France



  The high-frequency transformer (HFT) will produce sharp noise when working and the long-term excessive vibration will not only accelerate the aging of the equipment but also influence the surrounding environment, so it is great significance to study the vibration and noise characteristics of the HFT. In this paper, the core-type nanocrystalline high frequency transformer with capacity of 5400kVA and frequency of 5000Hz is simulated and analyzed by two factors of magnetostrictive and Maxwell. At last, a high frequency transformer is designed and a test platform is set up. The vibration and noise is tested and analyzed, and compared with the simulation results.&lt;br/&gt;&lt;i&gt;Index Terms&lt;/i&gt;—Nanocrystalline, high frequency transformer, vibration, noise&lt;br/&gt;Introduction&lt;br/&gt;The high-frequency transformer (HFT) of large capacity in DC/DC converter will be able to achieve voltage and power transmission in the electric power system, high and low voltage side electrical isolation between inverter and rectifier circuit through the magnetic coupling, which can more easily achieve the electrical control of DC/DC converter on both sides. The vibration and acoustic noise emission of electromagnetic devices is not a new research area. However, the focus in the past has been on electrical machines and line frequency transformers, which have been thoroughly investigated in [1-3]. A clear understanding of the vibration and noise characteristics of HFT is necessary for detecting electrical and mechanical faults in a transformer using vibration-based monitoring strategies.&lt;br/&gt;Vibration mechanism of iron core&lt;br/&gt;There are two main factors in the vibration of HFT, the first factor is the magnetostriction effect of the iron core and the second factor is Maxwell force at the air gap. From the perspective of conservation of mechanical and internal energy, the magnetostrictive intrinsic model which is suitable for grain oriented silicon steel sheets is established.&lt;br/&gt;The test platform is built to test the vibration and noise of the core-type HFT, the test platform is shown in Fig. 1(a). The measuring points are shown in Fig.1 (b), and the noise is measured at the front and side of HFT. The simulation results show that the displacement of point 3 at 1000Hz is 5.5×10&lt;sup&gt;-7&lt;/sup&gt;m when the flux density in the core is 0.6T, and the displacement of point 4 is 7.9×10&lt;sup&gt;-7&lt;/sup&gt;m. The displacement increased by 43.63% compared with point 3, which indicates that the air gap is greatly influenced by Maxwell force due to the large leakage magnetic field. The time domain vibration of three points working at 1000Hz and 0.6T is shown in Fig. 2(a), it can be seen that the vibration of the upper part of the iron core is more serious. The vibration and noise trend of HFT at different frequencies is shown in Fig. 2(b). It can be seen that the vibration and noise of HFT gradually become larger with the increase of the frequency of excitation. At the same time, the vibration and noise are much larger than the conventional transformers, and the noise values are completely beyond the tolerable range. Therefore, it is necessary to study the vibration and noise characteristics of the high frequency transformer.&lt;br/&gt;Acknowledge&lt;br/&gt;This work was supported in part by National Natural Science Foundation of China under Grant 52007192. and in part by the Fundamental Research Funds for the Central Universities (2020XJJD02).

**References:**

[1] B. Weiser, H. Pfutzner, and J. Anger, “Relevance of magnetostriction and forces for the generation of audible noise of transformer cores,” IEEE Transactions on Magnetics, vol. 36, no. 5, pp. 3759–3777, 2000.&lt;br/&gt;[2] R. S. Masti, W. Desmet, and W. Heylen, “On the influence of core laminations upon power transformer noise,” in Proceedings of ISMA, 2004, pp. 3851–3862.&lt;br/&gt;[3] A. Moses, P. Anderson, T. Phophongviwat, and S. Tabrizi, “Contribution of magnetostriction to transformer noise,” in 45th International Universities Power Engineering Conference (UPEC), 2010, pp. 1–5.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/acda7613f831c6d092bf97fe19ccfc34.jpg)
Fig. 1 The experiment set-up and the structure and the vibration measuring points

![](https://assets.underline.io/uploads/markdown_image/1/image/2b0f337098d90de7df3ebf6144a4dbff.jpg)
Fig. 2 The vibration time domain waveform and the change of vibration and noise with magnetic flux density

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 Study on Vibration and Noise Characteristics of Nanocrystalline High-frequency Transformer

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The high-frequency transformer (HFT) will produce sharp noise when working and the long-term excessive vibration will not only accelerate the aging of the equipment but also influence the surrounding environment, so it is great significance to study the vibration and noise characteristics of the HFT. In this paper, the core-type nanocrystalline high frequency transformer with capacity of 5400kVA and frequency of 5000Hz is simulated and analyzed by two factors of magnetostrictive and Maxwell. At last, a high frequency transformer is designed and a test platform is set up. The vibration and noise is tested and analyzed, and compared with the simulation results. Index Terms—Nanocrystalline, high frequency transformer, vibration, noise Introduction The high-frequency transformer (HFT) of large capacity in DC/DC converter will be able to achieve voltage and power transmission in the electric power system, high and low voltage side electrical isolation between inverter and rectifier circuit through the magnetic coupling, which can more easily achieve the electrical control of DC/DC converter on both sides. The vibration and acoustic noise emission of electromagnetic devices is not a new research area. However, the focus in the past has been on electrical machines and line frequency transformers, which have been thoroughly investigated in [1-3]. A clear understanding of the vibration and noise characteristics of HFT is necessary for detecting electrical and mechanical faults in a transformer using vibration-based monitoring strategies. Vibration mechanism of iron core There are two main factors in the vibration of HFT, the first factor is the magnetostriction effect of the iron core and the second factor is Maxwell force at the air gap. From the perspective of conservation of mechanical and internal energy, the magnetostrictive intrinsic model which is suitable for grain oriented silicon steel sheets is established. The test platform is built to test the vibration and noise of the core-type HFT, the test platform is shown in Fig. 1(a). The measuring points are shown in Fig.1 (b), and the noise is measured at the front and side of HFT. The simulation results show that the displacement of point 3 at 1000Hz is 5.5×10-7m when the flux density in the core is 0.6T, and the displacement of point 4 is 7.9×10-7m. The displacement increased by 43.63% compared with point 3, which indicates that the air gap is greatly influenced by Maxwell force due to the large leakage magnetic field. The time domain vibration of three points working at 1000Hz and 0.6T is shown in Fig. 2(a), it can be seen that the vibration of the upper part of the iron core is more serious. The vibration and noise trend of HFT at different frequencies is shown in Fig. 2(b). It can be seen that the vibration and noise of HFT gradually become larger with the increase of the frequency of excitation. At the same time, the vibration and noise are much larger than the conventional transformers, and the noise values are completely beyond the tolerable range. Therefore, it is necessary to study the vibration and noise characteristics of the high frequency transformer. Acknowledge This work was supported in part by National Natural Science Foundation of China under Grant 52007192. and in part by the Fundamental Research Funds for the Central Universities (2020XJJD02).

