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Inhomogeneous Winding for Loosely Coupled Transformers to Reduce Magnetic Loss

Inhomogeneous Winding for Loosely Coupled Transformers to Reduce Magnetic Loss Hindawi Wireless Power Transfer Volume 2021, Article ID 9453966, 6 pages https://doi.org/10.1155/2021/9453966 Research Article Inhomogeneous Winding for Loosely Coupled Transformers to Reduce Magnetic Loss 1,2,3 2,3 2 Jing Zhou , Jiazhong He , and Fan Zhu Hainan Institute, Zhejiang University, Sanya 572025, China College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China Polytechnic Institute, Zhejiang University, Hangzhou 310015, China Correspondence should be addressed to Jing Zhou; jingzhou@zju.edu.cn Received 25 June 2021; Accepted 14 September 2021; Published 5 October 2021 Academic Editor: Giuseppina Monti Copyright © 2021 Jing Zhou et al. )is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Wireless power transfer has been proved promising in various applications. )e homogeneous winding method in loosely coupled transformers incurs unnecessary intense magnetic field distribution in the center and causes extra magnetic loss. An inho- mogeneous winding method is proposed in this paper, and a relatively homogeneous magnetic field distribution inside the core is achieved. )is paper investigated the magnetic loss of homogeneous winding and inhomogeneous winding for wireless power transfer. A theoretical model was built to evaluate magnetic loss under inhomogeneous winding. )e coupling coefficient and magnetic loss were investigated individually and comparisons were made between different width ratio combinations. )eoretical analysis was validated in experiments. Moreover, if we divide the core into several sections, the core 1. Introduction loss in each section is incurred not only by its own windings Wireless power transfer eliminates the need for wires to but also by its adjacent windings. Alternatively, FEM sim- connect the load from power source, and it has broad ulation software is widely applied to calculate core loss prospects in implantable medical devices, electric vehicles, [11, 12]. However, this method is very time-consuming, etc. Several approaches to improve the energy efficiency of especially for more accurate 3D models. In addition, the the wireless coupled coils have been developed [1–5]. optimization of system parameters can only by realized by Homogeneous winding, i.e., maintain the same distance sweeping design parameters. )e optimized point could be between each turn, is widely applied in loosely coupled missed since it lacks an overall understanding of the whole transformers [6–8]. And, this traditional winding method optimization region. In the view of these problems, a incurs the inhomogeneous internal magnetic field distri- magnetic circuit model [13] is proposed in this paper; it is bution; the magnetic induction intensity is concentrated in valid for solenoid winding structure and convenient to the central area, which results in greater loss in core center. obtain flux distribution. An inhomogeneous winding method is proposed in this It would be desirable to reduce the magnetic loss while paper: coils were loosely winded in the center while tightly maintaining tight and compact windings. In this paper, winded on two ends (Figure 1), so as to realize homogeneous different winding parameters were investigated and com- magnetic field distribution inside the core (Figure 2) and pared, in terms of coupling coefficient and magnetic loss. reduce magnetic loss. )is paper is arranged as follows. A magnetic circuit model Steinmetz equation is the most used method to char- is proposed in Section 2 to calculate the magnetic loss under acterize core losses [9, 10]. However, for wireless power inhomogeneous winding. Section 3 investigates the influence transfer system, the uneven flux density distribution in the of winding parameters. )e experimental setup and results are discussed in Section 4. Conclusions are drawn in Section 5. core makes it difficult to employ Steinmetz equation directly. 