France



1 Introduction&lt;br/&gt;In a dynamical mass-spring system with many discrete mass points, when the spring has nonlinearity, a special localized vibration mode occurs in which only a limited number of masses vibrate. This is called the intrinsic localized mode (ILM) [1]. Many researchers have been interested in the ILM because of its unique features that are not found in the linear systems. Particularly in mobile ILMs [2], in which the kinetic energy of the system is localized in a small number of masses and the localized energy propagates to adjacent masses, have high potential for engineering applications through experiments [3,4].&lt;br/&gt;However, the shape, frequency and speed of the ILM were determined by the parameters of the dynamic vibration system (mass, spring constant, and initial vibration). Hence, control of the generated ILM was not possible and therefore, there has been no significant progress in engineering applications. Here, we propose a new magnetic spring structure that can variably handle the nonlinear spring characteristics of dynamic vibrating systems.&lt;br/&gt;In this paper we would like to describe the ILM in dynamic vibrating systems. Then, a variable magnetic spring structure (VMS structure) is proposed, and the variable magnetic spring properties are verified from the finite element analysis (FEA) results of the proposed structure. Lastly, by solving the differential equations of the dynamic oscillating system, we show the possibility of controlling the ILM by varying the nonlinear spring properties of the dynamic vibrating system.&lt;br/&gt;2 Variable magnetic spring structure&lt;br/&gt;For ILM generation, multi-mass and nonlinear springs are required. Since we are dealing with rotating bodies, the mass is replaced by inertia and the nonlinear spring has restoring torque. A large number of rotating bodies with the same inertia are connected by nonlinear restoring torques with neighboring rotating bodies. The nonlinear restoring torques structure with VMS is shown in Fig. 1(a). The VMS consists of two rotors, the outer rotor with electromagnets and the inner rotor with interior permanent magnets (IPM). The outer rotor coil consists of two phases with opposite phases and applies DC current. The magnetic flux due to permanent magnet is shown by the solid blue loop, and the magnetic flux due to the applied current is shown by the dotted red loop. The restoring torque of the VMS is generated by the relative angle between the inner and outer rotors.&lt;br/&gt;Fig. 1(b) shows the relationship between the relative angle and the restoring torque when 2A/mm&lt;sup&gt;2&lt;/sup&gt; to 8A/mm&lt;sup&gt;2&lt;/sup&gt; is applied to the two-phase coil with opposite phases obtained from the FEA. The restoring torque &lt;i&gt;T&lt;/i&gt; can be approximated as follows:&lt;br/&gt;&lt;i&gt;T=k&lt;sub&gt;3&lt;/sub&gt;θ&lt;sup&gt;3&lt;/sup&gt;+k&lt;sub&gt;1&lt;/sub&gt;θ&lt;/i&gt;...(1)&lt;br/&gt;Here, &lt;i&gt;θ&lt;/i&gt; is the relative angle (rad), &lt;i&gt;k1&lt;/i&gt; (Nm/rad) is the spring constant, and &lt;i&gt;k3&lt;/i&gt; (Nm/rad) is the nonlinear coefficient. Also, the nonlinear ratio is defined as . It decreases continuously from 20.52 at an applied voltage of 2A/mm&lt;sup&gt;2&lt;/sup&gt; to 11.99 at 8A/mm&lt;sup&gt;2&lt;/sup&gt;.&lt;br/&gt;3 Control of ILM&lt;br/&gt;In this chapter we numerically solve the differential equations for a rotating nonlinear mass-spring system. The equation of motion with consideration of the nonlinear coefficients of the rotating spring in Fig. 2(a) is the following differential equation&lt;br/&gt;&lt;i&gt;Jd&lt;sup&gt;2&lt;/sup&gt;θ&lt;sub&gt;n&lt;/sub&gt;/dt&lt;sup&gt;2&lt;/sup&gt;=k&lt;sup&gt;1&lt;/sup&gt;&lt;sub&gt;n+1&lt;/sub&gt;(i)(θ&lt;sub&gt;n+1&lt;/sub&gt;-θ&lt;sub&gt;n&lt;/sub&gt;)+k&lt;sup&gt;3&lt;/sup&gt;&lt;sub&gt;n+1&lt;/sub&gt;(i)(θ&lt;sub&gt;n+1&lt;/sub&gt;-θ&lt;sub&gt;n&lt;/sub&gt;)&lt;sup&gt;3&lt;/sup&gt;-k&lt;sup&gt;1&lt;/sup&gt;&lt;sub&gt;n&lt;/sub&gt;(i)(θ&lt;sub&gt;n&lt;/sub&gt;-θ&lt;sub&gt;n-1&lt;/sub&gt;)-k&lt;sup&gt;3&lt;/sup&gt;&lt;sub&gt;n&lt;/sub&gt;(i)(θ&lt;sub&gt;n&lt;/sub&gt;-θ&lt;sub&gt;n-1&lt;/sub&gt;)&lt;sup&gt;3&lt;/sup&gt;&lt;/i&gt;...(2)&lt;br/&gt;Here, &lt;i&gt;J&lt;/i&gt; is the inertia of the VMS, &lt;i&gt;θ&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt; is the absolute angle of the nth VMS, &lt;i&gt;k&lt;sup&gt;1&lt;/sup&gt;&lt;sub&gt;n&lt;/sub&gt;(i)&lt;/i&gt; is the linear spring constant at current density &lt;i&gt;i&lt;/i&gt; between the (n-1)th and nth VMS, and &lt;i&gt;k&lt;sup&gt;3&lt;/sup&gt;&lt;sub&gt;n&lt;/sub&gt;(i)&lt;/i&gt; is the nonlinear spring coefficient at current density &lt;i&gt;i&lt;/i&gt; between the (n-1)th and nth VMS.&lt;br/&gt;Fig. 2 shows the numerical results of the differential equation (2). There are 21 VMS’s used, and the inertias are all 1.34×10&lt;sup&gt;-4 &lt;/sup&gt;kg×m&lt;sup&gt;2&lt;/sup&gt;. Initially, the oscillations were such that the ILM was generated from the center. Magnetic springs of 2A/mm&lt;sup&gt;2&lt;/sup&gt; (nonlinear ratio 20.52) and 4A/mm&lt;sup&gt;2&lt;/sup&gt; (nonlinear ratio 16.25) were used as shown in Fig. 1(b). In (b-1), a magnetic spring with a nonlinearity factor of 20.52 was used for the entire simulation time. This resulted in the initial ILM remaining centered until the end of the simulation. In (b-2), we used a magnetic spring of 20.52 for the simulation time of 0-1 sec, and changed &lt;i&gt;k&lt;sup&gt;1,3&lt;/sup&gt;&lt;sub&gt;-5~0&lt;/sub&gt;&lt;/i&gt; to a magnetic spring of 16.25 for 1-2 sec. In 2-3 seconds, &lt;i&gt;k&lt;sup&gt;1,3&lt;/sup&gt;&lt;sub&gt;-5~10&lt;/sub&gt;&lt;/i&gt; were changed to magnetic springs of 16.25. From (b-1) and (b-2), it is clear that the ILM can be controlled by changing the nonlinear rate of the magnetic spring.&lt;br/&gt;In the final paper, we will discuss the cause of the nonlinear magnetic spring property of the proposed VMS structure by FEA, and furthermore, discuss the movement speed and trend of ILM according to the nonlinear rate.

**References:**

[1] S. Takeno, K. Kisoda, and A.J. Sievers, Progress of Theoretical Physics Supplement, No. 94, pp. 242-269 (1988).&lt;br/&gt;[2] M. Kimura, R. Tsujisaka, T. Hikihara, Y. Taniguchi, and Y. Matsushita, A study on reflection of moving intrinsic localized modes at a junction of two different nonlinear lattices, 2014.&lt;br/&gt;[3] Y. Watanabe, M. Nishimoto, and C. Shiogama, Nonlinear Theory and Its Applications, IEICE, vol. 8, pp. 146-152, 2017.&lt;br/&gt;[4] S. Lee, K. Hirata, M. Kato, &lt;i&gt;Electrical and Electronic Engineering (ISEF)&lt;/i&gt;, Nancy, France, 2019, pp. 1-2, doi: 10.1109/ISEF45929.2019.9097039.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e64e22e28e1532cd6e9efdacc9622225.jpg)
Fig.1 (a) Proposed VMS structure. (b) The relative angle and the restoring torque by applied current density.