**References:**

[1] B. Weiser, H. Pfutzner, and J. Anger, “Relevance of magnetostriction and forces for the generation of audible noise of transformer cores,” IEEE Transactions on Magnetics, vol. 36, no. 5, pp. 3759–3777, 2000. [2] R. S. Masti, W. Desmet, and W. Heylen, “On the influence of core laminations upon power transformer noise,” in Proceedings of ISMA, 2004, pp. 3851–3862. [3] A. Moses, P. Anderson, T. Phophongviwat, and S. Tabrizi, “Contribution of magnetostriction to transformer noise,” in 45th International Universities Power Engineering Conference (UPEC), 2010, pp. 1–5.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/acda7613f831c6d092bf97fe19ccfc34.jpg)
Fig. 1 The experiment set-up and the structure and the vibration measuring points

![](https://assets.underline.io/uploads/markdown_image/1/image/2b0f337098d90de7df3ebf6144a4dbff.jpg)
Fig. 2 The vibration time domain waveform and the change of vibration and noise with magnetic flux density

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Introduction In the field of wireless charging for electric vehicles, the limitation of vehicle-mounted space is a major constraint for the on-board device. It is impossible to ask the drivers to park their vehicle at the same exact position and drivers often park the car with more than a few centimetres of misalignment [1]. Currently, unipolar coils are widely used; these have an upper limit for the coupling coefficient k. With a certain secondary coil size and air gap, a maximum coupling coefficient of the coupler at the aligned position can be estimated using a Dagum distribution [2]. However, the horizontal misalignment has a significant impact on the coupling coefficient, which makes it difficult to tune the resonance of the compensation. With the decrease in k, the primary inverter output may operate in an overcurrent mode with series-series compensation. This is a challenge for the power semiconductors. At the same time, the misalignment will affect the power transfer capability and efficiency. The system performance, within reasonable misalignment, should be robust which will make the system usable for practical charging systems. Proposed Primary Coupler In order to enhance the power transfer capability with a relatively large misalignment, this work investigates a unipolar transmitter coil and its robust optimization design process. Several design parameters of the coupler are shown in Fig. 1, including the pitches, the length and width of the coil, the types of Litz wire. The coupler is analysed and verified with finite element (FE) modelling. Earlier research has shown that by reducing the main coil inductance and connecting with the assistive coil in series, a superposition effect in the magnetic field can be produced to a certain extent. By optimizing the design parameters, a higher coupling coefficient can be obtained under a specific primary inductance. For example, the analysis results show that by increasing gap B between the Litz wires, the self-inductance can be reduced which effectively enhances the lateral and longitudinal freedom of movement of the magnetic coupler. Reducing the centre distance G between the assistive coils and the main coil can increase the self-inductance linearly, but this will weaken the smoothness of the magnetic field. Analysis and Comparison The magnetic field of the receiver pad is more consistent within the controllable misalignment range, and comparing to [3], all the coils are series connected with one high frequency power source. Fig. 2 shows a comparison of the simulation results of the traditional unipolar coil, which is fully optimized using the Dagum distribution, and the proposed coil proposed in this work. These results are with the same offset condition, same receiver coil, and other external conditions. The X and Y directions are the driving and door-to-door direction respectively. The newly designed emitter coil produces a smoother coupling coefficient over a wider range. Inductive Charging Coupler Robust Design Optimization To achieve less performance variation in the face of misalignment variation caused by the vehicle driver, which is off the control in the design phase, a robust design can be introduced. The misalignment distribution is regarded as the uncertainty parameter in the robust design. The relationship between the coupler design parameter and the coupler circuit parameter is analysed through the FE simulation. The system performance parameters are derived from the circuit. The primary inverter output current, the output power and efficiency of the inductive power transfer system are combined with the distribution of the misalignment in the robust design optimization to form the robust design object. The coupler is optimized using the robust design object. Conclusion and Future work In the full paper, the impact of the additional coil on the magnetic field will be analysed extensively. A robust optimization design process based on the coupler design will be described. A prototype will verify the simulation results.

**References:**

[1] S. A. Birrell, D. Wilson, C. P. Yang, “How driver behaviour and parking alignment affects inductive charging systems for electric vehicles,” Transportation Research Part C: Emerging Technologies. [2] L. Li, Z. Wang, F. Gao, “FEA-Assisted Optimization Design of Asymmetric DD Type Structure Magnetic Coupler for Wireless Electric Vehicle Charger,” in 2020 IEEE ISIE, Delft, Netherlands. [3] S. Wang, D. G. Dorrell, Y. Guo, and M.-F. Hsieh, “Inductive Charging Coupler With Assistive Coils,” IEEE Trans. Magn., vol. 52, no. 7, pp. 1–4, 2016.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/499ca208c0ff9238ebb1b3a17d7a856c.jpg)
Fig. 1 The proposed coupler design and optimization parameters

![](https://assets.underline.io/uploads/markdown_image/1/image/136654cbfc86dce9028b2ea4b405226e.jpg)
Fig. 2. The FEA simulation result comparison of misalignment tolerance a) Traditional unipolar coil, b) Proposed unipolar coil.

 The Electric Vehicle Wireless Charging Application Oriented Coupler Robust Optimization Design With Multiple Series Unipolar Coils