2 Wireless Power Transfer Aluminum shield Receiver Winding Ferrite Core Gap Tramsitter Winding length Core length Figure 1: Structure of inhomogeneous winding for loosely coupled transformers. H[A_per_meter] H[A_per_meter] 6.5000e+001 6.5000e+001 6.0000e+001 6.0000e+001 5.6000e+001 5.6000e+001 5.2000e+001 5.2000e+001 4.8000e+001 4.8000e+001 4.4000e+001 4.4000e+001 4.0000e+001 4.0000e+001 3.6000e+001 3.6000e+001 3.2000e+001 3.2000e+001 2.8000e+001 2.8000e+001 2.4000e+001 2.4000e+001 2.0000e+001 2.0000e+001 1.6000e+001 1.6000e+001 1.2000e+001 1.2000e+001 8.0000e+000 8.0000e+000 4.0000e+000 4.0000e+000 0.0000e+000 0.0000e+000 0 150 300 (mm) 0 150 300 (mm) (a) (b) Figure 2: Internal magnetic field. (a) Homogeneous winding. (b) Inhomogeneous winding. 2. Magnetic Losses of Ferrites under Inhomogeneous Winding Loosly coupled transformers A typical wireless power transfer system is illustrated in Figure 3. It contains a full-bridge inverter and rectifier and corresponding compensating topology. )e loosely coupled C C U i s o transformer contains a transmitter coil, a receiver coil, and corresponding magnetic cores. In this paper, the transmitter and receiver coils are both solenoid winding. On the primary side, the resonant capacitor C connects in series with the - transmitter coil, to form the resonant network. On the Figure 3: Typical wireless power transfer system. secondary side, the resonant capacitor C connects in par- allel with the receiver coil. A typical flux distribution of the solenoid structure is shown in Figure 4. )e total flux concerns the internal leakage flux, external leakage flux, and mutual flux, among which the internal leakage flux comprises the majority of Mutual flux Mutual flux leakage flux since its path length is much shorter than others. Corresponding equivalent magnetic reluctance network Internal flux Leakage flux is analyzed in Figure 5. As seen in Figure 5, the core is Leakage flux divided into 7 parts in longitudinal direction. In order to clearly demonstrate the magnetic motive force and the magnetic reluctance in each flux path, at least 7 divisions have to be provided. With more divisions, theoretically, we Figure 4: Flux distribution of the solenoid structure. can obtain a more accurate result, but the calculation complexity will increase dramatically. )e discretization number is a trade-off between precision and complexity. source in series with magnetic reluctance. )e voltage source Each core section is modelled as magnetic reluctance, while corresponds to the number of turns and current excitation in core section with excitation winding is modelled as a voltage the winding, represented by α · i in Figure 5. p Wireless Power Transfer 3 ϕ ϕ ϕ r2 r1 r2 R R R R R R R C C C C C C C R R R R m2 m1 m4 m5 R R m1 m1 L2 ϕ ϕ m1 m1 l11 L1 l11 +- +- +- +- +- ϕ ϕ ϕ ϕ ϕ ϕ 2 2 1 3 4 4 3 R R R R R R R a·j a·j C a·j C a·j C a·j C C C C P P P P P L3 l12 ϕ ϕ lb1 lb1 l12 L4 lb1 Figure 6: Lumped magnetic reluctance model. in Internal flux a·i Leakage flux out (4) P � k · f · B , Mutual flux where B is the peak induction of a sinusoidal excitation with Figure 5: Equivalent magnetic reluctance network. frequency f, P is the time-average power loss per unit volume, and k and α are material parameters which can be A lumped magnetic reluctance model was built in obtained from the material datasheet. Figure 6, concerning voltage source and reluctance inside By substituting (3) into (4), the magnetic loss in each the core and in the air. section can be calculated. Generally, the highest flux density In the situation of uneven flux distribution, values of is designed well under saturation; thus, the ferrite usually parameters {R , R , R , R } and {R , R , R , R } l1 l2 l3 l4 m1 m2 m3 m4 works in the linear region and the overall magnetic loss can cannot be derived using the empirical equation. FEM be summed. simulation is applied once to obtain flux distribution {ϕ , ϕ , 1 2 ϕ , ϕ }. Substitute the flux values into the model in Figure 6; 3 4 3. Influence of Winding Parameters the magnetic reluctance values can be derived according to Kirchhoff’s voltage law. To investigate the influence of winding parameters, we In addition, the magnetic reluctance R can be calculated as constructed two coupled coils, each with the same number of turns in total and different winding spaces between each R � , (1) turn. )e receiver coil is designed to be homogeneous μ μ A 0 r c winding, while the transmitter coil was constructed with where l is the length of each individual core, μ is the c 0 different spaces between each turn. vacuum permeability, and μ is the relative permeability of r It would be desirable to reduce the magnetic loss while cores. maintaining tight and compact windings. In this paper, )e total flux density along y-axis is different coil winding width