![](https://assets.underline.io/uploads/markdown_image/1/image/dc8c8c61d27adff43220446c01abd40c.jpg)
Fig.2 (a) Spring-mass system. (b) Numerical result of ILM with VMS.

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 A New Method to Control Intrinsic Localized Mode Using a Variable Magnetic Spring Structure

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1 Introduction In a dynamical mass-spring system with many discrete mass points, when the spring has nonlinearity, a special localized vibration mode occurs in which only a limited number of masses vibrate. This is called the intrinsic localized mode (ILM) [1]. Many researchers have been interested in the ILM because of its unique features that are not found in the linear systems. Particularly in mobile ILMs [2], in which the kinetic energy of the system is localized in a small number of masses and the localized energy propagates to adjacent masses, have high potential for engineering applications through experiments [3,4]. However, the shape, frequency and speed of the ILM were determined by the parameters of the dynamic vibration system (mass, spring constant, and initial vibration). Hence, control of the generated ILM was not possible and therefore, there has been no significant progress in engineering applications. Here, we propose a new magnetic spring structure that can variably handle the nonlinear spring characteristics of dynamic vibrating systems. In this paper we would like to describe the ILM in dynamic vibrating systems. Then, a variable magnetic spring structure (VMS structure) is proposed, and the variable magnetic spring properties are verified from the finite element analysis (FEA) results of the proposed structure. Lastly, by solving the differential equations of the dynamic oscillating system, we show the possibility of controlling the ILM by varying the nonlinear spring properties of the dynamic vibrating system. 2 Variable magnetic spring structure For ILM generation, multi-mass and nonlinear springs are required. Since we are dealing with rotating bodies, the mass is replaced by inertia and the nonlinear spring has restoring torque. A large number of rotating bodies with the same inertia are connected by nonlinear restoring torques with neighboring rotating bodies. The nonlinear restoring torques structure with VMS is shown in Fig. 1(a). The VMS consists of two rotors, the outer rotor with electromagnets and the inner rotor with interior permanent magnets (IPM). The outer rotor coil consists of two phases with opposite phases and applies DC current. The magnetic flux due to permanent magnet is shown by the solid blue loop, and the magnetic flux due to the applied current is shown by the dotted red loop. The restoring torque of the VMS is generated by the relative angle between the inner and outer rotors. Fig. 1(b) shows the relationship between the relative angle and the restoring torque when 2A/mm2 to 8A/mm2 is applied to the two-phase coil with opposite phases obtained from the FEA. The restoring torque T can be approximated as follows: T=k3θ3+k1θ...(1) Here, θ is the relative angle (rad), k1 (Nm/rad) is the spring constant, and k3 (Nm/rad) is the nonlinear coefficient. Also, the nonlinear ratio is defined as . It decreases continuously from 20.52 at an applied voltage of 2A/mm2 to 11.99 at 8A/mm2. 3 Control of ILM In this chapter we numerically solve the differential equations for a rotating nonlinear mass-spring system. The equation of motion with consideration of the nonlinear coefficients of the rotating spring in Fig. 2(a) is the following differential equation Jd2θn/dt2=k1n+1(i)(θn+1-θn)+k3n+1(i)(θn+1-θn)3-k1n(i)(θn-θn-1)-k3n(i)(θn-θn-1)3...(2) Here, J is the inertia of the VMS, θn is the absolute angle of the nth VMS, k1n(i) is the linear spring constant at current density i between the (n-1)th and nth VMS, and k3n(i) is the nonlinear spring coefficient at current density i between the (n-1)th and nth VMS. Fig. 2 shows the numerical results of the differential equation (2). There are 21 VMS’s used, and the inertias are all 1.34×10-4 kg×m2. Initially, the oscillations were such that the ILM was generated from the center. Magnetic springs of 2A/mm2 (nonlinear ratio 20.52) and 4A/mm2 (nonlinear ratio 16.25) were used as shown in Fig. 1(b). In (b-1), a magnetic spring with a nonlinearity factor of 20.52 was used for the entire simulation time. This resulted in the initial ILM remaining centered until the end of the simulation. In (b-2), we used a magnetic spring of 20.52 for the simulation time of 0-1 sec, and changed k1,3-5~0 to a magnetic spring of 16.25 for 1-2 sec. In 2-3 seconds, k1,3-5~10 were changed to magnetic springs of 16.25. From (b-1) and (b-2), it is clear that the ILM can be controlled by changing the nonlinear rate of the magnetic spring. In the final paper, we will discuss the cause of the nonlinear magnetic spring property of the proposed VMS structure by FEA, and furthermore, discuss the movement speed and trend of ILM according to the nonlinear rate.

**References:**

[1] S. Takeno, K. Kisoda, and A.J. Sievers, Progress of Theoretical Physics Supplement, No. 94, pp. 242-269 (1988). [2] M. Kimura, R. Tsujisaka, T. Hikihara, Y. Taniguchi, and Y. Matsushita, A study on reflection of moving intrinsic localized modes at a junction of two different nonlinear lattices, 2014. [3] Y. Watanabe, M. Nishimoto, and C. Shiogama, Nonlinear Theory and Its Applications, IEICE, vol. 8, pp. 146-152, 2017. [4] S. Lee, K. Hirata, M. Kato, Electrical and Electronic Engineering (ISEF), Nancy, France, 2019, pp. 1-2, doi: 10.1109/ISEF45929.2019.9097039.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e64e22e28e1532cd6e9efdacc9622225.jpg)
Fig.1 (a) Proposed VMS structure. (b) The relative angle and the restoring torque by applied current density.

![](https://assets.underline.io/uploads/markdown_image/1/image/dc8c8c61d27adff43220446c01abd40c.jpg)
Fig.2 (a) Spring-mass system. (b) Numerical result of ILM with VMS.

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Introduction MnZn ferrites are widely used in power electronics for high frequency transformers and inductors since they offer a good compromise between low core losses, permeability and saturation flux density. For properly designing magnetic components, the effective permeability and the core losses must be determined. Different phenomena, like magnetic hysteresis or eddy-currents, lead to core losses. State-of-the-art loss models are often based on the Steinmetz equation or extensions such as Generalized Steinmetz Equation [1]. These approaches aim to model the overall losses at once using a power law based on three (or more) coefficients. A given set of parameters is only accurate around the operating point used for determining these parameters, for the various phenomena scale differently with frequency and flux density. This results in reduced operating ranges in which the methods are accurate. In contrast, with the Bertotti method [2] hysteresis and classical eddy current losses as well as an extra term, called excess losses, are considered separately. The three terms are calculated as with the Steinmetz model but with specific coefficients for each loss term. Even if using three loss components widens the frequency and flux density ranges, the parameters remain frequency dependent and the excess losses lack a proper physical explanation. Therefore, this work presents a physical approach based on the combination of an electrical model of the material structure with the flux distribution resulting from solving Maxwell equations. The new model is used to explain and estimate the frequency dependency of complex permeability as well as the eddy-current and excess core losses that can be then combined with hysteresis losses predicted by classical methods. Equivalent electrical model of material structure The sintering process leads to a meta-material made of grains that are insulated one from each other. Such a structure reduces significantly eddy-current losses since the effective conductivity is small due to the insulating layer between grains. However, the apparent conductivity and permittivity of ferrite depend on frequency because the grain boundary interface acts like a capacitor (Fig 1.a). Its impedance reduces at higher frequencies what short-circuits the high resistivity of the boundary (cf. [3] for NiZn ferrites and [4] for MnZn ferrite). As proposed in [3], a two series cells model could be used to describe the grain and the boundary (Fig. 1.b) for calculating the overall conductivity and permittivity. Each cell is composed of a parallel conductance and capacitance, representing for one cell the admittance of the grains and for the other cell the admittance of the boundaries. By taking the limit of the admittances when the cross section dA and the length dl converges to zero, one can obtain the apparent conductivity and permittivity. These quantities are then a function of the frequency and of the material parameters, i.e.: conductivities and permittivities of the boundary and of the grain. Model of flux distribution vs. frequency The dielectric and ferromagnetic nature of ferrite results in standing waves in the core when the frequency increases. This affects the flux density distribution and induces eddy-currents. To model those effects, two approaches can be considered: lumped elements circuit [5] or full wave equation solution [6]. The first one assumes that induced currents flow only around the cross section in concentric loops, which is satisfied if only the first mode is excited. A more general approach is to solve the wave equations, as proposed in [6] for toroid and pot cores. The solution given in [6] converges quickly with respect to the number of considered spatial harmonics, reducing the computational cost. Proposed model Based on the electrical model of the material structure and on the solution for the flux distribution, a new core loss model is presented in this paper. This model allows to compute the complex permeance of a toroid core, even if the electrical material parameters of the material change with frequency. The effective complex permeability is derived by dividing the complex permeance by the ratio of the effective cross section over the effective magnetic length of the core. The overall core losses are calculated by adding the losses associated with the imaginary part of the permeance to the hysteresis losses. The latter are obtained from low frequency measurements and are then scaled linearly with frequency (similar to Bertotti model). Experimental validation The proposed approach is validated on a R36 toroid core made of N87. The complex effective permeability and the core losses are measured between 10 kHz and 1 MHz for various flux densities, at room temperature using an IWATSU SY-8219 BH Analyzer. The model is then fitted with complex permeability measurements using MATLAB curve fitting toolbox. Results and discussion As shown in Fig 2, the presented model captures accurately the variations of both the complex permeability and the core losses. Furthermore, it can be concluded that the so-called excess losses are due to additional eddy-current losses due to the excitation of wave modes in the core and to the increasing effective conductivity with frequency.