I.Introduction By reducing the over-dependence on current battery technologies, wireless power transfer (WPT) provides a brand-new power-supply solution and changes the traditional style of the energy utilization for electric-driven devices [1]. Accompanied by the increasing utilization of practical application, the diverse requirements of customers and various standards of manufacturers pose challenging issues on this technique, for example, Wireless Power Consortium (WPC) regulates the operating frequency of 87-205 kHz, while AirFuel (AF) alliance holds the operating frequency of 277-357 kHz. Thus, a number of efforts have been focused on the multiple frequencies multiple pickups based WPT, which can be divided into three aspects: 1) single-inverter single-transmitter [2-4], 2) multiple-inverters single-transmitter [5], and 3) single-inverter multiple-transmitters [6]. Due to the simplicity and low cost, single-inverter single-transmitter becomes the optimal choice. However, in [2], energies are transmitted by time division method, which fails to concurrently transfer multiple frequency power, in [3], the distribution of multiple frequency power cannot be adjusted arbitrarily, and in [4], the cross-coupling effect among the pickups will significantly deteriorate the transmission performance. Accordingly, how to randomly transmit multiple frequency power simultaneously without unnecessary coupling becomes a critical technical concern. In this paper, a dual-resonating-frequency compensation topology is adopted and implemented for exciting the decoupled-double D transmitting coils. Concretely speaking, two double D coils are located orthogonally to obtain the effect of magnetically decoupled in both primary side and pickup side. Meanwhile, the proposed system can provide two randomly predefined operating frequencies and the power distribution of two different frequencies can be arbitrarily regulated based on the users’ requirement by adopting the proposed frequency overlay modulation (FOM). Moreover, owing to the nonexistent cross-coupling between decoupled-double D pickup coils and the characteristic of compact integrated, each pickup can maintain the maximum efficiency respectively. II.Methodology Fig.1(a) depicts the WPT system with a single-transmitter for two pickups, where the configuration of dual-resonating-frequency compensation topology which consists of a series-connected LC (Csc Lsl1 Lsl2) tank and a parallel-connected LC (Cpc Lpl) tank is presented. Meanwhile, the parameters design procedure needs massive calculation based on equation (1), thus this paper specifies the operating frequency of 100kHz and 300kHz and each of them satisfies WPC and AF standards, respectively. Then, a simplified lookup table design method for randomly predefined operating frequency is shown in Fig.1(b). Fig. 1(c) testify the effectiveness of the proposed compensation topology. Besides, the proposed FOM can overlap randomly dual frequencies with various magnitudes, where Fig. 1(d) elaborates the proposed FOM with the same magnitude for 100kHz and 300kHz, which can be confirmed by Fig. 1(e). As shown in Fig.1(g), both simulation and practical experiments validate that the proposed system can maintain a high transmission efficiency of over 90% for each pickup of more than 10W. From the perspective of the magnetic, since the y-axis coils and x-axis coils are located orthogonally, the magnetic fluxes are symmetrical regarding the central axes. It indicates that when the current flows in y-axis coils as shown in fig.2 (b), the amount of magnetic flux from y-axis coils that passes through the x-axis equals to that passes out of it. Consequently, the coupling between y-axis coils and x-axis coils is theoretically zero which means the y-axis coils and x-axis coils are decoupled. In this paper, the y-axis coils and x-axis coils are orthogonally compactly placed and series-connected as the transmitting coils. While y-axis coils and x-axis coils are only orthogonally compactly placed in the pickup side and are utilized to energized pickups independently. Specifically speaking, y-axis coils in the transmitting side are fully coupled with the y-axis in the pickup side, and so do x-axis coils. This mechanism can boost the coupling thus promoting the efficiency for both pickups. Fig.1(g) quantitatively analyses the efficiency under the coupling of 0.08 (traditional circular coils) and 0.12 (decoupled-double D Coils), respectively, which indicates a maximum efficiency improvement of 25.2%. III.CONCLUSION This paper proposes an artfully designed dual-resonating-frequency compensation topology with a simplified parameter design procedure. Meanwhile, the proposed FOM regulation method can arbitrarily produce the compound excitation. By adopting decoupled-double D coils, the dual-frequency WPT system holds the merit of zero cross-coupling in the pickup side, thus can promote the transmission efficiency for each pickup. Theoretical analysis, simulation, and experimental results will be given in more detail to verify the feasibility. Acknowledgment This work was supported by a grant (Project No. T23-701/20-R) from the Hong Kong Research Grants Council, Hong Kong Special Administrative Region, China.

**References:**

[1] 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, 2019. [2] Z. Zhang, H. Pang, S. H. K. Eder, and R. Kennel, “Self-balancing virtual impedance for multiple-pickup wireless power transfer,” IEEE Trans. Power Electron., vol. 36, no. 1, pp. 958-967, 2021. [3] W. Liu, K. T. Chau, C. H. T. Lee, C. Jiang, W. Han, and W. H. Lam, “Multi-frequency multi-power one-to-many wireless power transfer system,” IEEE Trans. Magn., vol. 55, no. 7, pp. 8001609: 1-9, 2019. [4] Z. Zhang, Xing. Li, H. Pang, H. Komurcugil, Z. Liang, R. Kennel, “Multiple-frequency resonating compensation for multichannel transmission of wireless power transfer,” IEEE Trans. Power Electron. doi: 10.1109/TPEL.2020.3027916. [5] F. Liu, Y. Yang, Z. Ding, X. Chen, and R. Kennel, “A multifrequency superposition methodology to achieve high efficiency and targeted power distribution for a multiload MCR WPT system,” IEEE Trans. Power Electron., vol. 33, no. 10, pp. 9005-9016, 2018. [6] C. Zhao, D. Costinett. “GaN-based dual-mode wireless power transfer using multifrequency programmed pulse width modulation,” IEEE Trans. Ind. Electron., vol. 64, no. 11, pp. 9165-9176, 2017

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7874a30861468e51bae13ac3af901dff.png)
Schematic of proposed dual-frequency WPT systems. (a) Configuration. (b) Simplified design scheme and key parameters. (c) Impedance characteristics. (d) Waveforms. (e) FFT analysis. (f)-(g)Characteristics of the transmission power and transmission efficiency.

![](https://assets.underline.io/uploads/markdown_image/1/image/0558ed582c372a01a5f6cd67e05b3733.png)
(a) Structure of decoupled double-D coils. (b) Magnetic field distributions of coils.

 Decoupled-Double D Coils Based Dual-Resonating-Frequency Compensation for Wireless Power Transfer

A CPT (contactless power transfer) device is designed in this paper. It removes the traditional contact slip-ring in the device where power transfer from stationary to rotary side is needed. The structure is designed and simulated. Compensation are added to improve the coupling coefficient between the primary and secondary sides. To improve the system power rate, high frequency power converter is utilized. At last, a prototype is built and tested. From the results, the performances of the device are well verified. I. Introduction Mechanical slip ring is widely used as a method of power transfer from a stationary component to a rotary one. However, mechanical slip ring is very easy to wear and needs frequent maintenance.[1] CPT solves this problem. System diagram of the system is shown in Fig. 1. The low frequency AC source is first rectified, and then converted by the high frequency inverter circuit. Through electromagnetic induction, voltage is induced in the secondary winding. At last, the power is transferred from the stationary to the rotary side load after rectifying. II. System Design The CPT device is like a rotating transformer in structure. The device is consisting of iron core and windings. The basic structure of the device is shown in Fig. 2(a). There is an air gap between the device primary side and secondary side. Thus, one side could rotate relatively to the other side. However, the system is operating at high frequency, producing large losses in both ferromagnetic materials and copper windings. To overcome this problem, high frequency ferrite and litz wires are utilized. Due to the fragile mechanical performances of the ferrite, pre-manufactured U-shape ferrite pieces are utilized and assembled as shown in Fig. 2(b). III. Simulations Results The device is modeled and simulated using FEM method. No-load and load condition is calculated and the system inductance is obtained. Results are shown in Table I. As the device magnetic circuit will change while rotating in this special design, the inductances of teeth-to-teeth and teeth-to-air position are compared IV. Experimental Analysis The prototype is manufactured and its electromagnetic performances is tested. The test platform is shown in Fig. 3. The voltage and current waveform under load condition are shown in Fig. 4. From the figure, the voltage and current have identical phase in both primary and secondary side. Under this condition, the load power reaches 1kW with efficiency of 92% and no obvious temperature rise is monitored. V. Conclusion This paper analyzes the contactless power transfer system applied to rotating application. The special design of the device could decrease the system loss and increase the couple between primary and secondary sides. Electromagnetic parameters of the device are simulated by FEA. It shows good consistency with the measurement results. Also, the experiments are carried out and it turns out that the power is transferred successfully with high efficiency.

**References:**

References: [1] J. Yang, Y. Zhang and D. Jiang, "A Contactless Power transfer Device Applied to the CT System," 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), Harbin, China, 2019, pp. 1-5.

