1]-[2]. According to the bias magnetic circuit, radial HMBs can be divided into homopolar HMBs and heteropolar HMBs. However, the axial length of homopolar HMB is long, which limits the critical speed of rotor. Comparing with DC 4-pole HMB and AC 3-pole HMB, the AC 6-pole HMB not only has the advantages of symmetrical structure, but also can be driven by the three-phase inverter to decrease the volume and cost. Therefore, a novel AC 6-pole HMB are proposed in this paper. Firstly, the structure and suspension mechanism of the proposed HMB are introduced. Secondly, the equivalent magnetic circuit is established. Then the main parameters of the HMB are designed. Finally, the electromagnetic simulation is carried out by software MagNet to verify the theoretical analysis. II.Configuration And Suspension Principle The proposed novel AC 6-pole HMB includes stator, permanent magnets, control coils and rotor, as shown in Fig. 1. Six permanent magnets arrange with NS-SN-NS-SN-NS-SN, embedded in the stator slots of each pole, which forms heteropolar magnetic flux distributions. There are three outer air gaps under pole A, B and C, and the air gap reluctance are noted as RA~RC. The air gap reluctance of the inner air gaps are noted as R1~R6. The control windings, marked as A, a, B, b, C, and c, are wound on the poles. The solid lines denote the control flux, and the dotted lines describe the bias flux. The bias flux generated by permanent magnet starts from N pole and return to S pole, one passing through internal stator core, inner air gap, the other passing through internal stator core, outer air gap, stator suspension pole and external stator core. The coils of A and b, B and c, C and a, are respectively connected in series. Then the coils of A, B and C, the coils of a, b and c, are respectively connected in parallel as three phase control winding. Then, the three-phase winding is electrified by one three-phase inverter. Assume that the rotor has the displacement to the pole b, the three phase symmetrical currents flow into A~c coils. As a result, the air gap flux density increases under the poles A, a and c, while decreases under the poles b, B and C. Thus, the suspension force pointing to pole A will pull the rotor back to the balance position. III.Main Parameter Design The average inner air-gap length, noted as gn, is 0.5mm and the outer air-gap length noted as gw is 2mm. The diameter of the rotor is 50.5mm. The outer diameter of the stator is 106 mm. The turn number of coil A, B and C is 200T, and the turn number of coil a, b and c is 40T. The axial length of the stator is 45mm. The equivalent magnetic circuits are analyzed. According to the equivalent magnetic circuit, the resultant suspension forces of the rotor in the x and y directions, are deduced as Fxmax=(Bs×Bs+B0×Bs)Sn÷(2μ0) Fymax=√3×Bs×Bs×Sn÷(2μ0) where µ0 is the permeability of vacuum, BS is the saturated flux density, B0 is bias flux density, Sn is the internal pole area. A.Inner and Outer Air-Gap In order to avoid magnetic saturation, the saturation magnetic induction (BS) is 1.2T, inner air gap bias flux (B0) is designed as 0.6T. Ri=Rn (i=1,2,3,4,5,6), Rj=Rw (j=A,B,C). According to the equivalent control magnetic circuit, the relationship of the inner and outer air-gap can be obtained （gn÷Sn）×（Sw÷gw）=1/4 B.Number of Coil Turns According to equivalent control magnetic circuit, the relationship of the turn number of coil A,B,C, noted as Nw, and the turn number of coil a,b,c, noted as Nn, as described by Nw:Nn=5:1 IV.Finite Element Analysis The analysis model is established by MagNet 3D. Fig. 2(a) presents the permanent magnetic static bias flux density distribution in the bearing. Fig. 2(b) shows the control flux in produced by coil A, B and C. Fig. 2(c) shows the control flux in produced by coil a, b and c. And the corresponding resultant flux is shown in Fig. 2(d). Fig. 2(e) shows the maximum suspension force can be obtained in +x direction, while the force in y direction is close to zero, which shows a good linearity. And the theoretical value is consistent with the calculated value. V.Conclusions In this paper, the novel AC 6-pole HMB is proposed and designed. The structure and suspension mechanism are analyzed. The magnetic circuits are presented. According to the main design parameters, the analysis model is established by MagNet 3D. Then, the electromagnetic performances of the novel AC 6-pole HMB are researched. The simulation results have shown that correctness of the structure, magnetic circuit and mathematical models.

**References:**

[1]T. Schuhmann, W. Hofmann, and R. Werner, “Improving operational performance of active magnetic bearings using Kalman filter and state feedback control,” IEEE Transactions on Industrial Electronics, vol. 59, no. 2, pp. 821–829, 2012 [2]H. Q. Zhu, Y. X. Shen, and Q. H. Wu, “Modeling and control system for AC hybrid magnetic bearing,” Proceedings of the CSEE, vol 29, no. 18, pp. 100-105, 2009.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/097c5a7e789b66006b6a10abe26e9bdb.jpg)
Fig. 1. Structure of novel AC 6-pole RHMB: 1-external stator core, 2-control windings, 3-permanent magnet, 4-internal stator core, 5-inner air gap, 6-shaft, 7-rotor core, 8-outer air gap, 9-stator suspension teeth, 10-bias flux, 11-control flux.