**References:**

[1] J. Li, T. Abdallah and C.R. Sullivan, Conference Record of the 2001 IEEE Industry Applications Conference. 36th IAS Annual Meeting, IEEE, (2002) [2] G. Bertotti, IEEE Transactions on Magnetics, Vol. 24, p. 621-630 (1988) [3] C. G. Koops, Physical Review, Vol. 83, p. 121-124 (1951) [4] M. Kacki, M.S. Rylko, J.G. Hayes and al., 2020 IEEE Applied Power Electronics Conference and Exposition (APEC) (2020) [5] C.R. Sullivan, PSMA 2019 Magnetics Workshop (2019) [6] W. Hauser, Modellbildung für strukturabhängige Effekte in Ferritkernen (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7b6236946e32bac2c3dcdb7b998f4ba2.jpg)
Fig. 1: a) The granular microstructure of Ferrites leads to a capacitive behaviour that can be represented by a 1D model. b) Equivalent two cells model for the permittivity and conductivity of ferrites.

![](https://assets.underline.io/uploads/markdown_image/1/image/07e6234e666009d4a326fcb26db45258.jpg)
Fig. 2: Loss density against frequency for various flux density values.

 New Core Loss Model for Ferrite Cores Based on a Meta-Material Approach

I. INTRODUCTION Magnetoencephalographs (MEGs) require a magnetically shielded room (MSR) made of mu-metal to protect against very slow and small range of magnetic field (micromagnetic field) noise. As magnetic shields tend to be very expensive, the evaluation of the magnetic shielding factor SF of the MSR in advance is crucial. The permeability μ of the shielding material is the main factor affecting the magnetic properties, which influence the SF. Conventionally, an index of permeability at H = 4 mA/cm, which we denote as “μ4” in this paper, is used to evaluate the performance of a mu-metal. However, as we explained in a previous study [1], permeability at a lower range than 4 mA/m, such as the Rayleigh region [2], is important for magnetic shielding materials in MSRs used for MEGs. We also explained that the measurement system of permeability against a very low-frequency micromagnetic field fluctuation and heat treatment process can improve the permeabilities of a mu-metal [3]. The SF is also affected by the shape of the magnetic shield. As a first step for predicting the SF of an MSR model, we examined a cylindrical-shell magnetic shield (material thickness, t = 1 mm; length, L = 640 mm; diameter, D = 100 mm), which can be considered as infinitely long and can be applied with SF = 1+µt/D [4]. We propose a prediction method for the SF by using this formula and the estimated μ. The permeability index, μ, of a ring-shaped test piece (ring TP) was measured at a magnetic field strength of 0.001–0.675 A/m, which comprises the linear region in the μ–H curve, to detect the initial permeability, μi, and Rayleigh constant ν; Rayleigh’s law states the μ–H curve is present for μ = μi + νH. Before we apply two equations to calculate SF, we need to know the internal magnetic field of the material H = Hi, whose value is attenuated from applied magnetic field He due to the demagnetization effect of its cylindrical-shell shape. Although the demagnetizing factors of spheres and ellipsoids are known, it is difficult to calculate these values for other shapes. Therefore, we used magnetic field analysis to estimate the internal magnetic field Hi of the cylindrical shell. In this study, a prediction method of the SF for a cylindrical shell was demonstrated for three types of mu-metals, and its accuracy was verified by an experiment on the SF. II. METHOD We prepared three types of mu-metals (mu-metals 1, 2, and 3), which exhibited different properties. A ring TP and cylindrical shell were fabricated from mu-metals 1, 2, and 3. The ring TPs and cylindrical shells were simultaneously magnetically annealed in the same heat-treatment furnace. The prediction of the SFs was performed in three steps. First, ring TPs were measured in an alternating magnetic field of 1 Hz, and μi and ν were obtained via the least-squares method that was applied to the μ data of the linear region. Second, the Hi values of the cylindrical shells were estimated using magnetic simulation software ELF/MAGIC (ELF corporation). A cylindrical shell was modeled as a 3D object that was divided into 180 cells along its circumferential direction, 64 along the length, and using a single cell along the thickness. Hi was obtained as the average value of all dividing elements; He was varied as 0.01, 0.1, 1, and 10 A/m (0 to peak); and Hi was calculated for each level of He. Third, SF was predicted as SF = 1 + µt/D using the equation μ = μi + νHi. Fourth, the cylindrical shells fabricated from mu-metals 1, 2, and 3 were placed in a uniform magnetic field strength of He that varied at 1 Hz, and the magnetic field at the center of the shell Hp was measured. The SF was obtained as He/ Hp and compared with the predicted result. III. RESULT AND DISCUSSION The μ–H curve, μi and ν of the ring TPs are displayed in Fig. 1. The internal magnetic fields Hi of the cylindrical shell calculated using the magnetic simulation software were 1/1608 to 1/418 of He, and were in the Rayleigh region. Fig. 2 shows the predicted SF using Hi values of each He and the experimental results for the three types of cylindrical shells. It showed that mu-metal 3 has the highest μ in the Rayleigh region, mu-metal 2 has the lowest μ, and so as the order of the SF. Both results of the prediction and experiment show the tendency that the SF increases with an increase in He, and are in good agreement. IV. CONCLUSION To develop an accurate prediction method for the magnetic shielding factor in the design of an MSR, we proposed a prediction method for cylinders as a preliminary step and verified its accuracy via the comparison with the result of the experiment. The value of Hi indicate that only few of He can penetrate inside the material of cylindrical shell, and thus μ of micromagnetic field such as the Rayleigh region is important for a magnetic shield against even large magnetic field noise of 10 A/m. As shown in Fig. 2, it was confirmed that the value of μ calculated using Rayleigh’s law is linked to the magnetic shielding effect, and the result also indicated the possibility of applying it to predict SF of MSR.

**References:**

[1] M. Sakakibara, S. Muto, M. Okuda, Y. Adachi, and G. Uehara, IEEJ Trans. Magn. 140, 331 (2020). [2] R. M. Bozorth, IEEE Magnetics Society, 489 (1993). [3] M. Sakakibara, Y. Adachi, and G. Uehara, T. Meguro, IEEE Trans. Magn. (2020). [4] Wills, A.P., Phys. Rev. 9 pp. 193 213 (1899)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9310565b4f277b2dd9bdbf5c7589b14e.jpg)
Fig.1 Plots of μ–H. In (a) and (b), H denotes values in the range of 0 – peak. μ4 is an index of permeability at H = 4 mA/cm, which is conventionally used to evaluate the shielding factor.

![](https://assets.underline.io/uploads/markdown_image/1/image/11e87de63365dc520ed55ec59662c45a.jpg)
Fig.2 Estimated value of the shielding factor SF compared with the experimental results; (a) mu-metal 1, (b) mu-metal 2, and (c) mu-metal 3.