ratio combinations were in- vestigated and compared, in terms of coupling coefficient B � , (2) and magnetic loss. )e system configurations are as follows. )e magnetic where A is the cross-sectional area of the core in the x-z c core is made of ultra-low-loss soft magnetic material plane. DMR47. )e overall dimension of the core is After obtaining all of the parameters in the lumped 500∗ 380∗12 mm, which is formed by small magnetic cubes magnetic reluctance model, the magnetic flux density under (50∗ 38∗ 6 mm). )e number of primary and secondary coil different working conditions can be acquired: turns is both 45 turns. )e air gap between primary and − 1 secondary coils is 200 mm. )e system works at its resonant A U (3) B � , frequency 50 kHz. )e input voltage is 160V and the load of the system is 50 Ω. where U is the magnetic motive force (MMF) matrix and A is )e coils were equally divided into 5 portions. )e number of portions determines the number of combination the magnetic reluctance coefficient. It is worth noting that the flux density in the primary possibilities of winding density. With more portions, we can core is excited not only by the primary winding but also by obtain a much more accurate result, but the calculation the secondary winding. By combining the results generated complexity will increase dramatically. )e discretization by primary and secondary excitations, the flux density number is a trade-off between precision and complexity. )e distribution in the primary core can be calculated. current in each section α · i corresponds to the number of As a result, for cores under sinusoidal current excitation, turns. Serially connect the 5 portions, and calculate the the magnetic loss can be calculated using the Steinmetz coupling coefficient of the receiver side with the transmitter equation: side. Apply different current in each portion to realize the 4 Wireless Power Transfer B [tesla] B [tesla] 1.0750E-02 1.0750E-02 1.0099E-02 1.0099E-02 9.4476E-03 9.4476E-03 8.7963E-03 8.7963E-03 8.1451E-03 8.1451E-03 7.4939E-03 7.4939E-03 6.8427E-03 6.8427E-03 6.1915E-03 6.1915E-03 5.5402E-03 5.5402E-03 4.8890E-03 4.8890E-03 4.2378E-03 4.2378E-03 3.5866E-03 3.5866E-03 2.9353E-03 2.9353E-03 2.2841E-03 2.2841E-03 1.6329E-03 1.6329E-03 9.8168E-04 9.8168E-04 (a) (b) B [tesla] 1.0750E-02 1.0099E-02 9.4476E-03 8.7963E-03 8.1451E-03 7.4939E-03 6.8427E-03 6.1915E-03 5.5402E-03 4.8890E-03 4.2378E-03 3.5866E-03 2.9353E-03 2.2841E-03 1.6329E-03 9.8168E-04 (c) Figure 7: Magnetic field distributions in core with different winding parameters. (a) Homogeneous winding (9 : 9 : 9 : 9 : 9). (b) Winding parameters (10 :10 : 5 :10 :10). (c) Winding parameters (17 : 4 : 3 : 4 :17). effects of inhomogeneous winding. A one-row five-column Table 1: Comparison of core loss in theoretical and simulation results. array indicates the current value in 5 portions. As seen in Figure 7, (9 : 9 : 9 : 9 : 9) indicates 9 turns in each portion. Winding parameters )eoretical loss (W) Simulation loss (W) )e receiver coil remains homogeneous winding, while (9 : 9 : 9 : 9 : 9) 16.05 16.08 different winding parameters of the transmitter coil were (10 :10 : 5 :10 :10) 15.55 15.58 studied to seek for the optimal combination. Typical the- (17 : 4 : 3 : 4 :17) 15.10 15.12 oretical results were compared with simulations in ANSYS Maxwell; the effects of inhomogeneous winding were shown in Figures 7(a)–7(c) under the same magnetic induction winding parameters, relative low magnetic field density in intensity scale. )e simulation results agree well with the- the core center helps to reduce the overall core loss. oretical analysis, as shown in Table 1. In order to illustrate the effects of inhomogeneous 4. Experimental Result and Discussion winding on magnetic loss, the variations of coupling coef- ficient and core loss are depicted with different winding Measurements for wireless power transfer system under parameters, as shown in Figure 8. inhomogeneous winding were obtained to evaluate whether )e horizontal axis represents the coupling coefficient, the power loss reduction found for inhomogeneous winding while the vertical axis is 1/core loss. )e desired winding translated to improve power efficiency well. parameters are with high coupling coefficients and low core Primary coil turns are winded around the core with losses, so points positioned in the top right region are preferred. different spaces between each turn. )e total number of As