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/d6a3305dbadcd8f4595e3ac21fa52482.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/792407e0b276acec96ffd79d96f2e598.jpg)

 Design, Manufacture, and Test of a Contactless Power Transfer Device for Rotating System

1 Introduction High-intensity magnetic field around the system will be generated when the wireless charging system of electric vehicles(EV) is working, which will reduce the transmission efficiency of the system and pose risks to human health[1]. Ferrite core has been widely used to shield the magnetic flux leakage on the back side of the coil and improve the magnetic coupling between the primary and the secondary sides due to its high permeability and large resistivity. However, this shielding method is not very effective in shielding the magnetic field in the non-working area on the side of the system. As a supplement to the passive shielding method, the main idea of the active shielding method is to use the reverse magnetic field generated by the shielding coil to cancel the magnetic field leakage in the target area. The reactive shielding method based on resonance of a passive compensation loop has been proven to be an effective method to offset the magnetic leakage in the target area, but adjustment of the shielding circuit impedance is complicated[2]. The shielding coil with independent power supply can be controlled to produced a magnetic field that is completely opposite to the incident magnetic field, but it inevitably reduces the overall transmission efficiency of the system[3]. A good solution is to make active shielding coil be in series with the branch where the energy transfer coil is located[4]. It should be noted that the active shielding coil may be coupled with the main magnetic linkage. Under this condition, the equivalent magnetic coupling between the primary and the secondary sides becomes smaller, which will reduce the output power of the system. In this paper, a dual-loop active shielding coil directly connected in series with the primary side is designed to reduce the reverse magnetic coupling between the primary and the secondary sides and the magnetic flux leakage around the wireless charging system of EV. The parameters of the shielding coil are determined by multi-objective optimization. Finally, a prototype with an input power of 1.2kW is built. The proposed active shielding coil has superior performance in system transmission efficiency and shielding effect on the target surface comparing to conductor shielding. 2 Active Shielding Coil Design Circuit theory is adopted to model the wireless power transmission system with double LCC compensation topology as shown in Fig. 1, where L1 and L2 are self-inductances, L3 is the self-inductance of shielding coil. To prevent load power from being affected by the shielding coil, what we need to do is to minimize the mutual inductance M23 between the active shielding coil and the secondary side. The proposed dual-loop active shielding coil shown in Fig. 2 is only arranged on the primary side, since the steel plate of the car chassis has a good shielding effect on the magnetic field around the secondary side. The inner diameters of the inner loop coil is set to a fixed value of 50cm, and the target surface is set at a distance of 55cm from the center of the coil. The number of turns and outer diameter of the shielding coil are optimized through ANSYS simulation. The outer diameter of the shielding coil is optimized in the range of 29cm to 44cm with a step length of 3cm. In addition, the number of turns of the inner loop and outer loop is optimized in the range of 1 to 3 and 1 to 4, respectively. The optimization targets are the mutual inductance between the active shielding coil and the secondary side, the maximum magnetic flux density on the target surface, and the length of the active shielding coil. To solve the multi-objective optimization problem, the constraints are set as follows: M23≤0.5μH B&lt;27μT L≤13m To further determine the optimal solution, an evaluation function F(d) is constructed and defined as the normalized objective function f i multiplied by their respective weight coefficients ωi as follows: F(d)=Σωi|f i-f i* |/(fset-f i*) (i=1,2,3) where f i* is the ideal value with a value of 0, and fset is the constraint value of the objective function.The solution with the smallest evaluation function value is adopted for subsequent simulation and experimental verification. The magnetic field distribution on the target surface is compared in three condition through ANSYS simulation: no shielding, with aluminum shielding and active shielding. When the active shielding is applied, the maximum magnetic flux density of the target surface is reduced to 16.2uT comparing to the case of 33.05uT when only the ferrite core is applied. However, the maximum magnetic flux density is 20.01uT in the case of aluminum shielding. The proposed active shielding design is verified by a prototype with an output power of 1.2kW. To investigate the effect of shielding methods on transmission efficiency, the input voltage needs to be adjusted to keep the system input power constant. The results of the experiment will be presented in the final paper. 3 Conclusion This paper introduced a dual-loop active shielding coil connected in series with the primary side to reduce the magnetic leakage around the system. An evaluation function has been proposed to optimize the number of turns and outer diameter of the shielding coil. The proposed shielding method obtains a superior shielding effect on the target surface than conductor shielding, and has less passive impact on the transmission efficiency of the system.

**References:**

[1] S. Park, IEEE Transactions on Magnetics., vol. 54, p.1-8 (2018). [2] H. Moon, S. Kim and H. H. Par, IEEE Transactions on Magnetics., vol. 51, p.1-4 (2015). [3] T. Campi, S. Cruciani and F. Maradei, IEEE Transactions on Electromagnetic Compatibility., vol. 62, p.1398-1405 (2020). [4] S. Y. Choi, B. W. Gu and S. W. Lee, IEEE Transactions on Power Electronics., vol. 29, p.5770-5783 (2014).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ba4c9472340bfaa611896a8f76f1e87a.jpg)
Figure. 1: Equivalent circuit of the system with active shielding coil

![](https://assets.underline.io/uploads/markdown_image/1/image/d4a13eecc734961c4e8612dfaa91b4a3.jpg)
Figure. 2: Design of dual-loop active shielding coil

 Active Shielding Coil Design for Wireless Charging System of Electric Vehicle

Microrobots have been studied for medical applications, allowing surgical operations with minimal invasion to the human body [1, 2]. Due to the small size of the microrobot, it has the advantage of being able to move freely within the vessel and perform various missions. For this reason, a lot of research groups have worked on the propulsion of microrobot. Most prevalent microrobot propulsion method is external magnetic field based microrobot propulsion [2-4]. However, due to the lack of electric power source, these kinds of microrobots are able to perform only limited missions. To expand their utilization, wireless power transfer system applied microrobot have been proposed. One of them, microrobots that can simultaneously receive electrical energy and generate propulsion force have been introduced [5-8]. They verified the propulsion of microrobot through the water surface movement experiments. However, since the microrobot supposed to be located inside of blood vessel, moving motion of microrobot should be consider their environment as inside of a tube. In this paper, a mm-sized magnetic material embedded microrobot, located in the tube is analyzed. Depending on their dimensional differences the environment of microrobot can be regarded as free-stream or non-free stream conditions. Fig. 1 (a) and (b) represents the velocity profile of internal flow condition and external flow condition. In case of external flow condition, the diameter of the tube is large enough, so the effect of fluid bypassing the object does not change the entire flow of the fluid. On the other hands, if the size of an object is comparable to its internal diameter, the flow of fluid that bypasses the object has a significant impact on the velocity profile and therefore, the fluid velocity profile of the internal flow condition is more influenced by duct as illustrated in Fig. 1(b). If we assume that the diameter of vein is 5 mm and the microrobot designed in this research has the 3.5 mm diameter with 10 mm length, interpreting the microrobot inserted in tube as internal flow condition is reasonable. Fig. 2 illustrates the propulsion force that required to achieve certain velocity of microrobots depending on their various structure shape. As illustrated, under the condition of that the surface diameter which is face to the stream is identical, the sphere and air foil structure have much more efficient for the propulsion. However, in this research, a bar-type magnetic material is applied, a capsule shaped structure is applied for enclose the microrobot. In this case, for example, if the microrobot tried to reach the speed of 3 mm/s, it requires 7 μN propulsion force. The magnetic force when the incident time-varying magnetic field applied to the magnetic material, can be derived as follows; F(t) = 2πμmr3×((μp-μm)/(μp+2μm))▽H(sin(ωt))2, where, μm,μp, r, ▽H, and ω are represents permeability of magnetic material, permeability of media, radius of magnetic material, gradient incident magnetic field and angular frequency of incident magnetic field, respectively [9]. When we considered that the size of transmitting coil is 170 mm x 170 mm and the distance between transmitting coil and microrobot is 50 mm away, the required current to achieve 7 uN is determined as 200 Ampere-turn. To verify theoretically obtained value, simulation with 3D FEM simulator, Ansys Electronics Maxwell, is conducted. As expected, by exciting 200 Ampere-turn in the transmitting coil, it is able to generate 7 uN magnetic force which is enough to move the velocity of 3 mm/s in the tube whose diameter is 5 mm.