 Prediction of cylindrical magnetic shielding performance by considering the magnetic field strength inside the material

1.INTRODUCTION Wireless power transfer (WPT) has been widely used in various applications due to its great convenience of contactless energy delivery [1,2]. Generally, WPT systems can be categorized into single-phase type and multi-phase type. Compared to traditional single-phase WPT systems, the multi-phase type WPT systems can have more uniformed magnetic field, more compact coil structure and less output current ripple [3]. However, additional interphase mutual inductance is a problem in multi-phase WPT system, making the modeling and control more difficult [3,4]. Also, most multi-phase WPT systems are based on two-level inverters, and three-level inverters surpass traditional two-level inverters in many applications because of advantages like lower voltage stress on power switches and smaller electromagnetic interference (EMI). Among the various three-level topologies, the T-type neutral point clamp (TNPC) topology has high overall efficiency and equal conduction loss of all used power switches [5]. In this paper, a three-phase three-level WPT system based on TNPC inverter is proposed. First, a compact three-phase coil structure are designed to achieve symmetric interphase mutual inductance. Next, with a simplified modeling method, each phase of the three-phase system is simplified to a single-phase system. Further, a novel output regulation method with specific switching sequence is proposed to control the amplitude of the output voltage. Finally, the effectiveness of the proposed three-phase WPT system is verified by both the simulation and experimental results. 2.SYSTEM CONFIGURATION The main topology of the proposed WPT system with series-series compensation is shown in Fig. 1(a). The 3D coil structure is shown in Fig. 1(d) where every two of the six coils have a mutual inductance. The primary coils and the secondary coils have the identical shape. The three coils on the same side are in the same plane and occupy 120° of a circle. With this unique coil structure, the space is highly utilized, and the three-phase coils keep symmetric and has the same interphase mutual inductance. Mpp is the mutual inductance of the primary coils, Mss is the mutual inductance of the secondary coils, Msp1 is the mutual inductance of the aligned coils from the primary side and secondary side, and Msp2 is the mutual inductance of the coils which are not aligned from the primary side and secondary side. Based on the first harmonic approximate (FHA) method, the equivalent circuit is shown in Fig.1 (b), where RL=6Rdc/π2 [6]. When the three phases keep balanced, the voltage across o1 and n1, U1on=0, and the voltage across o2 and n2, U2on=0. Therefore, a simplified equivalent circuit can be derived, as shown in Fig.1 (c). In Fig.1 (c), each phase of the system is approximately equivalent to a single-phase system, where the inductance of the primary side is L1-Mpp, the inductance of the secondary side is L2-Mss, and the mutual inductance is Msp1-Msp2. 3.OUTPUT VOLTAGE REGULATION METHOD The inverter output voltage U1xo is subject to the switching states. Supposing the switching state of the phase x is S=[Sx1 Sx2 Sx3 Sx4], when S+1=[1 1 0 0], U1xo=+0.5Udc; when S0=[0 1 1 0], U1xo= -0.5Udc; when S-1=[0 0 1 1], U1xo=-0.5Udc. In order to reduce the state change of each controlled switches and make the control signal symmetric, a specific switching sequence is chosen for the proposed WPT system, that is S0-S+1-S0-S-1-S0. As shown in Fig. 2 (a) and (b), each of S+1 and S-1 account for 0.5aT in a period time T. The drive signals of each power switches are symmetric in half a period time, and the states of each controlled switches only change twice in a single period time, which makes the driver signals easy to produce. By using fourier decomposition method, the amplitude of the first harmonic can be expressed as m1=2Udcsin(aπ/2)/π (0&lt;=a&lt;=1). Also, the ratio of U2xn and U1xn in Fig.1 (c) can be obtain by U2xn/U1xn =[jw(Msp1-Msp2)]/[(R2+RL)R1+4π2fr2(Msp1-Msp2)2]. Therefore, by regulating the value of a, the transferred power can be controlled. 4.SIMULATION AND EXPERIMENTS In order to verify the effectiveness of the proposed WPT system, simulations are done in MATLAB/SIMULINK. Also, as shown in Fig.2(c), a 500W three-phase prototype is established. Fig.1(b) is the experiment results of the three-phase current and the voltage of U1xo at a=0.3. More analysis and experiment results will be given in full paper. 5.CONCLUSION In this paper, a three-phase three-level WPT system is proposed. Each phase of the system is approximately equivalent to a single-phase system which effectively simplify the system model. A novel output regulation method is proposed to control the output voltage. Simulation and experiment results show a good performance of the proposed WPT system and effectiveness of the control and modeling method, and indicate the proposed WPT system has a better output voltage spectrum and reduced voltage stress compared to traditional three-phase two-level WPT system. Acknowledge This work is supported in part by NSFC (52077186&51677159), in part by STIC Shenzhen Municipality (JCYJ20180307123918658), and in part by ITF (ITP/027/19AP), HK.

**References:**

[1]X. Gao, C. Liu, Y. Huang, "Design of An UAV-Oriented Wireless Power Transfer System with Energy-Efficient Receiver," IECON 2020, Singapore, 2020, pp. 2025-2030. [2]Y. Xiao and C. Liu, "Direct Load Voltage Control for Electrolytic Capacitor-less Wireless Power Transfer System Without DC/DC Converter," in IEEE Transactions on Industrial Electronics. doi: 10.1109/TIE.2020.3013780 [3]J. Pries et al., "A 50-kW Three-Phase Wireless Power Transfer System Using Bipolar Windings and Series Resonant Networks for Rotating Magnetic Fields," in IEEE Transactions on Power Electronics, vol. 35, no. 5, pp. 4500-4517, May 2020. [4]G. A. Covic, J. T. Boys, M. L. G. Kissin and H. G. Lu, "A Three-Phase Inductive Power Transfer System for Roadway-Powered Vehicles," in IEEE Transactions on Industrial Electronics, vol. 54, no. 6, pp. 3370-3378, Dec. 2007. [5]Z. Yuan et al., "Design and Evaluation of Laminated Busbar for Three-Level T-Type NPC Power Electronics Building Block With Enhanced Dynamic Current Sharing," in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 8, no. 1, pp. 395-406, March 2020. [6]C. Wang, C. Zhu, G. Wei, J. Feng, J. Jiang and R. Lu, "Design of Compact Three-Phase Receiver for Meander-Type Dynamic Wireless Power Transfer System," in IEEE Transactions on Power Electronics, vol. 35, no. 7, pp. 6854-6866, July 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/25b52455841eb9658cbdc6202cde8c47.jpg)
Fig. 1. Proposed three-phase three-level WPT system. (a) Main topology. (b)Equivalent circuit. (c) Simplified equivalent circuit. (d) 3D model of the primary coils and the secondary coils.

![](https://assets.underline.io/uploads/markdown_image/1/image/906d0bfa8e0f16fee8207cba065151e9.jpg)
Fig. 2 Primary voltage and experiment of the proposed WPT system. (a) Voltage waveform when a=0.37. (b) Voltage waveform when a=0.88. (c) Testbed. (d) Inverter output voltage in phase A and three-phase currents.

 A Novel Output Voltage Regulation Method for Three-phase Three-level Wireless Power Transfer Based on A Simplified System Model