![](https://assets.underline.io/uploads/markdown_image/1/image/dc12d4bb225c2275b30260c6a68ec5e2.jpg)
Flux distributions and the force-current relationships

 Electromagnetic Analysis of a Novel AC Six-Pole Hybrid Magnetic Bearing

Magnetoelectric (ME) inductors are one of the promising elements of tunable energy efficient electronics. The main attention is paid to the possibility of controlling the inductance of such devices by electric field [1]. In this paper, we consider magnetic and electric tuning for two ME ring inductors of different geometries. The devices were manufactured as follows. Ferromagnetic (FM) layers of an amorphous magnetic alloy Metglas 2605SA1, 23 μm thick and 5 mm wide, were glued using cyanoacrylate adhesive to the outer (sample 1) or inner (sample 2) side of the piezoelectric PbZrTiO3 (PZT) ring (see Fig.1). The rings with Ag-electrodes had an inner diameter of 16 mm, thickness of 1 mm, and height of 1 mm. The rings were poled in the radial direction. The samples were placed inside a plastic frames and then 100 turns of wire with a diameter of 0.2 mm were wound around them. A constant electric voltage of up to 1 kV was applied to the PE rings parallel to the direction of polarization, which generated inside PE an electric field up to E=1 kV/cm. A constant magnetic field H=0-200 Oe, created by Helmholtz coils, was applied along or perpendicular to the axis of the devices. The frequency dependences of the inductance L(f) were measured in the frequency range 100 Hz – 5 MHz, and the inductance tuning coefficient γ = (L0-L)/L, at a frequency f = 300 Hz was calculated. Here L is the inductance in a given electric or magnetic field, L0 is the inductance in the absence of fields. The possibility of tuning the inductance with the simultaneous application of electric and magnetic fields is also shown for both samples. Fig. 1 shows measured dependences of the devices’ inductance on the electric field. With an increase in E, a decrease in the inductance of the structures was observed from 74 μH to 41.4 μH for sample 1. The inductance tuning coefficient in a field E = 1 kV/cm was γ ≈ 78% for sample 1, and γ ≈ 34% for the sample 2. Fig. 2 shows similar dependences when a constant magnetic field was applied to the structure. With an increase in H, the tuning coefficient nonlinearly increased and then saturated following the saturation of the FM layer. The tuning coefficient for sample 1 reached 1000% for in-plane magnetization at H = 20 Oe and 700% for magnetization along the axis at H = 200 Oe. Tuning coefficients for the sample 2 reached 1300% for both directions of magnetization.When the structures were magnetized with a field created by additional coil, the tuning coefficient reached ~850% at H ≈ 9 Oe. The observed dependences can be explained as follows. When an electric field E is applied to the PZT ring, it deforms as a result of the inverse piezoelectric effect. This deformation is transferred to the FM layer and generates an effective uniaxial magnetic anisotropy field as a result of the Villari effect. Thus, magnetic permeability µ and L becomes proportional to ~ 1/E. Since the magnitude of tensile strains on the outer side of the PE ring exceeds the magnitude of compression strains on the inner side, the tuning coefficient for the sample 1 is almost 2 times higher [2]. During magnetization of the FM layer with external magnetic field H, the change in inductance L is associated with a change in the magnetic permeability µ. The magnetic field inside the FM layer is Hin ≈ H/(1+χ×N), where χ is magnetic susceptibility, N is the demagnetizing factor [3]. Thus, upon in-plane magnetization of the samples, a decrease in the tuning coefficient was observed in an order of magnitude smaller magnetic fields. We have shown a possibility of creation ME inductors which inductance can be tuned by both electric and magnetic fields. The control of inductance by an electric field is more effective for the structure with a FM layer on the outer side of the PZT ring. At the same time, a larger magnetic field tuning coefficient was observed for a structure with an FM layer on the inner side of the PZT ring. The work was supported by the Russian Science Foundation, grant 19-79-10128.

**References:**

1. G. Srinivasan, N.X. Sun, SPIN, v. 2, p. 1240004 (2012). 2. Y. Yan, L.D. Geng, L. Zhang et al, Scientific reports, v.7, p. 16008 (2017). 3. J.A. Osborn, Phys. Rev., v. 67, p. 1351-1357 (1945).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8b623528f938c46bcee8bbeb40942191.jpg)
Fig. 1. Dependences of the inductance tuning coefficient γ on the electric field E for both samples.