**References:**

[1] J. Li, et al., “Micro / nanorobots for biomedicine : Delivery , surgery , sensing , and detoxification,” Sicnec Robotics, vol. 2, pp. 1–10, 2017. [2] B. J. Nelson, et al., “Microrobots for Minimally Invasive Medicine,” Annu. Rev. Biomed. Eng., vol. 12, pp. 55–85, 2010. [3] A. M. Maier, et al., “Magnetic Propulsion of Microswimmers with DNA-Based Flagellar Bundles,” Nano Lett., vol. 16, pp. 906–910, 2016. [4] G. Bin Jang, et al., “A Spiral Microrobot Performing Navigating Linear and Drilling Motions by Magnetic Gradient and Rotating Uniform Magnetic Field for Applications in Unclogging Blocked Human Blood Vessels,” IEEE Trans. Magn., vol. 51, p. 9100404, 2015. [5] D. Kim, et al., “Magnetic resonant wireless power transfer for propulsion of implantable micro-robot,” J. Appl. Phys., vol. 117, p. 17E712, 2015 [6] R. Narayanamoorthi, et al., “Frequency splitting-based wireless power transfer and simultaneous propulsion generation to multiple micro-robots,” IEEE Sens. J., vol. 18, pp. 5566–5575, 2018. [7] A. Hajiaghajani, et al., “Patterned Magnetic Fields for Remote Steering and Wireless Powering to a Swimming Microrobot,” IEEE/ASME Trans. Mechatronics, vol. 25, pp. 207–216, 2020. [8] D. Kim, et al., “Propulsion and Rotation of Microrobot Based on a Force on a Magnetic Material in a Time-Varying Magnetic Field Using a Wireless Power Transfer System,” IEEE Trans. Magn., vol. 56, pp. 1–5, 2020. [9] D. Kim, et al., “Instantaneous Magnetic Force Evaluation on a Magnetic Material for Wireless Power Transfer Based Microrobot Propulsion,” 2020 IEEE Wireless Power Transfer Conference (WPTC 2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/41dc04e7ae1fb429f1629f85b69ba695.jpg)
Velocity profile depending on the flow types. Simulation results of external flow (a) and internal flow (b).

![](https://assets.underline.io/uploads/markdown_image/1/image/5fc9e32b09cf7ecc739f4c81bdcb0f5b.jpg)
Required propulsion force depending on the velocity of microrobot in tube.

 Propulsion of magnetic material embedded microrobot in tubes based on wireless power transfer system

I.Introduction By means of the high power density, the low cost as well as the compact design, the wireless power transfer (WPT) with one single transmitter for multiple pickups (STMP) has obtained increasing attentions for both academic researchers and the industrial engineers in recent years. In order to simplify the circuit modeling, the cross-coupling effect among pickup coils is normally ignored in the theoretical analysis. In practical applications, however, the cross-coupling effect cannot be taken as zero since multiple pickup coils locate within a limited and narrow area. As a result, the corresponding coupling effect between the transmitting coil and each pickup coil is inevitably affected by the cross-coupling effect. In addition, the variation of relative position between the transmitter and the pickup also results in the fluctuation of the mutual inductance. The resulted non-constant coupling effect cannot be measured directly and accurately, which means that STMP-WPT faces with more challenged by comparing with 1-to-1 transmission. This paper proposes a modeless prediction scheme by using the neural network (NN) to predict variable mutual inductance between the transmitting and the pickup coils for STMP-WPT systems. In traditional model-based predictive control, the accuracy significantly depends on parameters of the system model. However, the parameters such as the inductance and the capacitance inevitably deviate from the normal value due to the variable working temperature and the operating frequency. Accordingly, the proposed modeless prediction scheme can realize the prediction of the mutual inductance by using the offline-trained NN instead of the system model, which cannot only avoid the impact of the parameter disturbance on the prediction accuracy but also enhance the dynamic response performance by means of the parallelism of data processing and the generalization ability of NN. II.Proposed Modeless Prediction In this paper, a WPT system with one single transmitter for three pickups is adopted as an exemplification. Fig. 1(a) shows the circuit diagram, where the primary current (ip) and the secondary currents (is1, is2, and is3) can be measured by using the current sensor and then taken as inputs of NN-based controller. By adopting the offline training, the NN-based controller generates the coupling coefficients between the transmitting coil and each pickup coil, such as Kps1, Kps2, and Kps3. The corresponding mutual inductance can be obtained, accordingly. Additionally, the experimental prototype is set up as shown in Fig. 1(b), which consists of a H-bridge inverter (MOSFET C3M0065090D) to produce the 100-kHz AC exciting power, a DSP28335 microcontroller to implement the proposed NN-based prediction and generate the PWM for the inverter, a current sensor (LA25-NP/AD637) to measure primary and secondary currents, a DC power supply (ITECH IT6722A), a transmitting coil, and three pickup coils. In order to verify the feasibility of the proposed modeless prediction scheme, simulation and experimental verifications are both carried out by adjusting the relative positions between the transmitting coil and each pickup coil to vary the coupling effect. By using JMAG for the magnetic field analysis and the MATLAB/SIMULINK for the circuit analysis, Fig. 2(a)-(c) shows primary and secondary currents as well as the corresponding mutual inductance, namely 8.97μH, 5.29μH, and 7.67μH. Meanwhile, the experiment is also carried out by taking into account the variation of the coupling effect caused by the transmission distance as shown in Fig. 2(d)-(f) and the load as shown in Fig. 2(g)-(i). Accordingly, the simulated results well agree with the experimentally measured results, which illustrates the feasibility of the proposed modeless prediction scheme for the coupling effect between the transmitting and multiple pickup coils. Besides, the detailed parameters, comparison with traditional method, theoretical analysis, simulated results, and experimental waveforms will be presented in the full manuscript. III.Conclusion This paper proposes a modeless prediction scheme to predict variable coupling effect between the transmitting and the pickup coils for STMP-WPT systems. The proposed data-driven prediction scheme only requires the value of currents rather than the detailed parameters of the equivalent mutual inductance model, thus effectively enhancing the accuracy of the coupling effect prediction under parameter disturbances. By using the offline trained NN, the primary and secondary currents can be fitted to the mutual inductance. Accordingly, it can effectively predict the non-constant coupling effect caused by the variation of relative position between the transmitting coil and each pickup coil as well as the load. ACKNOWLEDGEMENT This work was supported in part by the National Natural Science Foundation of China (Project No. 51977138), and in part by the Humboldt Research Fellowship (Ref 3.5-CHN-1201512-HFST-P) and in part by Carl Friedrich von Siemens Research Fellowship (Ref 1201512).