I. INTRODUCTION Due to the ability to maintain system operation after electrical failure, fault-tolerant machines are increasingly used in safety-critical applications, for instance, automobiles, aviation and armament [1]-[2]. In this paper, based on the dual-winding fault-tolerant permanent magnet motor (DFPMM) which not only inherits permanent magnet synchronous motors’ advantages of high torque density and high efficiency but also has high-performance of fault-tolerance, a novel electric machine drive system is proposed and studied. The 12-slot/10-pole DFPMM, with two separate sets of three-phase single-layer concentrated windings wound on alternate teeth, is capable of restricting fault propagation. The drive system is equipped with two independent drive circuits, while only one DC power supply is needed. With the proposed drive system, fault-tolerant performance to cope with open-circuit faults can be implemented by applying corresponding control strategies. Especially when the one-phase open-circuit fault occurs, system utilization rate is larger compared with the traditional drive system. Simulation and experimental results incorporating current, torque and speed under conditions of one-phase open circuit fault are exhibited respectively. The results verify the effectiveness of the proposed fault-tolerant control strategies and the high reliability of the proposed DFPMM motor drive system. II. THE DFPMM SYSTEM CONFIGURATION AND DESIGN The structure of the proposed electric drive system is shown in Fig. 1(a), which contains a DFPMM, two sets of three-phase full-bridge drive circuits, two triacs, six fuses, and an independent 270V DC power supply. The two sets of windings of the DFPMM are independent of each other, and the ABC windings are controlled by T1 to T6, while the XYZ windings are controlled by T7 to T12. The triac TR1 is connected to the neutral point of the ABC windings and the midpoint of the capacitors, and TR2 is in a similar way. Fuses F1-F6 prevent a shoot-through fault caused by a simultaneous breakdown of power switches in the same phase. During normal operation, two independent three-phase bridge drive circuits control the two windings, each with the same power output which is 50% of the total output power, and the two triacs are kept off. III. FAULT TOLERANT CONTROL STRATEGIES Based on the principle of constant magnetomotive force, control strategies after faults occur will be introduced in the full paper in detail. With the double d-q mathematical model of DFPMM, it is a vector control system that consists of two separate speed controllers, current controllers and SVPWM modules for both two sets of windings. When an open-circuit fault occurs in one set of the windings, the corresponding triac will be turned on, forming a power conversion circuit with a neutral point, as the conductive triac will add a degree of freedom to control the system under the fault condition. Meanwhile, two capacitors are used to perform amplitude and phase modulation on the remaining two-phase currents. IV. SIMULATION AND EXPERIMENTAL VERIFICATION Simulation and experiments are carried out under the conditions of open-circuit faults occurring in one phase, to verify the effectiveness of the proposed electric drive system and its control strategies. The test platform is shown in Fig. 1(b). The results are shown in Fig. 2, including three-phase current of the fault set of windings, speed and torque waveforms. Simulation waveforms of current, torque and speed when an open-circuit fault occurs in phase-A with and without the fault-tolerant control strategies are shown in Fig. 2(a) and Fig. 2(b), respectively. And experimental waveforms of current, torque and speed when an open-circuit fault occurs in phase-A with and without the fault-tolerant control strategies are compared in Fig. 2(c) and Fig. 2(d). From these results, the motor with the proposed drive system maintains the normal performance after the fault occurs, by applying the corresponding control strategy. Thus, the damage caused by open-circuit faults can be avoided. V. CONCLUSION In this paper, a highly-reliable DFPMM drive system aiming at ensuring a normal operation after open-circuit faults is proposed. By applying the control strategies and corresponding actions to typical types of faults, both simulation and experiments have done, proving the effectiveness of the proposed highly-reliable electric drive system. It can cope with open-circuit faults in different situations, and it is suitable for safety-critical applications. More detailed theoretical analysis and experimental verification will be presented in the full paper. ACKNOWLEDGEMENT This work was supported in part by the National Natural Science Foundation of China under Project 51807094, and in part by the Project funded by China Postdoctoral Science Foundation under Project 2020M671499, and in part by Jiangsu Planned Projects for Postdoctoral Research Funds under Grant 2020Z145.

**References:**

[1] B. Wang, J. Wang and A. Griffo, "Stator Turn Fault Detection by Second Harmonic in Instantaneous Power for a Triple-Redundant Fault-Tolerant PM Drive", IEEE Transactions on Industrial Electronics, vol. 65, no. 9, pp. 7279-7289 (2018) [2] X. Jiang, D. Xu and L. Gu, "Short-Circuit Fault-Tolerant Operation of Dual-Winding Permanent-Magnet Motor Under the Four-Quadrant Condition", IEEE Transactions on Industrial Electronics, vol. 66, no. 9, pp. 6789-6798 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3a7fa4ccb4534a2d2dfda84bf2bd5503.jpg)
Fig. 1. The proposed DFPMM drive system. (a) Configuration topology. (b) Test platform.

![](https://assets.underline.io/uploads/markdown_image/1/image/f6b8eac2831d1c3d6d19a84a0d792b69.png)
Fig. 2. The waveforms of three-phase currents, torque, and speed under conditions of phase-A open-circuit fault. (a) Simulation waveforms when no fault-tolerant control strategy is adopted. (b) Simulation waveforms when the fault-tolerant control strategy is adopted. (c) Experimental waveforms when no fault-tolerant control strategy is adopted. (d) Experimental waveforms when the fault-tolerant control strategy is adopted.

 Analysis of Highly Reliable Electric Drive System Based on Dual-Winding Fault-Tolerant Permanent Magnet Motor

1. Introduction Due to the rapid growth in global energy consumption, it is imperative to improve the efficiency of electrical machines and other electrical devices. Iron loss is a crucial part of electrical machines, and has received increasing attention in the past few years. It is significant for both optimizing electrical machine design and improving thermal efficiency. Over the years, several iron loss models have been developed, such as the loss separation models [1] and various hysteresis models [2]. In order to evaluate the iron loss, the most traditional way is to analyze the machine using finite element method (FEM), and calculate the iron loss employing a loss separation model. However, it is deficient, especially when dealing with inverter-fed electrical machines, in which higher-order harmonics exist. In some cases, the estimation error exceeds one hundred percent [3], which is critical for iron loss prediction. On the other hand, in order to precisely describe the materials properties, several hysteresis models are developed. One benefit of hysteresis models is that the iron loss can be directly obtained if the B-H hysteresis loops are known. This paper introduces an iron loss estimation method based on the loss surface (LS) hysteresis model and has applied it on several specimens. The verification process is shown in Fig. 1. The LS hysteresis model is constructed based on the B-H hysteresis loops measured from a toroidal specimen laminated of non-oriented electrical steel sheets. A C-type specimen constructed by the same material is taken as the test object, and is analyzed using the finite element method. The obtained field results combined with the LS hysteresis model are used for iron loss calculation. The calculation results are compared with measured ones. The verification is carried on for both sinusoidal and non-sinusoidal cases. 2. The Proposed Procedure As the iron loss can be calculated directly from the integral of the hysteresis loop without the empirical values. Therefore, it is important to get the magnetic field intensity (H) from the flux density (B) and its derivative(dB/dt). The method begins with the measurement of the B-H hysteresis loops, which is performed on a toroidal specimen according to the International Standard IEC 60404-6 [4]. A primary winding is used for the excitation, and another winding is the measuring coil. The B-H hysteresis loops under different magnetic flux density magnitudes Bm have been measured to demonstrate the material behavior more precisely. The LS model, therefore, can be represented by the function between the magnetic field intensity(H) and the flux density (B) and its derivative (dB/dt) and its maximum value (Bm). The calculated object is first performed field analysis by using finite element method. The magnetic flux density distribution can be computed in all elements, which is also taken as the input of the LS model. Combined the derivative of magnetic flux density (dB/dt) and the magnitude Bm, the corresponding magnetic field intensity (H) can be obtained, therefore, the B-H hysteresis loops for arbitrary waveforms can be construed, from which iron loss can be calculated. 3. Verification First, a C-type specimen with the same material is manufactured to verify the proposed procedure, as shown in Fig. 1. In order to check the LS hysteresis modeling accuracy, a magnetic flux density with 0.8T amplitude and 50Hz fundamental frequency, combined with 35% of the third harmonic with a phase shift of 90°is taken as the input, and the magnetic field intensity and hysteresis loops are shown in Fig. 2. The modeled results match well with measured ones. The iron loss of the test C-type specimen is calculated by using both the proposed method and the loss separation model. The measured iron loss is 1.699W, and for the proposed method, the calculated iron loss is 1.530W, whereas for the loss separation models, the calculated iron loss is 1.282W. 4. Conclusion The proposed iron loss calculation procedure based on the LS hysteresis model has been developed and the verification of a C-type specimen has been done. Compared with actual measured results, the proposed iron loss calculation method is more accurate than loss separation model. Verification and analysis on more topologies will be discussed in the full paper.

**References:**

[1] G. Bertotti, "General properties of power losses in soft ferromagnetic materials," in IEEE Transactions on Magnetics, vol. 24, no. 1, pp. 621-630, Jan. 1988. doi: 10.1109/20.43994. [2] Chevalier, T., Kedous-Lebouc, A. and Cornut, B. et al. A new dynamic hysteresis model for electrical steel sheet. Physica B: Condensed Matter, 275(1-3), 197-201. [3] Tekgun, B., Sozer, Y., and Tsukerman, et al. Core loss estimation in electric machines with flux-controlled core loss tester. IEEE Transactions on Industry Applications, 55(2), 1299-1308. [4] Methods of measurement of the magnetic properties of magnetically soft metallic and powder materials at frequencies in the range 20hz to 200khz by the use of ring specimens”, International Standard IEC 60404-6: 2003.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5ada5b095a3f2f7807d1aa9820381674.jpg)
Fig1TheLSmodelVerificationProcess

![](https://assets.underline.io/uploads/markdown_image/1/image/fb3c33aaca38a830099708fa21c2bbaf.jpg)
Fig2LSModelEstimatedAndMeasuredResults

 Iron Loss Calculation Based on Loss Surface Hysteresis Model and Its Verification

