France



 In order to study the electromagnetic and vibration performance of transformer under different tensile and compressive stresses.This paper firstly studies the magnetic properties of core silicon steel sheets for transformers under different tensile and compressive stresses,the B-H curves, B-P curves, and permeability curves of silicon steel sheets under different tensile and compressive stresses are given.Secondly, based on the test results of magnetic characteristics of the silicon steel sheet, the electromagnetic performance and vibration of a 3kVA transformer are simulated and analyzed. In the simulation process, the influence of different tensile and compressive stresses on the performance of the silicon steel sheet core of the transformer is considered. It provides a new idea for the electromagnetic-vibration analysis of transformers.&lt;br/&gt;1 Introduction&lt;br/&gt;The magnetostrictive property of silicon steel sheet is the main reason for the vibration and noise of electrical equipment such as transformers and reactors, and its characteristics are particularly sensitive to the mechanical stress[1].Based on the analysis of the mechanism of core vibration noise and experimental verification, the influence of magnetic properties and magnetostrictive effect of electrical steel sheet on the performance of power transformer under different stress is studied.&lt;br/&gt;This paper, by using a magnetostriction stress effect of the magnetic properties of measuring equipment and measuring instrument system, on oriented silicon steel (brand: 27 sqgd090) along the rolling direction under different tension and compression stress and magnetic properties of magnetostrictive properties were tested and the research of silicon steel sheet under different tension and compression stress are given B-H curve, B-P curve and permeability curve and curve of single value, as shown in figure 1 flow chart of research.Secondly, based on the above-mentioned measurement results, the model material library was established. Based on the finite element analysis software COMSOL, the finite element analysis was carried out on a 3KVA transformer under different tensile and compression stress conditions.Finally, an experimental study is carried out to verify the correctness of the proposed scheme, which provides a reference for the study of power transformer vibration noise under different tension and compression stresses.&lt;br/&gt;2 Simulation study of power transformer under different stresses&lt;br/&gt;The results obtained by substituting the magnetic characteristic curves in Fig. 1 into the transformer FEM model considering the boundary conditions are shown in Fig. 2. The compressive stress increases the magnetostriction, while the tensile stress reduces the magnetostriction, magnetostriction is particularly sensitive to the compressive stress. The stress reduces the magnetic conductivity of electrical steel sheet.When there is no external force,the maximum magnetic density reaches 1.7T.&lt;br/&gt;3 conclusion&lt;br/&gt;In this paper, the magnetic characteristics and magnetostrictive characteristics of silicon steel sheet are measured firstly, and then the electromagnetic and vibration characteristics of power transformer under different stresses are studied by using finite element analysis software.The results show that the compressive stress increases the magnetostriction, and the tensile stress decreases the magnetostriction, and the compressive stress is especially obvious.Detailed test results and simulation analysis will be shown in the full text.

**References:**

Anderson P I, Moses A J, Stanbury H J. An automated system for the measurement of magnetostriction in electrical steel sheet under applied stress [J]. Journal of Magnetism and Magnetic Materials, 2000, 215: 714-716.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8573aa5ce5a099e60e45effcfc62de79.jpg)
Fig.1 Reserch process flowchart

![](https://assets.underline.io/uploads/markdown_image/1/image/eda33ec72433e01bb513537c5910d8c6.jpg)
Fig.2 Simulation result

INTERMAG 2021

 Study of Electromagnetic Characteristics of Silicon Steel Sheet and Transformer Vibration Under Different Tension/Compression Stress

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In order to study the electromagnetic and vibration performance of transformer under different tensile and compressive stresses.This paper firstly studies the magnetic properties of core silicon steel sheets for transformers under different tensile and compressive stresses,the B-H curves, B-P curves, and permeability curves of silicon steel sheets under different tensile and compressive stresses are given.Secondly, based on the test results of magnetic characteristics of the silicon steel sheet, the electromagnetic performance and vibration of a 3kVA transformer are simulated and analyzed. In the simulation process, the influence of different tensile and compressive stresses on the performance of the silicon steel sheet core of the transformer is considered. It provides a new idea for the electromagnetic-vibration analysis of transformers. 1 Introduction The magnetostrictive property of silicon steel sheet is the main reason for the vibration and noise of electrical equipment such as transformers and reactors, and its characteristics are particularly sensitive to the mechanical stress[1].Based on the analysis of the mechanism of core vibration noise and experimental verification, the influence of magnetic properties and magnetostrictive effect of electrical steel sheet on the performance of power transformer under different stress is studied. This paper, by using a magnetostriction stress effect of the magnetic properties of measuring equipment and measuring instrument system, on oriented silicon steel (brand: 27 sqgd090) along the rolling direction under different tension and compression stress and magnetic properties of magnetostrictive properties were tested and the research of silicon steel sheet under different tension and compression stress are given B-H curve, B-P curve and permeability curve and curve of single value, as shown in figure 1 flow chart of research.Secondly, based on the above-mentioned measurement results, the model material library was established. Based on the finite element analysis software COMSOL, the finite element analysis was carried out on a 3KVA transformer under different tensile and compression stress conditions.Finally, an experimental study is carried out to verify the correctness of the proposed scheme, which provides a reference for the study of power transformer vibration noise under different tension and compression stresses. 2 Simulation study of power transformer under different stresses The results obtained by substituting the magnetic characteristic curves in Fig. 1 into the transformer FEM model considering the boundary conditions are shown in Fig. 2. The compressive stress increases the magnetostriction, while the tensile stress reduces the magnetostriction, magnetostriction is particularly sensitive to the compressive stress. The stress reduces the magnetic conductivity of electrical steel sheet.When there is no external force,the maximum magnetic density reaches 1.7T. 3 conclusion In this paper, the magnetic characteristics and magnetostrictive characteristics of silicon steel sheet are measured firstly, and then the electromagnetic and vibration characteristics of power transformer under different stresses are studied by using finite element analysis software.The results show that the compressive stress increases the magnetostriction, and the tensile stress decreases the magnetostriction, and the compressive stress is especially obvious.Detailed test results and simulation analysis will be shown in the full text.