**References:**

[1] Z. Zhang, H. Pang, and A. Georgiadis, IEEE Trans. Ind. Electron., vol. 66, no. 2, pp. 1044-1058, 2019. [2] Z. Zhang, X. Li and R. Kennel, IEEE Trans. Power Electron., DOI: 10.1109/TPEL.2020.3027916. [3] X. Li, Z. Zhang, and Z. Liang, IEEE Trans. Magn., DOI: 10.1109/TMAG.2020.3017804.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/827470686ebb90af4b5f1e9848ff5170.jpg)
Fig. 1. STMP-WPT with modeless prediction scheme: (a) Circuit; (b) Prototype.

![](https://assets.underline.io/uploads/markdown_image/1/image/7510c4660e5e2e1d4bdc437c17a6c346.jpg)
Fig. 2. Results: (a) Simulated currents at Position 1; (b) Simulated currents at Position 2; (c) Simulated currents at Position 3; (d) Measured primary current at Position 1; (e) Measured primary current at Position 2; (f) Measured primary current at Position 3; (g) Measured secondary current (load=1Ω); (h) Measured secondary current (load=5Ω); (i) Measured secondary current (load=10Ω).

 Modeless Prediction of Variable Coupling Effect for Multiple-Pickup Wireless Power Transfer

I. Introduction Currently, the wireless power transfer (WPT) system is mainly used to wirelessly supply power to resistive loads [1]. In industrial application scenarios, the loads are mostly motors, which brings challenges to the wide application of WPT technology [2]. This paper proposes to apply simultaneous wireless information and power transfer (SWIPT) technology to drive permanent magnet brushless DC (BLDC) motors. The power transmission part is used to provide power to the motor, and the information transmission part is used to control the motor. This paper studies the equivalent impedance characteristics of the motor port in the SWIPT-BLDC system, establishes a mathematical model including the SWIPT system and the BLDC system, provides the conditions for the stable operation of the system, and builds an experimental platform to verify the scheme. II. Theoretical Analysis The SWIPT-BLDC system consists of a SWIPT system modulated by MFPWM [3], a motor controller and a BLDC motor. The SWIPT system uses MFPWM modulation to transmit two frequencies at the same time, which are used to drive the BLDC motor and control the motor speed. In order to reduce the volume of the coil and improve the transmission performance, a coil with a tap is designed in this paper to simultaneously transmit power and information. 2.1 System Structure and Control Method As shown in Fig. 1(a), the SWIPT module and the BLDC module form the SWIPT-BLDC motor system. On the primary side, the MFPWM inverter generates a dual-frequency signal. The capacitor and the tapped coil form a magnetic coupling resonance tank. On the secondary side of the system, two rectifiers respectively convert AC signals of different frequencies into DC. The BLDC driver contains a three-phase inverter. The rectified low frequency signal is input to the BLDC controller to drive the motor. The rectified high frequency signal is input to the BLDC controller as the given speed of the motor. The motor speed is proportional to the voltage of the given speed signal. 2.2 Magnetic Field Analysis of Coupled Coils The tapped coil reduces the system volume. As shown in Fig. 2(b), a finite element simulation model of the tapped coil is established. The magnetic fields of the two frequencies have overlapping regions. The simulation results show that the mutual inductance of the inner and outer coils is very small, and the tapped coil does not affect the signal transmission efficiency. 2.3 Analysis of Loading BLDC motor load is different from resistive load. The equivalent impedance of the motor load includes inductance and back electromotive force (EMF). The back-EMF of the motor load is related to the phase angle, torque and magnetic flux of the motor. During the motor operation, the back-EMF is constantly changing. This paper analyzes the voltage when the motor is loaded, and establishes the transfer relationship from the SWIPT system to the motor load. The deduction process and results will be presented in the full manuscript. III. Results and Discussion The simulation result of SWIPT-BLDC motor system is shown in Fig. 2. The blue line is the voltage to drive BLDC motor on the secondary side, the yellow line is the DC voltage of desired speed, the green line is the motor drive current in one phase, and the red line is motor speed. As shown in Fig. 2, giving the speed signal and the primary DC voltage, the induced voltage on the secondary side can drive the motor. The motor starts smoothly and the speed is stable. With the speed setting signal switching at 5s and 10s, the motor speed changes. The simulation results show that the structure proposed in this paper realizes motor driving and speed control. The actual measured results will be shown in the full manuscript. The research has also been experimentally verified. Due to the space limitation, the specific theoretical analysis and experimental results will be presented in the full manuscript.

**References:**

[1] X. Li, Z. Zhang, W. Si, R. Wang and Z. Liang, IEEE Trans. on Magnetics., doi: 10.1109/TMAG.2020.3017804. [2] L. Yang, Z. Q. Zhu, H. Bin, Z. Zhang and L. Gong, IEEE Trans. on Industry Applications., vol. 57, p.306-315 (2021) [3] J. Wu, H. Zhang, P. Gao, Z. Dou, N. Jin and V. Snášel, Sustainability., vol. 12(10), p.4189 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/003416396f8af2375173b5d790182094.jpg)
Fig. 1 (a) Circuit diagram of BLDC motor system based on SWIPT. (b) Finite element simulation model of tapped coil. The blue streamline represents the magnetic flux density. The colored section represents the magnetic flux density magnitude (T).

![](https://assets.underline.io/uploads/markdown_image/1/image/e33779fb51d049cb4c38ee2880d1423e.jpg)
Fig. 2 Circuit Simulation Waveform of BLDC Motor System based on SWIPT.

 Brushless DC Motor Driver and Control System based on Simultaneous Wireless Information and Power Transfer