The aim of this paper is to investigate the feasibility of a hybrid ferromagnetic bonding in a stack used in electrical machines. In a context of growing energy needs and the absolute need to reduce greenhouse gases, the stakes are high. For instance, with the electrification of aircraft in full development, it is essential to improve the power density of on-board electric actuators. Beyond aeronautics, the advantage of improving machine performance through its intrinsic performance of its materials is that this increase in efficiency does not depend on the application and becomes possible in all sectors of activity. This study which is supported by the French ADEME (Agency of the Environment and the Control of Energy) focuses on steel sheet stack intrinsic performance improvement for electrical machine applications. Generally, a laminated stack is composed by electrical steel sheet. An epoxy-based bonding is often used to ensure a structural cohesion of the stack in order to be manipulated and integrated. It also helps to keep a proper electrical insulation between sheets, limiting eddy current circulation. This study proposes to add iron powder to the epoxy bonding as described on Fig. 1, in order to improve the permeability of the bonding, which is magnetically neutral, becoming then a SMC. However, SMCs are generally used as a magnetic yoke [1] and not as an adhesive layer. The powder load is only intended to exploit a magnetically inert volume. The magnetic flux which will circulate in the packet will do so essentially through the sheets, but the gain in permeability envisaged to make pass more flux under the same magnetic field. The powder load could also improve the thermal conduction along the z axis, improve the thermal performance of the sheet package. Nevertheless, the circulation of eddy currents must remain limited between the sheets and the composite joints. It is necessary to limit the powder load to ensure this. Actually, the method proposed here does not really reproduce the SMC manufacturing process (pressure at temperature of the dielectric mixture - magnetic powder). In the case of a conventional SMC, the process ensures inter-grain isolation [2], making these materials particularly efficient at high-frequency. In the composite joint proposed here, the inter-grain (and therefore inter-sheet) insulation relies only on the residue of the epoxy adhesive around the grains once the sheets have been bonded. The distribution and the quantity of the adhesive being difficult to control, it is essential to keep a sufficient margin, and therefore to limit the powder load. On the other hand, the addition of a magnetic filler has been shown to improve the permeability of a mixture, especially at high frequency [3]. This feasibility study is based on ring core characterization. In order to limit parameters, the thickness and the number of sheets are set, respectively at 0.2 mm and 10 per stack. The thickness of the composite joint is also set at 50 µm. Actually, the powder grains must be large enough to retain interesting magnetic properties. A thickness of 50 µm is a good compromise in the context of a feasibility study. Finally, the only variable parameter is the powder charge. It has been decided to set it at 25%, 50% and 75% of the mass of the composite joint. A joint of the same thickness but loaded at 0% will be used as a reference. The magnetic permeability of the joint is actually determined by the powder volume / joint volume ratio. However, it is much simpler to proceed by mass ratio and to use density to calculate the corresponding volume ratio (4.5%, 13% and 30%). Besides, two types of iron powder are used (AHC 300 and MH300, both 300 mesh for grain size), each with specific properties. Therefore, each ring core corresponds to electrical steel sheet stack with a determined load of specific type of iron powder. Then, ring cores are manufactured and their windings are designed to reach 2 T at 400 Hz and 1000 Hz, and 1 T at 5000 Hz. Specific iron losses (W/kg) are measured and gathered in Fig. 2. This study demonstrates that adding iron powder to adhesive bonding of steel sheet is technically possible. The gain observed is significant and appears promising from the perspective of a more developed study. However, some technical points must be improved. More measurement should be proceeded, including reproducibility measurement. It would appear interesting to charge the adhesive with a metal powder of the same thermal conductivity as iron (or similar) but which would be non-magnetic. It could then be determined whether the performance is improved via magnetic permeability or via thermal conduction. In order to fully characterize these samples, optimization by numerical simulation could be considered, in order to precisely determine the parameters essential to performance. Finally, it seems essential to perform tests on a machine and not on ring cores, in order to ensure the real potential gains.

**References:**

[1] A. Jakubas, P. Gebara, S. Seme, “Magnetic properties of SMC cores produced at a low compacting temperature”. Acta Phys. Pol. A, 131(5), 1289-1293. [2] Y. X. Pang, S. N. B. Hodgson, J. Koniarek, “The influence of the dielectric on the properties of dielectromagnetic soft magnetic composites. Investigations with silica and silica hybrid sol–gel derived model dielectric.” Journal of magnetism and magnetic materials, 310(1), 83-91. [3] Belyaev, B. A., & Tyurnev, V. V. (2018). “Electrodynamic calculation of effective electromagnetic parameters of a dielectric medium with metallic nanoparticles of a given size.” Journal of Experimental and Theoretical Physics, 127(4), 608-619.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/398f5db97656d15612bd89dc54d799a1.jpg)
Fig. 1: Representation of the hybrid bonding in an electrical steel sheet stack.

![](https://assets.underline.io/uploads/markdown_image/1/image/8beea0f22ed5225ed70e5c7b610947ed.jpg)
Fig. 2: Results of specific iron losses measured in the samples for AHC300 and MH300 iron powder, at several frequencies and magnetic flux densities.

 Experimental study of a hybrid bonding in ferromagnetic stacks for electrical machine applications

Introduction. Additive manufacturing, also known as 3D printing, has experienced a tremendous development over the past twenty years. This process enables fast prototyping and it offers the ability to create complex shapes that would otherwise be difficult to produce using classical techniques. This process has been applied to a wide range of polymer, nowadays different research interests [1] focus on functional materials, such as metals or ceramics, to create components with enhanced physical properties. In this way, electromagnetic systems and power applications could exploit printed soft magnetic materials to be designed in a shorter amount of time and benefit from a wider range of feasible shapes. In this work, additively manufactured inductor made using two different printing feedstock types are presented. The simulation of a new geometry is made using finite element method in an attempt to explore the influence of the form on the flux density distribution. Finally, modeling and magnetic characterizations were carried out to compare the performances with a reference material. The specificity of this work consists in the usage of magnetic materials shaped with 3D printing. 1. Additive manufacturing of magnetic materials. Fabrication of objects is realized through the Fused Deposition Modeling technic. A first approach is to use a feedstock that comes as a filament loaded with metallic particles [2]. For this, two filaments from Proto Pasta and Virtual Foundry were used to produce shapes that could be used in an electrical system, like toroidal or E-shaped inductor. To achieve a greater concentration of the target materials, a pellet type feedstock was also used to perform MIM-like additive manufacturing with material from PolyMIM. In order to get good magnetic performances, the binding polymer has to be removed from the final part, so that it is only composed of the loaded material. Finally, the densification of the object has to be performed through a heat treatment. These last two steps are called debinding and sintering. Both processes will be undertaken in future works. 2. Modeling. In order to predict the behavior and performances of a toroidal inductor, a multi-physical modeling has been realized. It takes into account the analytical computation of the flux density, the thermal behavior due to the losses and the impact of heat on magnetic permeability. This model was then compared to a finite element simulation for validation. The simulation was performed using the software Opera-3D. The whole is put into perspective with practical tests. 3. New printable geometry. The main benefit from creating 3d printed objects is the variety of shapes that becomes accessible [3]. Complex geometry could be considered in the design process to suit requirements or even to modify the behavior of a component without using a different material [4]. To explore this possibility, an inductor with a complex shape was studied using finite element method. It consists in a torus that is distorted, along its axis, in a cyclic manner. The result is a wavy body that can be seen on figure 1.a. This core will be coiled and simulated as if it was made out of a ferromagnetic material. The geometry has been created to follow a wrapped-up sinus curves and to ensure a constant section along the path. This way, the circulation of the magnetic field can be modified without increasing the torus radius. Conductor were placed around each antinodes of the waves. Finally, different amplitudes were tried and the distribution of the magnetic field inside the core was observed. In figure 1.b, we can see that the magnetic field repartition can be tilted depending on the ripple range. 4. Magnetic characterization. To evaluate the performance of the different printed materials, a serie of magnetic characterizations was conducted. For this, the TX42/26/13 ferrite core from Ferroxcube was taken as a reference and several components with the same dimensions were printed with the feedstocks stated previously. Some examples of wound components are shown in figure 2.a. Magnetic variables such as magnetic permeability, maximum flux density and iron losses were observed. As it can be seen in the work of Bollig et al. [5], performances are way smaller than the reference material. This is due to the fact the first materials tested were made out of powder enclosed in a polymer binder, hence the density of magnetic material is very low. In figure 2.b, the magnetic permeability versus the density of the material is presented. Conclusion. To conclude, the use of additive manufacturing with magnetic materials offers a wide range of feasible shapes that can be used advantageously in the design process. However, the performances of such objects need to be improved . In future work, the density of the printed parts will be greatly enhanced by using a pellets based printing process and by going through the thermal treatments. Furthermore, a soft magnetic material that is similar to the reference presented earlier, will be used as feedstock for future prints.