**References:**

Anderson P I, Moses A J, Stanbury H J. An automated system for the measurement of magnetostriction in electrical steel sheet under applied stress [J]. Journal of Magnetism and Magnetic Materials, 2000, 215: 714-716.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8573aa5ce5a099e60e45effcfc62de79.jpg)
Fig.1 Reserch process flowchart

![](https://assets.underline.io/uploads/markdown_image/1/image/eda33ec72433e01bb513537c5910d8c6.jpg)
Fig.2 Simulation result

poster

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

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

 Fourier-Based Semi-Analytical Method for Current Distribution of Foil Wound Solid-State Transformers

This paper aiming to solve the vibration and noise problem of transformer core under DC bias, the magnetostrictive characteristics of 30ZH120 oriented silicon steel sheet in rolling direction and vertical rolling direction were studied firstly based on the measurement system of silicon steel sheet, and the influence rules of different DC bias on the magnetostrictive butterfly characteristics in different directions were studied. Secondly, the vibration and noise of transformer under the condition of DC bias are simulated, and the calculation results under different DC bias conditions are given. Thirdly, by means of modal numerical calculation and modal experimental study, the elastic modulus assignment methods and intervals suitable for modal calculation of transformers of different sizes are obtained and determined. Finally, the vibration and noise of the transformer are studied experimentally, and the correctness of the simulation content is verified. Key words: DC bias, vibration noise, magnetostriction, modal analysis 1 Introduction DC transmission grid, geomagnetic changes and other reasons can cause the ground potential of the transformer neutral point to rise, the presence of DC magnetic flux in the core, resulting in increased transformer no-load losses, vibration noise, and bring safety hazards to the power system transmission and distribution networks. Therefore, the study of transformer vibration noise is important. [1] simulated the 2-D magnetic properties of a silicon steel sheet and proposed a vector J-A hysteresis model considering the non-hysteresis magnetization intensity, and simulated its rotational magnetic properties. In [2], the magnetic properties of silicon steel sheets were studied at different temperatures and DC bias conditions, and the magnetization curves, permeability curves and loss curves were given. In [3], the magnetostriction characteristics of the silicon steel sheet were measured and the results were taken into the MagNet finite element software to study the vibration and noise of the power transformer, but the effect of DC bias on the vibration and noise of the transformer was not considered. This paper investigates the vibration noise of the transformer under DC bias through simulation and experimental verification. As in the research flowchart of Fig.1, the measured magnetic characteristic curves of the silicon steel sheet under DC bias magnetism can be brought into the transformer FEM model to obtain more accurate results. Finally, modal numerical calculations and modal experimental studies of transformers are also carried out to obtain and determine the elastic modulus assignment methods and intervals applicable to modal calculations of transformers of different sizes. 2 Simulation and experiment of vibration and noise under DC bias of transformer The results obtained by substituting the magnetic characteristic curves in Fig. 1 into the transformer FEM model considering the boundary conditions are shown in Table 1. The results show that the vibration and noise of the transformer increase with the increase of the DC bias. When the DC bias is greater than 2.3A, the vibration displacement reaches 0.4442 μm and the noise reaches 72.96 dB. In addition, the noise distribution curve of the transformer under DC bias shows that the noise increases with the increase of DC bias, but the noise remains stable when the DC bias is greater than 2.3A, indicating that the transformer core is saturated. 3 conclusion This paper first measures the magnetic properties of silicon steel wafers, and then uses finite element analysis to investigate the vibration noise performance of transformers under DC bias magnetism, and conducts experimental verification. The results show that the vibration and noise simulation results are in good agreement with the experimental results. Detailed experimental results and comparisons as well as modal analysis results will be shown in the full paper.