seen from Figure 8, the range of coupling coefficient is turns remains constant, and the working frequency is un- limited between 0.118 and 0.122. Homogeneous winding (9, changed, so the copper loss is assumed to be the same, and so 9, 9, 9, 9) has the worst performance, with the lowest is the eddy-current loss. )e circuit always works at the soft coupling coefficient and highest core loss, compared with switching mode, so the switching loss remain unchanged. other cases with coarse winding in center. Inhomogeneous )erefore, with different winding parameters, the variation winding effectively reduced the magnetic loss in the ferrite in core loss results in the change in system efficiency. )e core. )e optimal situation within consideration range, with overview of the experiment system is shown in Figure 9. winding parameter (17, 4, 3, 4, 17), reduced the core loss by )e diagram of setups for measuring is shown in Fig- 5.6% compared with the homogeneous case, while the ure 10. Test waveforms of the system are shown in Figure 11, coupling coefficient increased by 1.9%. When designing the including the primary current i , secondary current i , and p s Wireless Power Transfer 5 0.066 Coupling coefficient/Core loss 0.078 (17,4,3,4,17) 0.0655 0.065 0.077 (14,6,5,6,14) (12,9,3,9,12) 0.0645 (13,7,5,7,13) 0.064 0.0635 (11,8,7,8,11) (9,11,5,11,9) 0.063 (9,9,9,9,9) 0.0625 0.118 0.1185 0.119 0.1195 0.12 0.1205 0.121 0.1215 0.122 Coupling Coefficient Figure 8: Variation of core loss and coupling coefficient with different winding parameters. Figure 11: Test waveforms of the system. 16.4 Figure 9: Experimental setup for wireless power transfer under inhomogeneous winding. 15.6 15.2 i i 14.8 p s C R 14.4 o o C u C U i p s o (9:9:9:9:9) (10:10:5:10:10) (14:7:3:7:14) (17:4:3:4:17) Calculation results Experimental results Figure 12: Variation of core loss with different winding parameters. Figure 10: )e diagram of the setups for measuring. output voltage of the inverter u . u represent the gate winding losses by using a LCR meter, the switching device p g driving signal for MOSFET in the inverter bridge. )e losses, and the diode losses by integrating the voltage and system works under ZVS condition, as not much of a voltage current waveforms using a HDO4034 oscilloscope. )e spike is observed in the waveform. variation of measured core loss agrees well with the cal- )e experimental and calculation results are compared culated results, assuming the winding loss and switching loss in Figure 12. Since it is difficult to directly obtain the core remain unchanged under the same frequency. )e system loss, the experimental core losses were obtained by sub- power loss significantly reduces as coils are wound relatively tracting the measured total losses with the measured coarsely in the center and tightly at two ends. -1 1/Core Loss (W ) Core loss (W) 6 Wireless Power Transfer wireless electric vehicle charging,” IEEE Sensors Journal, 5. Conclusions vol. 19, no. 5, pp. 1683–1692, 2019. [8] T. Gonda, S. Mototani, K. Doki, and A. Torii, “Effect of air A novel inhomogeneous winding method for loosely cou- space in waterproof sealed case containing transmitter and pled transformers is proposed in the paper. A magnetic receiver of wireless power transfer in sea water,” Electrical reluctance model for solenoid structure is built to calculate Engineering in Japan, vol. 206, pp. 24–31, 2019. the core loss under inhomogeneous winding. Sweeping [9] J. Muhlethaler, J. Biela, J. W. Kolar, and A. Ecklebe, “Core maps with different primary winding parameters were losses under the DC bias condition basedon steinmetz pa- provided to investigate the optimal combination. )e ob- rameters,” IEEE Transactions on Power Electronics, vol. 27, tained experimental results show great agreement with the no. 2, pp. 953–963, 2012. presented optimization. Compared with traditional homo- [10] S. C. Tang and N. J. McDannold, “Power Loss analysis and geneous winding, the new inhomogeneous winding method comparison of segmented and unsegmented energy coupling effectively reduces magnetic loss in the ferrite core, while coils for wireless energy transfer,” IEEE Journal of Emerging maintaining tight coupling between primary and secondary and Selected Topics in Power Electronics, vol. 3, no. 1, pp. 215–225, 2015. coils. [11] K. E. I. Elnail, X. L. Huang, X. Chen, L. L. Tan, and H. Z. Xu, “Core Structure and electromagnetic field evaluation in WPT Data