![](https://assets.underline.io/uploads/markdown_image/1/image/43db9d722ecb02c0d6ccff76eda7b146.jpg)
Fig. 2. Dependences of the inductance tuning coefficient γ on the magnetic field H for in-plane magnetization and for magnetic field created by additional coil for sample 1.

 Magnetoelectric inductor tuned by electric and magnetic fields

Permanent magnet eddy current coupling (PMECCs) are electromagnetic devices which can transmit power from a motor to a load with no electrical or mechanical connections. Therefore, resulting in vibration isolation, low maintenance, and overload protection. However, PMECCs which have been considered so far, exhibit relatively lower efficiencies due to their torque slip- speed characteristics. Consequently, their industrial applications as power transmission devices has been limited, and they have mostly been employed in braking and damping applications. PMECCs topologies described in the literature have mainly employed plain copper sheets as a conducting material [1][2]. Although, these were simpler and more cost-effective solutions, they suffered from relatively lower efficiencies. The effiency, η, of a PMECC is given by: η=1-ΔΩ/Ω (1) Where, Ω is the input speed and ΔΩ is the slip-speed corresponding to the transmitted torque. From (1), it can be seen that the efficiency of PMECCs increase with larger speeds and reduced slip-speeds. In [3], it was theoretically shown that employing short-circuited conductors in slots (SCCSs), has the potential to improve efficiency, and it was proposed that high efficiency PMECCs can be employed as limited-slip differentials in electric vehicles. Nevertheless, in more recent investgations, SCCSs have been used in configurations which didn't fully exploit their potential in improving efficiency, thereby, resulting in PMECCs, with efficiencies similar to those using conductor sheets [4][5]. Therefore, in this paper an investigation into the design and analysis of PMECCs for power transmission applications, where efficiency is a primary requirement, is undertaken. The performances of radial and axial field topologies, using conductor sheets and SCCSs, in terms of torque slip-speed characteristics and efficiency are compared. It is shown, that when appropriately employed, SCCSs result in significant improvement in efficiency, even when less conductive materials, such as Aluminium, are employed. Fig. 1 shows schematics of radial and axial field PMECCs employing SCCSs, and Fig. 2 shows the variation of transmitted torque with slip-speed for a prototype radial field PMECC employing SCCSs. It can be seen that a good agreement between measured and predicted results exists. It can also be seen that the slip-speed corresponding to the maximum transmitted torque is only 100rpm. This represents a signficant improvement when compared to previously published PMECCs [1][2][4][5], where the slip-speed corresponding to the maximum transmitted torque can typically vary between hundreds of rpm to more than a 1000rpm.

**References:**

[1] A. Canova and B. Vusini, IEEE Transactions on Industrial Appllications, Vol. 39 (2003). [2] A. S. Erasmus, M. J. Kamper, IEEE Energy Conversion Congress and Exposition, (2015) [3] K. Atallah, J. Wang, IEEE Transactions on Magnetics, Vol. 47, (2011) [4] X. Dai,Q. Liang, J. Cao, Y. Long Y, J. Mo J and S. Wang, IEEE Transactions Magnetics, Vol. 52, (2016) [5] Z. Li , L. Yan, B. Qu and K. Fu, International Journal Appllied Electromagnetics and Mechanics, Vol. 62, (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8854de6ae3b3234a0fd274b02b0e6bc1.jpg)
Fig. 1 Radial and axial field PMECCs with SCCSs.

![](https://assets.underline.io/uploads/markdown_image/1/image/14a3776cff9b258ba9ed5d20060399a8.jpg)
Fig. 2 Variation of transmitted torque with slip-speed.

 High efficiency eddy current couplings

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:**

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Fig.1 Proposed wireless motor drive. (a) Configuration. (b) Magnetic field distributions of bipolar coils.

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Fig.2 Experimental verification. (a) Prototype. (b) Measured waveforms.