— Recently, omnidirectional wireless power transfer(WPT) systems with high flexibility compared to single-directional wireless power transmission systems have been actively studied. In this paper, we compare a system with a WPT structure in one direction and with a multi-axis transmitting coil(Tx) structure. The location of the receiver and the degree of flexibility and efficiency of the angle were compared in many cases, depending on the angle from the center axis of the Tx and the distance from the virtual sphere center, which is mainly influenced by the magnetic field induced from the Tx. In both cases, the input frequency was set to 60kHz under the same magnetomotive force and constructed a structure that considered the actual type. We construct a circuit in which magnetic fields occur in the direction of the Z and X axis in the Tx. The experiment allowed us to analyze the changes in electromotive force according to the distance and the angle tilted from the center axis when the Tx was composed of multiple axis. Keywords— WPT, Inductively Coupled Power Transfer (ICPT), multi-axis, spherical structure, induced electromotive force I. Introduction Wireless power transfer(WPT) technology is rapidly gaining traction and is used in a variety of applications, starting with Tesla coil and charging electric cars, cell phones and hearing aids [1]-[2]. WPT technology has been studied divided into magnetic resonance and magnetic induction methods [3]-[4]. Magnetic inductive methods have the disadvantage of reducing transmission distances, but have been used in various fields as they enable the coil to be compact. It is researched to increase the efficiency of transfer to loads in a magnetic inductive method [5]. In various fields, WPT is becoming more important, and as devices are compacted, it becomes more difficult to match the receiver of the device to the axis of the transmitter. For example, medical devices are developing due to the aging and diseases, and wirelessly charged hearing aids often require to be placed in the correct position and direction, even though they are wirelessly charged. Therefore, in this paper, we have adopted a charging method as long as it is located within the case, regardless of position and angle, to make it easier for the elderly to use, and we analyze its tendency. In Bowl-Shape hearing aids, the analysis of the distance-dependent magnetic field was conducted [2]. Bowl-Shape’s hearing aids have only Z-axis directions of magnetic fields induced by the Tx and adjust the diameter of the coil inducing the magnetic field of the Z-axis to make the radial-directional magnetic field perpendicular to the Z-axis. In contrast, in this paper, we set the Tx to multi-axis to control the direction of the induced magnetic field and compare it to a single-axis system. II.SIMULATION AND EXPERIMENT Figure1(a) sets the structure with the change in angle and (b) sets the structure with the change in position as FEM (Finite Element Method) and predicts the results. At this time, the magnetomotive force was 6.66 [At] for both the single and the multi-axis under the same conditions. In the experiments, the input frequency was set to 60 kHz, taking into account the range that does not interfere with the trunked radio system in the multi-axis experiment. In the case of Tx, a 1.8mm litz wire was wound around 9 turns, and the inner diameter of the coil forming the magnetic field in the z-axis was set to 75mm and the inner diameter of the coil forming the x-axis was set to 85mm. In the case of Receiving coil(Rx), a 0.3mm copper wire was used to wind 40 turns, and the inner diameter was set to 20mm. III.ANALYSIS Experiments were conducted with the same conditions as FEM. From the center of the Tx, the distance was increased by 2mm from 0mm to 20mm, moving in the z axis and measuring the electromotive force at the Rx. The Tx voltage was the same at 6V and 60kHz, and the electromotive force measured at the receiver tends to decrease as the distance increases to 3.36V when the distance is 0mm and 1.84V when the distance is 20mm. Measurements of electromotive force, moving in the X-axis direction, from 0mm to 20mm, and increased the size of electromotive force at the receiver as it moved from the center of the coil to the edge. In addition, electromotive force at the receptor decreased from 0 to 70 deg and increased from 70 to 90 deg as the angle increased by 10deg relative to 0deg in the same direction as the x-axis Tx. IV.CONCLUSION A single axis has high efficiency but low flexibility for location, while a multi-axis has low efficiency but high flexibility. This trade-off needs to be studied in depth and will be dealt with in full-paper.

**References:**

[1] C. C. Mi, G. Buja, S. Y. Choi and C. T. Rim, "Modern Advances in Wireless Power Transfer Systems for Roadway Powered Electric Vehicles," in IEEE Transactions on Industrial Electronics, vol. 63, no. 10, pp. 6533-6545, Oct. 2016 [2] J. Kim, D. Kim, K. Kim and Y. Park, "Free-positioning wireless charging system for hearing aids using a bowl-shaped transmitting coil," 2014 IEEE Wireless Power Transfer Conference, Jeju, 2014, pp. 60-63 [3] H. Hu and S. V. Georgakopoulos, "Wireless power transfer in human tissue via Conformal Strongly Coupled Magnetic Resonance," 2015 IEEE Wireless Power Transfer Conference (WPTC), Boulder, CO, 2015, pp. 1-4 [4] H. Nong and J. Lin, "Design of loosely coupled inductive power transfer systems for instrumented wheelset," 2009 9th International Conference on Electronic Measurement & Instruments, Beijing, 2009, pp. 1-670-1-674 M. Pinuela, D. C. Yates, S. Lucyszyn and P. D. Mitcheson, "Maximizing DC-to-Load Efficiency for Inductive Power Transfer," in IEEE Transactions on Power Electronics, vol. 28, no. 5, pp. 2437-2447, May 2013

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e9500297a62900fe22d9a79b082b42cf.jpg)
Fig. 1.(a) Structure according to angular changes, (b) position changes

![](https://assets.underline.io/uploads/markdown_image/1/image/776f54418c903d9f675a5ea2ccf76bab.jpg)
Fig. 2.(a) Experiment of position changes, (b) angular changes, (c) Data of experiments on angles

 Analysis and Comparison of Variable Positioning Wireless Power Transfer using Multi-Axis Coil

The research for the temperature distribution of the transformer is significant for design [1]. Methods applied pervasively in academic field are thermal-network method [2], finite element method [3] and Computational Fluid Dynamics (CFD) [4]. Although CFD method can improve the accuracy of the transformer temperature field calculation, it is time-consuming and difficult to mesh finely for some sophisticated structures such as the insulating paper between foil windings. In this paper, an equivalent thermal-network model for a SCB2500kVA dry-type transformer with foil winding as low-voltage (LV winding) and subsection and layer winding as high-voltage (HV winding) is established under natural convection. Considering the nonuniformity of the power loss density in LV winding [5], the heat sources at different positions need to be corrected by using correction factor. The cooling conditions are different with the varying locations in transformer such as the airways with asymmetric one-adiabatic-side heat flux density between HV winding and insulating barrier and the groove surrounded by LV coils with approximately symmetrical heat flux density [6]. To settle this, corresponding experimental formulas are applied to solve the convective heat dissipation coefficients and the thermal parameters like thermal resistances, heat capacities and heat sources of each part [7]. After all of this, temperature rise curves are obtained. Simulation by computational fluid dynamics (CFD) is conducted to verify the validity of thermal network model. The results are consistent with the data from analytical method and experiments. Ι. The Establishment of Thermal Network Model Separated by DMD insulation prepreg papers, each layer of LV winding is one turn. Consisted of enameled rectangular copper wires, the HV segmented layers windings are divided into four sections, which are insulated by glass fiber mesh cloth. Upon core part, 9 nodes are selected as shown in Fig1(a), among which 5 points are from the core limb, 2 from half of core yokes and 2 from the lapping joints of core limb and yoke. The LV winding is divided into 6 sections along the axial direction as shown in Fig1(b), so 6 nodes are achieved. The HV winding is segmented into 9 sections as shown in Fig1(c) according to the location of the heat source distribution. The single-phase thermal network model of the transformer is set up. ΙΙ. Calculation of Thermal Parameters Thermal parameters in the thermal network model are heat source, heat resistance and heat capacity. The heat sources mainly come from core loss and winding loss. Due to the existence of the transverse leakage magnetic field, eddy currents are induced in the ends of foil coils, which lead to inhomogeneous distributions of currents and power losses among the LV winding. The current density can surge up to be 3 times at the ends than in the middle. Based on electromagnetic FEM computing software, parameter Ce is introduced to characterize this effect and correct the input power loss at end. The thermal resistances contain the conduction thermal resistance, the convection heat resistance and the radiant thermal resistance, which happen to be the three heat transfer pathways. The equivalent thermal conductivity can be obtained by Fourier's law. According to the diverse thicknesses, spatial directions, heat transfer areas and material compositions in different positions, thermal resistances between nodes can be calculated respectively. The radiant thermal resistance is related to the surface temperature and emissivity, which can be calculated by the Stephen Boltzmann equation. In view of the fact that when the dry-type transformer reaches heat dissipation equilibrium, the temperature in most areas can up to more than 100 degrees, the heat emitted to the environment by radiation is too considerable to neglect. Since the convective heat transfer coefficients are affected by the internal structural complexity of the transformer, the asymmetry heat sources and the buoyancy lift of natural convection, it is obviously inaccurate to apply an average value for the whole plane. By analyzing the heat dissipation conditions at different planes as shown in Fig1(d), the Nusselt number of vertical surface and horizontal are calculated. ΙΙΙ. Numerical Simulation The methods for solving convective heat dissipation coefficient include analytical method, experimental method and numerical analysis method. The numerical analysis is a wide used method for solving the problems of various shapes and boundary conditions at present. By finite volume method, the results of temperature rise and velocity distribution can be obtained not only, but also the convective heat dissipation coefficient on different surfaces. ΙV. Experiment In order to verify the validity of the model, the temperature rise experiment of load is carried out. The experimental results show that the hottest spot is located in the highest disc of outer HV winding with the temperature of 425.15K, which is in good agreement with the results of thermal network model and CFD simulation. V. Conclusion: According to the thermoelectric analogy effect, the thermal network method simulates the temperature field through the method of circuit. By considering the heat source, thermal resistance and heat capacity of different structures respectively, the average temperature rise curve of every node is obtained. The precision of the hottest spot by thermal network method is reliable.