Availability systems for charging electric vehicles,” Energies, vol. 11, no. 7, p. 1734, 2018. )e experimental data used to support the findings of this [12] X. Zhang, S. L. Ho, and W. N. Fu, “Quantitative analysis of a study are included within the article. wireless power transfer cell with planar spiral structures,” IEEE Transactions on Magnetics, vol. 47, no. 10, pp. 3200– 3203, 2011. Conflicts of Interest [13] Y. Tang, F. Zhu, and H. Ma, “Efficiency optimization with a novel magnetic-circuit model for inductive power transfer in )e authors declare that they have no conflicts of interest. EVs,” Journal of Power Electronics, vol. 18, no. 1, pp. 309–322, Acknowledgments )e authors acknowledge the funding of Zhejiang Key R&D Program, under Grant no. 2019C01044. References [1] S. Lee, D. H. Kim, Y. Cho et al., “Low leakage electromagnetic field level and high efficiency using a novel hybrid loop-array design for wireless high power transfer system,” IEEE Transactions on Industrial Electronics, vol. 66, no. 6, pp. 4356–4367, 2019. [2] M. Y. Li, X. Y. Chen, H. Y. Gou et al., “Conceptual design and characteristic analysis of a sliding-type superconducting wireless power transfer system using ReBCO primary at 50Hz,” IEEE Transactions on Applied Superconductivity, vol. 29, no. 2, Article ID 5501304, 2019. [3] Z. H. Ye, Y. Sun, X. Dai, and C. Tang, “Energy efficiency analysis of U-coil wireless power transfer system,” IEEE Transactions on Power Electonics, vol. 31, no. 7, pp. 4809–4817, [4] Z. Yan, Y. Li, C. Zhang, and Q. Yang, “Influence factors analysis and improvement method on efficiency of wireless power transfer via coupled magnetic resonance,” IEEE Transactions on Magnetics, vol. 50, no. 4, Article ID 4004204, [5] J. Liu, Q. Deng, D. Czarkowski, M. K. Kazimierczuk, H. Zhou, and W. Hu, “Frequency optimization for inductive power transfer based on AC resistance evaluation in litz-wire coil,” IEEE Transactions on Power Electronics, vol. 34, no. 3, pp. 2355–2363, 2019. [6] Z. Cheng, Y. Lei, K. Song, and C. Zhu, “Design and loss analysis of loosely coupled transformer for an underwater high-power inductive power transfer system,” IEEE Trans- actions on Magnetics, vol. 51, no. 7, Article ID 8401110, 2017. [7] X. Liu, C. Liu, W. Han, and P. W. T. Pong, “Design and implementation of a multi-purpose TMR sensor matrix for http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Wireless Power Transfer Hindawi Publishing Corporation

Inhomogeneous Winding for Loosely Coupled Transformers to Reduce Magnetic Loss

Wireless Power Transfer , Volume 2021 – Oct 5, 2021

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Abstract

Hindawi Wireless Power Transfer Volume 2021, Article ID 9453966, 6 pages https://doi.org/10.1155/2021/9453966 Research Article Inhomogeneous Winding for Loosely Coupled Transformers to Reduce Magnetic Loss 1,2,3 2,3 2 Jing Zhou , Jiazhong He , and Fan Zhu Hainan Institute, Zhejiang University, Sanya 572025, China College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China Polytechnic Institute, Zhejiang University, Hangzhou 310015, China Correspondence should be addressed to Jing Zhou; jingzhou@zju.edu.cn Received 25 June 2021; Accepted 14 September 2021; Published 5 October 2021 Academic Editor: Giuseppina Monti Copyright © 2021 Jing Zhou et al. )is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Wireless power transfer has been proved promising in various applications. )e homogeneous winding method in loosely coupled transformers incurs unnecessary intense magnetic field distribution in the center and causes extra magnetic loss. An inho- mogeneous winding method is proposed in this paper, and a relatively homogeneous magnetic field distribution inside the core is achieved. )is paper investigated the magnetic loss of homogeneous winding and inhomogeneous winding for wireless power transfer. A theoretical model was built to evaluate magnetic loss under inhomogeneous winding. )e coupling coefficient and magnetic loss were investigated individually and comparisons were made between different width ratio combinations. )eoretical analysis was validated in experiments. Moreover, if we divide the core into several sections, the core 1. Introduction loss in each section is incurred not only by its own windings Wireless power transfer eliminates the need for wires to but also by its adjacent windings. Alternatively, FEM sim- connect the load from power source, and it has broad