**References:**

[1] Y. Yan, J. Moss, K. D. T. Ngo, Y. Mei, et G.-Q. Lu, « Additive manufacturing of toroid inductor for power electronics applications », in 2016 IEEE Energy Conversion Congress and Exposition (ECCE), Milwaukee, WI, USA, sept. 2016, p. 1-6, doi: 10.1109/ECCE.2016.7854826. [2] Y. Wang, F. Castles, et P. S. Grant, « 3D Printing of NiZn ferrite/ABS Magnetic Composites for Electromagnetic Devices », MRS Proc., vol. 1788, p. 29-35, 2015, doi: 10.1557/opl.2015.661. [3] F. Lorenz, J. Rudolph, et R. Wemer, « Design of 3D Printed High Performance Windings for Switched Reluctance Machines », in 2018 XIII International Conference on Electrical Machines (ICEM), sept. 2018, p. 2451-2457, doi: 10.1109/ICELMACH.2018.8506845. [4] L. Liu et al., « Design and Additive Manufacturing of Multi-Permeability Magnetic Cores », p. 6, 2017. [5] L. M. Bollig, P. J. Hilpisch, G. S. Mowry, et B. B. Nelson-Cheeseman, « 3D printed magnetic polymer composite transformers », J. Magn. Magn. Mater., vol. 442, p. 97-101, nov. 2017, doi: 10.1016/j.jmmm.2017.06.070.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2aa88ee44aa6d76f457a417e97a5c278.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/6ead33b37563f614f48b2d286d42878e.jpg)
Fig.2 Printed samples and magnetic characterization results (effective permeability over material density)

 Additive manufacturing for soft magnetic materials

1 Introduction In aviation field, direct drive permanent magnet (PM) rectifier generator is often used in Multi Electric Airplane (MEA). Multiphase AC windings and rectifier technology make DC generator an excellent DC source with low torque ripple and low voltage ripple. And by regulating the engine speed within specified range, the DC-link voltage can be maintained constant with various electric loading. The key point of designing such a kind of generator, is to predict the electromagnetic and thermal field accurately. To solve the problem above, most research focused on electromagnetic thermal coupling analysis based on computational fluid dynamics (CFD), which can accurately predict temperature distribution [1]. Obviously, CFD-based coupling analysis method is not fit for optimization of direct drive PM rectifier generator for CFD process is time-consuming. In this paper, we aim to adopt lumped parameter thermal network (LPTN) as a substitute to replace the CFD process, implementing an electrical circuit-electromagnetic field-thermal network coupling analysis algorithm, enabling a much faster solution to analyze and optimize a PM rectifier generator. 2 Coupling Analysis 2.1 Electrical Circuit and Electromagnetic Field Coupling Analysis Electrical circuit and electromagnetic field are coupled by electromotive force(EMF). Electromagnetic field analysis takes winding current as the input, and outputs EMF. Electrical circuit analysis takes EMF as the input, and outputs winding current. Electromagnetic field is usually solved by 2D time stepping FEM method. Electrical circuit is solved by branch current method. The coupling relation is so strong that magnetic vector potential and winding current can only be analyzed simultaneously. 2.2 Electromagnetic Field and Thermal Network Coupling Analysis Electromagnetic field analysis takes winding current as input, and outputs iron loss, copper loss, solid loss, etc. Thermal networks analysis takes loss as input, and output temperature of generator parts. The above is just one way coupling (designated as unidirectional) from electromagnetic field to thermal network, which is carried out by transferring and mapping loss data. In this paper, we have also considered the coupling from thermal network to electromagnetic field, involving material property, which will be described in Section 2.3. Here this is called bidirectional coupling method. As for the LPTN model of generator, thermal resistance of each part refers to Mellor’s T-shaped model [2]. The structure of each part is equivalent to a hollow cylindrical structure. Conduction, natural and forced convection are considered in the LPTN model. Model parameters and assumptions will be detailed in the full paper. 2.3 Material Property The temperature dependent material property is measured in the lab. The result is as follows: (1)For permanent magnet, coercivity and remanence decrease with temperature. (2)For silicon steel, the iron loss decreases with temperature. (3)For copper and permanent magnet, the resistivity increase with temperature. 2.4 Implementation Thermal network of generator is modelled and solved in Matlab, and electrical circuit and electromagnetic field are solved in ANSYS/Maxwell. Because the electromagnetic field and the temperature field have different time constant, during each iteration, several periods of electromagnetic field-circuit calculation are need to reach a steady state, followed by LPTN calculation. A control program is coded in Matlab to call thermal solver and Maxwell solver, and to transfer and map loss and temperature dependent material property. The convergence criterion is met if the temperature difference between adjacent iterations is less than 1°C. 2.5 Experiment Validation This prototype machine is an inner rotor PM generator with an integrated fan on the same shaft as rotor. The designed output power is 4.5kW at 7250rpm, and the DC link voltage is 50V. The generator is of 10 poles and 12 slots, filled with six phase double layer winding. The surface mounted PM is sintered SmCo30H. After 5 iterations, the coupled field analysis quickly reached convergence. The PM and winding temperature at each iteration and the corresponding loss is shown in Fig 2 . As shown in Fig 1, a load test has been carried out to validate the accuracy of the bidirectional coupling method. The servo motor drives the prototype at a constant speed and torque meter measures the mechanical torque. The rectifier circuit is connected to the terminal of the prototype. Two thermocouples are embedded in the end windings. Fig 2 shows the measured and simulated results. To illustrate the effect of temperature on electromagnetic field, the simulated result by unidirectional method is provided where the initial temperature is set to 25°C. Due to the consideration of thermal effect on material properties, the simulated result by bidirectional method is more accurate than unidirectional method. The prediction error of the bidirectional coupling method is within 5%. This paper proposed a much faster method to predict the electromagnetic and thermal field of direct drive PM rectifier generator. Lumped parameter thermal network (LPTN) is used as a substitute to replace the CFD process, greatly shortens the solution time. Furthermore, temperature effect on material property is considered, enabling a bidirectional coupling analysis in the paper. The experimental validation shows that the proposed method is enough accurate. The method can be applied to analyze and optimize a PM rectifier generator, as well as other typed motor.

**References:**

 [1] Yapeng Jiang , Dong Wang, Junquan Chen, "Electromagnetic-Thermal-Fluidic Analysis of Permanent Magnet Synchronous Machine by Bidirectional Method," IEEE Transactions on Magnetics, vol.3, no.54, pp. 1-5, 2018. [2] Mellor P.H, Roberts D, Turner D.R, "Lumped parameter thermal model for electrical machines of TEFC design," IEEE PROCEEDINGS-B, vol.138, no.5, pp.205-218, 1991.

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/55f231196743cfde6ee8b35ae9c9d637.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/9e3d5b7f8437466378caee97ef19984c.jpg)

 Coupled Electromagnetic and Thermal Analysis of Permanent Magnet Rectifier Generator Based on LPTN