**References:**

[1] X. Wang, Y. Zhang and W. Jiang, Transactions of China Electrotechnical Society., Vol. 12(33), p.257-262 (2016) [2] D. Chen, L. Fang and B. Kwon, AIP Advances., Vol. 7(5), 056682 (2017) [3] D. Chen, W. Zhao and B. Bai, International Journal of Applied Electromagnetics and Mechanics., Vol. 52(3-4), p.1477-1484 (2016)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9829e76ee06d93aac00152e448b05973.jpg)
Fig.1 Reserch process flowchart

![](https://assets.underline.io/uploads/markdown_image/1/image/47c70f202c70de0908ef9f5d55732d23.jpg)
Table.1 Simulation and modal experiment results

 Study of Vibration and Noise Considering DC Bias in Power Transformer

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

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

To improve the thermal stability, reduce vibration/noise and system cost of mediate frequency transformers for DC-DC converters in low-voltage DC distribution networks. This paper presents a design study of a 20kW three-winding medium frequency transformer using 0.15mm oriented silicon steel sheet. First, the magnetic properties of silicon steel wafers at different frequencies were measured based on a single silicon steel wafer magnetic property measurement system, and the B-H curve, B-P curve and excitation curve at different frequencies were given. Next, a three-winding mediate frequency transformer with 537V input and 375V and 48V output is designed using particle swarm algorithm with loss minimization as the optimization objective, and finite element simulation and magnetic performance experiments are conducted. The flux density, loss and temperature field distribution curves of mediate frequency transformers under different operating conditions, and B-H curves, hysteresis lines and B-P curves at different frequencies are given. Finally, the experimental platform of DC-DC converter is built and its characteristics under different load conditions (no-load, rated load and overload) are experimentally studied to verify the correctness of the proposed scheme. 1. Introduction Compared with AC distribution networks, DC distribution networks have significant advantages in terms of distributed energy access, improving system efficiency, reducing line losses and operating costs, and increasing system capacity. As one of the main links of the DC distribution network, the bi-directional full-bridge converter (power electronic transformer), through the introduction of power electronic converters on the primary and secondary sides of the primary and secondary side of the voltage amplitude and phase of real-time digital control, compared to the traditional power transformer, power electronic transformer can be more accurate, flexible, stable and reliable regulation of the output side voltage[1]. As shown in Fig. 1(a), the mediate frequency transformer, as an important component of the bi-directional DC-DC converter, has an important impact on the size, weight, loss, and price of the power electronics transformer[2]. This paper takes low-voltage DC distribution network as the application background, converts PV power generation into DC 375V and DC 48V through DC-DC converter, and directly enters the home to supply power for TV sets, refrigerators, washing machines, lighting, etc. in the home, eliminating the loss generated by the AC-DC link and saving energy significantly. Fig. 1(b) shows the technical roadmap of this paper. Firstly, the topology of power electronic transformer is analyzed and bi-directional CLLLC resonant converter topology is adopted. Secondly, the magnetic characteristics of 0.15mm electrical steel sheet are tested to lay the foundation for the subsequent design, performance analysis and prototype development of mediate frequency transformer. Then, the design study of mediate frequency transformer is carried out, and one three-port mediate frequency transformer is designed based on particle swarm optimization algorithm with loss minimization as the goal, and finite element analysis is carried out. Finally, a power electronic transformer is fabricated and experiments under no-load, load and overload are completed to verify the correctness of the proposed scheme. 2. Simulation and Experiment on the Medium Frequency Transformers Fig. 1 (c) shows the design process of the three-port mediate frequency transformer proposed in this article; Fig. 1 (d) shows the optimization flow chart of the mediate frequency transformer; Fig. 1(e) shows the 0.15mm electrical steel sheet test platform and test results; Fig. 1(f) shows the magnetic flux density, loss and temperature field distribution of the mediate frequency transformer. It can be seen from Fig. 1 that the medium frequency transformer has a flux density of 0.5T, core loss of 137W, copper consumption of 123W, and an average temperature of 84.4°C at rated load. The design scheme meets the system requirements. 3. Conclusion This paper has carried out systematic research work on power electronic transformers in low-voltage DC distribution networks. Based on the monolithic silicon steel wafer measurement system, the test work of magnetic characteristics of silicon steel wafers at different frequencies was completed. A 537V/375V/48V three-port mediate frequency transformer was designed with the goal of loss minimization. A three-dimensional finite element model with electromagnetic-temperature field coupling was established to analyze the magnetic properties and temperature characteristics of the mediate frequency transformer under different operating conditions, which provides guidance for the design of the mediate frequency transformer. Detailed experimental results and comparisons are shown in the full paper.

**References:**

[1] T. F. Wu, C. H. Chang, L. C. Lin. DC-Bus Voltage Control With a Three-Phase Bidirectional Inverter for DC Distribution Systems[J]. IEEE Transactions on Power Electronics, 2013, 28(4):1890-1899. [2] Posada Contreras J, Ramirez J M. Multi-Fed Power Electronic Transformer for Use in Modern Distribution Systems[J]. IEEE Transactions on Smart Grid, 2014, 5(3):1532-1541.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f50c2eae56786038dee6f506d77234cd.jpg)

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Study of Vibration and Noise Considering DC Bias in Power Transformer