**References:**

[1] M. Xiao and B. X. Du, IEEE Transactions on Dielectrics and Electrical Insulation., Vol. 23, p.2413–2420 (2016) [2] Cremasco, Andrea, and Wei, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering., Vol. 37, p.1039-1053 (2018) [3] Ahn. H. M, Oh. Y. H, and Kim J K, IEEE Transactions on Magnetics., Vol.48, p.819-822 (2012) [4] L. Caibo, IEEE Transactions on Magnetics., Vol.50, p.1-4 (2014) [5] L. Yongjian, IEEE Transactions on Magnetics., Vol.55, p.1-5 (2019) [6] L. moonhee, Electric Power Systems Research., Vol.80, p.121-129 (2010) [7] F. P. Incropera, D. P. Dewitt, and T. L. Bergman, Chemical Industry Press (2007)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7c40975f0961189391165df42ab36eb2.png)
Fig.1 The establishment of thermal network model

![](https://assets.underline.io/uploads/markdown_image/1/image/67d030081f6b28940cccc9706807bf09.png)
Fig.2 Results of simulation and experiment

 Thermal Network Model of A SCB2500kVA Dry-type Transformer Coupled with Electromagnetic Loss

Introduction Foil-wound transformers exhibit higher heat dissipation as well as high utilization of window area in SSTs, compared with Litz-wound ones. However, the frequency related winding loss becomes a dominating component in analyzing the general system operation performance in foil conductors. The predictions of the current distribution and the AC losses due to skin and proximity effects have been addressed in several studies. The most preferred method is a ‘’ready-to-use’’ Dowell’s 1D expression for AC resistance of transformer windings [1]. This method assumes the length of the windings equal to the length of the winding window, which enables the one-directional magnetic field and current density distribution along the foil height. Nevertheless, due to the electric field insulation requirements in higher voltage applications, the height of the winding is limited within the window area of the transformer. This constraint introduces some deviations from Dowell’s method. The magnetic field gets a second-dimensional component causing high current density concentrations in the foil corners, called the edge effect. Accurate estimation of the 2D current distribution in high-frequency applications is mostly done using FEM analysis, showing a good level of accuracy. However, FEMs require extra fine mesh implying high computational cost/time, making it a less-preferable choice for daily use by design engineers. Fig. 1 shows the deviation of Dowell’s method in calculating the AC resistance factor compared with FEM. It can be concluded from Fig. 1 that the accuracy of 1D Dowell’s approach reduces as the operating frequency increases. While the operating frequency is aimed to be increased for novel designs to utilize the high-frequency related advantages of MFTs, the deviation becomes dominant. Several researches contributed to 2D eddy loss calculations by either introducing geometry-based correction coefficients [2] and [3] or using empirical approaches [4]. However, these methods are mainly valid for specific geometries and not flexible for a wide range of designs. This study aims to develop a mesh-free, frequency-independent, accurate Fourier-based method to calculate the magnetic field distribution in the window area of foil-wound SSTs. Fourier-based magnetic field analysis is a well-known semi-analytical method to solve the differential form of Maxwell equations in Electromagnetic devices[5]. The proposed method is implemented on a foil-wound SST to find a 2D expression for magnetic vector potential inside the window area of the SST. Methodology The geometric assumptions and the implemented boundary conditions are shown in Fig. 2. This method utilizes harmonic decomposition of position-dependent current excitation and conductivity. In this method, the core is assumed as infinite permeable material due to the high relative permeability of core materials compared with the insulation, air, and conduction material. The window area has been divided into multiple conducting and non-conducting regions. To model the imposed and induced currents in the conducting regions, the segmentation approach introduced in [6] is used. For this purpose, the imposed current density and the conductivity of the foils is imaged with a periodicity in the x-axis using the complex form of the Fourier series. The magnetic field distribution is calculated based on the solution of the Laplace (1) and Poisson (2) equations for non-conducting and conducting regions, respectively. In (2) the current density is composed of two terms: the imposed current and the induced eddy current. Consequently: ▽2Az(x,y) = 0 (1) ▽2Az(x,y) = -μ [ Jimp(x) + σ(x) . ∂Az(x,y) / ∂t ] (2) To solve the equations (1-2), a set of boundary conditions is used: 1-the continuity of the tangential component of flux density; 2-the continuity of normal component of magnetic field intensity; 3-zero tangential component for the flux density on the upper and lower boundaries of the window area. The developed linear equations are solved for the established boundary conditions. To overcome the numerical errors coming from the geometric characteristics of the model the scaling method is used as explained in [5].

**References:**

[1] P. L. Dowell, Proc. Inst. Electr. Eng., vol. 113, p. 1387, 1966. [2] F. Robert, P. Mathys, J. P. Schauwers, IEEE Trans. Power Electron., vol. 16, p. 437–444, 2001. [3] D. Whitman, M. K. Kazimierczuk, IEEE Trans. Power Electron., vol. 34, p. 10425–10432, 2019. [4] F. Robert, P. Mathys, IEEE Trans. Magn., vol. 34, p. 1255–1257, 1998. [5] B. L. J. Gysen, K. J. Meessen, J. J. H. Paulides, and E. A. Lomonova, IEEE Trans. Magn., vol. 46, p. 39–52, 2010. [6] C. H. H. M. Custers, E. A. Lomonova, IEEE Trans. Magn., vol. 53, p. 1–6, 2017.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/641655dbdf228c6eb283d8c5c21af4c5.jpg)
Figure 1 The Comparison of Resistance Factor for 1D Dowell's Method and 2D FE Method

![](https://assets.underline.io/uploads/markdown_image/1/image/84fc25588a8b32147a765deea7d83a13.jpg)
Figure 2 The Geometric Model of the Window Area of a MFT and the Boundaries of the Implemented Method

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