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

Battery Electric Vehicles can significantly shorten battery life if not maintained at the proper temperature. PTC heater is used as a temperature control system for commercial vehicles. But PTC is heavy so the mileage of the vehicle is reduced. In addition, the insulation structure of PTC is complicated. Research on induction heaters is underway to compensate for the shortcomings of PTC in the ventilation industry. The structure of the induction heater consists of a workpiece and a coil. An alternating magnetic flux is generated by the coil to which the AC current is applied. Core loss occurs as heat in the workpiece by the alternating magnetic flux. This heating method does not require an insulating structure between the workpiece and the electrode, so it can increase mileage by reducing the volume and weight of the vehicle. The induction heater operates in a high frequency region, and the skin effect occurs due to the operation of the high frequency. Thus, the current is concentrated on the coil surface. Since a magnetic skin effect occurs in the workpiece, the magnetic flux generated by the current is concentrated on the inner and external workpiece surfaces adjacent to the coil. Due to the concentrated magnetic flux on the surface of the workpiece, the magnetic flux density from the surface of the workpiece rapidly with rising. So the relative permeability of the workpiece is high before the saturation point. Additionally, the coil is wound several times inside the induction heater. Therefore, a proximity effect occurs between coils by magnetic force generated when current flows. The current that is affected of the magnetic force is tilted inside the coil according to the direction and magnitude of the magnetic force, and the tilted direction and magnitude change continuously for a very short time by high frequency. The workpiece is directly affected by these phenomena. The skin effect and proximity effect occur due to the magnetic force between the coils and the high-frequency current, so these effects should be reduced for efficiency of induction heating. In this paper, the design of an optimal model was studied to increase the efficiency of the induction heater by considering skin effect and proximity effect. The induction heater is composed of a series resonance circuit among LC series resonance circuit and LC parallel resonance circuit. When the LC series resonance circuit operates at the resonance frequency, the reactance becomes 0 and the power factor approaches to 1. Since the reactance is zero at the resonant frequency, the impedance is minimized. Therefore, maximum current and magnetic flux can be generated with the same voltage. In other words, it is possible to maximize the output of the induction heater through the operation of the resonant frequency. For the operation of the resonance frequency of the induction heater, the required capacity of the capacitor is determined according to the inductance of the workpiece. And the capacity of the capacitor is proportional to the size and price. Small capacitors require high inductance to operate at resonant frequencies. For high inductance, proper workpiece design of induction heater is required. For example, if the workpiece is thicker more material is required. However, the magnetic flux is concentrated only on the workpiece surface due to the skin effect. Thus, the surface of the workpiece adjacent to the coil is saturated. Other regions except the surface have low flux linkage. As a result, the overall inductance of the workpiece is lowered. Conversely, if the workpiece is too thin, it becomes saturated due to overheating. So the inductance decreases and the required output is not obtained. Relative permeability is a parameter that directly affects inductance. In order to measure the exact relative permeability of the workpiece according to the skin effect, the magnetic flux density was derived by electromagnetic field analysis. After considering the saturation of magnetic flux density, the relative permeability of the workpiece was derived according to the distance from the coil. The average of the derived relative permeability was calculated to obtain the depth of penetration. The relative permeability of the workpiece was highest at the point depth of penetration, which is the result of calculation. Also, the magnetic force influencing the proximity effect was analyzed. The magnetic force was calculated by deriving the current density inside the coil by electromagnetic field analysis. And then a design flow chart was established and a basic model was selected. The 6kW induction heating model was chosen as the base model, a total of 101 coils consisted of two layers, and the workpiece was made of SUS430 material. For the basic model analysis, capacitance that satisfies the operation of capacity, voltage, and resonance frequency was derived using electromagnetic field analysis. In addition, a sensitivity analysis of the design parameters was performed and a high sensitivity parameter was derived. High sensitivity parameters included the height and thickness of the workpiece, the distance between the workpiece and the coil, the diameter of the workpiece, and the diameter of the coil. The optimal model was derived by comparing and analyzing the basic model with the model in which the height, thickness of the workpiece, and diameter of the coil were changed.

**References:**

[1] Hiroyuki Kagimoto, Daisuke Miyagi and Norio Takahashi, IEEE Trans. Magn., vol.46, no.8, pp.3018-3021 (2010) [2] Alexander Boadi, Yuji Tsuchida and Takashi Todaka, IEEE Trans. Magn., vol.41, no.10, pp.4048-4050 (2005) [3] M. Messadi, L. Hadjout and Y. Ouazir, IEEE Trans. Magn., vol.52, no.3 (2016) [4] Jesus Acero, Claudio Carretero and Rafael Alonso, IEEE Trans. Magn., vol.49, no.4, pp.1382-1389 (2013) [5] Nikolaos Tsopelas and Nicolaos J. Siakavellas, IEEE Trans. Magn., vol.44, no.12, pp.4711-4720 (2008)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c0288fa84de6d7a75c8e55271ba0e6f5.jpg)
Figure 1. 3D Base Model of the Induction Heater

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Figure 2. Magnetic Flux Density Distribution and Current Density Distribution

 A Study on Optimal Design of Induction Heater for Electric Vehicle Considering Proximity Effect and Skin Effect

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.

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 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://assets.underline.io/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.

![](https://assets.underline.io/uploads/markdown_image/1/image/1d56df332e4856385cac45d977f1f0df.jpg)
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.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0cdce8e7008289a1713701b1a491a8aa.jpg)
Figure 1. (a) Back-to-back experimental setup for IPMSMs. (b) SVPWM control block of IPMSMs.

![](https://assets.underline.io/uploads/markdown_image/1/image/64a751c98cd0383dbeee5cf08376ab82.jpg)
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.

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

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