I. Introduction Variable flux memory machines (VFMM) equipped with low coercive force (LCF) aluminum-nickel-cobalt (AlNiCo) magnets [1]-[4] can achieve high efficiency over a wide operation range by applying a current pulse to magnetize the LCF magnets with negeligible copper loss. Thus, VFMM is widely recognized as a competitive candidate for traction applications. For elevating the the electromagnetic performance of VFMMs, hybrid usage of high coercive force (HCF) and LCF magnets are applied in VFMMs. A novel hybrid-magnet-circuit VFMM (HMC-VFMM) is proposed in [5], which combines the design concepts and strengths of VFMMs with parallel and series magnetic circuit of HCF and LCF magnets. Due to the special hybrid magnetic circuit design, it is essential to provide an insightful understanding about the nonlinear hysteresis behavior of the LCF working point considering the resultant effects of parallel and series branches and to analyze the magnetic field variation phenomenon of the developed HMC-VFMM due to the transient current pulse by an effective solution. This paper attempts to reveal and investigate a balanced bidirectional-magnetization effect of the proposed HMC-VFMM, i.e., the required demagnetizing and remagnetizing current levels are basically similar, which will benefit the inverter rating reduction and online flux control. The balanced bidirectional-magnetization effect is analytically revealed by using a simplified Fourier-series based hysteresis model. In addition, the numerical hysteresis model is programmed with FE model so as to accurately investigate the magnetization characteristics of HMC-VFMM. Finally, the experimental results on a prototype are carried out to verify the theoretical analyses. II. Machine configuration and working principle The proposed 21-slot/4-pole HMC-VFMM is investigated, in which the cross-section is illustrated in Figs. 1(a). The proposed HMC design is characterized by a dual-layer PM structure. For the parallel branch, the “U”-shaped hybrid PM arrangement is employed. For the series branch, the HCF PMs form a spoke-type flux concentration type. The proposed HMC-VFMM can combine the advantages of wide flux regulation range in parallel type and excellent on-load demagnetization withstand capability in series type. The variable-flux principle of the proposed HMC-VFMM can be illustrated by the open-circuit field distributions under different magnetization states (MSs) in Fig. 1(b). It can be observed that the air-gap flux can be flexibly adjusted by applying a transient magnetizing or demagnetizing current pulse. Meanwhile, due to the variable flux property, the losses at different speeds and loads can be also manipulated to realize efficiency improvement over a wide operating range. III. Analytical Analysis of Balanced Bidirectional-Magnetization Effect The nonlinear hysteresis characteristics of the LCF PMs used in the proposed HMC-VFMM can be characterized by a simple Fourier-series based hysteresis model as shown in Fig. 2(a). The PM working point can track along different recoil lines by applying a specific remagnetizing or demagnetizing current pulse. The underlying mechanism of the balanced bidirectional-magnetization effect can be physically characterized by hysteresis curves of the LCF PM in Fig. 2(b). The load line of the HMC design is placed between the two load lines of the parallel and series cases, which allows a better balance between the magnetizing and demagnetizing current amplitudes. Meanwhile, the oversized inverter rating issue for either parallel or series VFMMs can be well avoided by appropriately reducing maximum remagnetizing currents. The detailed analysis and investigation of magnetization characteristics of HMC-VFMM will be given in the full paper.

**References:**

[1] V. Ostovic, "Memory Motors," IEEE Ind. Appl. Mag., vol. 9, no. 1, pp. 52-61, Jan./Feb. 2003. [2] H. Liu, H. Lin, Z. Q. Zhu, M. Huang, and P. Jin, "Permanent Magnet Remagnetizing Physics of a Variable Flux Memory Motor," IEEE Trans. Magn., vol. 46, no. 6, pp. 1679-1682, 2010. [3] Yu, C. and K. T. Chau . "Design, Analysis, and Control of DC-Excited Memory Motors," IEEE Trans. Energy Convers., vol. 26, no. 2, pp.479-489, 2011. [4] N. Limsuwan, T. Kato, K. Akatsu, and R. D. Lorenz, "Design and Evaluation of a Variable-Flux Flux-Intensifying Interior Permanent-Magnet Machine," IEEE Trans. Ind. Appl., vol. 50, no. 2, 2014. [5] H. Yang, S. Lyu, H. Lin, Z. Q. Zhu, H. Zheng and T. Wang, "A novel hybrid-magnetic-circuit variable flux memory machine," IEEE Trans. Ind. Electron., vol. 67, no. 7, pp. 5258-5268, 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fd15041edf173bd5308f52185a96915d.jpg)
Fig. 1 VFMM topology and open-circuit field distributions under different magnetization states. (a) Topology. (b) Open-circuit field distributions under different magnetization states.

![](https://assets.underline.io/uploads/markdown_image/1/image/c7f4e39097f597c7fe82679fc137ef9c.jpg)
Fig. 2 Illustration of Fourier-series based hysteresis model. (a) Simplified view for illustrating the variable flux principle. (b) Numerical representation.

 Investigation of Balanced Bidirectional-Magnetization Effect of a Novel Hybrid-Magnet-Circuit Variable Flux Memory Machine

The first energization of a power transformer in an energy distribution system is a critical issue in the transformer’s lifetime since the high currents experienced by the device in these conditions. Such currents are primarily due to magnetization of the iron core, which exhibits memory phenomena and saturation. Further, the initial phase strongly affects dynamics and could push the core in a saturation state, which, in turn, reduces the primary coil impedance and hence enables the current to rise (up to 10-15 times the full load current). This transient current is usually referred to as inrush current [1,2] and can be very dangerous for the device, causing electrodynamic stress, dissipations and consequent heating of the electrical insulations, harmonics production and their circulation in the power system. Such magnetizing currents focused great attention in the analysis of large transformers. The latest research activity was basically focused on the modeling, at the macroscopic scale, of the magnetization processes taking place in the transformer’s core, strongly affecting the circuit’s dynamics. The effort was therefore aimed to plug into the circuit model a suitable hysteresis operator. Different proposals discussed the effects of hysteresis models (e.g., Preisach, Jiles Atherton (J-A), etc., [3,4]) on the global behavior of the transformer dynamics, with particular emphasis to model’s accuracy and computational weight, [5,6]. The J-A model offers a tool to describe hysteresis, but it is able to describe too simplified memory phenomena, [3] and requires a nontrivial parameters identification (e.g., through a nonlinear optimization). Conversely, Preisach model (PM) provides a memory description that fits with the real macroscopic processes but requires some expertise and a large of measured data (i.e., first order reversals), which limits its use in non-specialized frameworks, as power circuits and industrial electronics. Therefore, the availability of well-behaved hysteresis operator suitably simplified with respect to, e.g., the Preisach model, would represent an interesting contribution to this field. In the present contribution, the core magnetization modeling of a power transformer in a network is provided through a Preisach-based operator (i.e., it is characterized by the Preisach memory updating rules), [7] offering a simpler implementation, inverse operator availability and a reduced set of measured data, than PM. Such operator, as detailed hereafter, is based on a weighted linear superposition of elementary operators (Play operators, see, [7]) and will be referred to as Prandtl-Ishilinskii (P-I) operator. Further, due to its simpler structure and reduced numbers of parameters, it allows the inrush current process analysis in a wide range of magnetization conditions with low effort. The P-I model, describing the B-H characteristic, along with the circuit’s equations, referred to the same circuit as in [6], are reported in Fig. 1. In the first frame, Pr[.] is the play operator, while μ(r) is a weight function and the saturation magnetization, Ms = 1.5T. In the second frame, R1 is the primary resistance, E the voltage amplitude, while F is the hysteresis operator linking the flux linkage to the primary current. The secondary current is assumed zero during the analysis. The model so conceived is able to fairly describe the behavior of a realistic core, as shown in the same figure. The circuit’s behavior has been preliminary tested in the same conditions as in [6]. However, in Fig. 2 its behavior has been studied in conditions where the great arise of (inrush) currents clearly appears. In the same figure the impact of hysteresis with respect to a memoryless description is outlined. Aim of the paper will be a thorough testing of the proposed model, in terms of accuracy, computational efficiency for the analysis of inrush currents phenomena in power transformers. The characteristics of the hysteresis operator would allow an immediate analysis of the basic magnetic parameters affecting the inrush currents dynamics. In particular, the influence of remanence, coercive field and permeability at current reversal, will be investigated. For the latter (initial permeability at the branch start), during the transient, the material experiences an up and forth current variation, allowing the branching to arise and to affect (in the starting part of the branch characterized by low permeability) the whole current dynamics. Such effect, which strongly relies on the initial magnetization state of the iron core (Mr), could be easily described by the proposed model and of course, cannot be taken into account when a nonlinear memoryless modeling is employed.

**References:**

[1] R. Yacamini, C.Eng., and A. Abu-Nasser, IEE Proceedings, Vol. 133, Pt. B, No. 1, 1986. [2] J.C. Yeh, C.E. Lin, C.L. Huang, Electric Power Systems Research 30, 93-102, 1994. [3] I. D. Mayergoyz, Springer, 1991. [4] D.C. Jiles, D.L. Atherton, J. of Magnetism and Magnetic Materials, vol. 61, 1–2, pp. 48-60, 1986. [5] A. A. Adly, IEEE Trans on Magnetics, vol. 37, no. 4, 2001. [6] X. Wang, D. W. P. Thomas, M. Sumner, IEEE Trans. on Magnetics, 44, 3, 2008. [7] C. Visone, M. Sjöström, Physica B: Condensed Matter, vol. 343, 1–4, pp. 148-152, 2004.

**Images:**

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A New Method to Control Intrinsic Localized Mode Using a Variable Magnetic Spring Structure

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A New Method to Control Intrinsic Localized Mode Using a Variable Magnetic Spring Structure

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