ulation software is widely applied to calculate core loss prospects in implantable medical devices, electric vehicles, [11, 12]. However, this method is very time-consuming, etc. Several approaches to improve the energy efficiency of especially for more accurate 3D models. In addition, the the wireless coupled coils have been developed [1–5]. optimization of system parameters can only by realized by Homogeneous winding, i.e., maintain the same distance sweeping design parameters. )e optimized point could be between each turn, is widely applied in loosely coupled missed since it lacks an overall understanding of the whole transformers [6–8]. And, this traditional winding method optimization region. In the view of these problems, a incurs the inhomogeneous internal magnetic field distri- magnetic circuit model [13] is proposed in this paper; it is bution; the magnetic induction intensity is concentrated in valid for solenoid winding structure and convenient to the central area, which results in greater loss in core center. obtain flux distribution. An inhomogeneous winding method is proposed in this It would be desirable to reduce the magnetic loss while paper: coils were loosely winded in the center while tightly maintaining tight and compact windings. In this paper, winded on two ends (Figure 1), so as to realize homogeneous different winding parameters were investigated and com- magnetic field distribution inside the core (Figure 2) and pared, in terms of coupling coefficient and magnetic loss. reduce magnetic loss. )is paper is arranged as follows. A magnetic circuit model Steinmetz equation is the most used method to char- is proposed in Section 2 to calculate the magnetic loss under acterize core losses [9, 10]. However, for wireless power inhomogeneous winding. Section 3 investigates the influence transfer system, the uneven flux density distribution in the of winding parameters. )e experimental setup and results are discussed in Section 4. Conclusions are drawn in Section 5. core makes it difficult to employ Steinmetz equation directly. 2 Wireless Power Transfer Aluminum shield Receiver Winding Ferrite Core Gap Tramsitter Winding length Core length Figure 1: Structure of inhomogeneous winding for loosely coupled transformers. H[A_per_meter] H[A_per_meter] 6.5000e+001 6.5000e+001 6.0000e+001 6.0000e+001 5.6000e+001 5.6000e+001 5.2000e+001 5.2000e+001 4.8000e+001 4.8000e+001 4.4000e+001 4.4000e+001 4.0000e+001 4.0000e+001 3.6000e+001 3.6000e+001 3.2000e+001 3.2000e+001 2.8000e+001 2.8000e+001 2.4000e+001 2.4000e+001 2.0000e+001 2.0000e+001 1.6000e+001 1.6000e+001 1.2000e+001 1.2000e+001 8.0000e+000 8.0000e+000 4.0000e+000 4.0000e+000 0.0000e+000 0.0000e+000 0 150 300 (mm) 0 150 300 (mm) (a) (b) Figure 2: Internal magnetic field. (a) Homogeneous winding. (b) Inhomogeneous winding. 2. Magnetic Losses of Ferrites under Inhomogeneous Winding Loosly coupled transformers A typical wireless power transfer system is illustrated in Figure 3. It contains a full-bridge inverter and rectifier and corresponding compensating topology. )e loosely coupled C C U i s o transformer contains a transmitter coil, a receiver coil, and corresponding magnetic cores. In this paper, the transmitter and receiver coils are both solenoid winding. On the primary side, the resonant capacitor C connects in series with the - transmitter coil, to form the resonant network. On the Figure 3: Typical wireless power transfer system. secondary side, the resonant capacitor C connects in par- allel with the receiver coil. A typical flux distribution of the solenoid structure is shown in Figure 4. )e total flux concerns the internal leakage flux, external leakage flux, and mutual flux, among which the internal leakage flux comprises the majority of Mutual flux Mutual flux leakage flux since its path length is much shorter than others. Corresponding equivalent magnetic reluctance network Internal flux Leakage flux is analyzed in Figure 5. As seen in Figure 5, the core is Leakage flux divided into 7 parts in longitudinal direction. In order to clearly demonstrate the magnetic motive force and the magnetic reluctance in each flux path, at least 7 divisions have to be provided. With more divisions, theoretically, we Figure 4: Flux distribution of the solenoid structure. can obtain a more accurate result, but the calculation complexity will increase dramatically. )e discretization number is a trade-off between precision and complexity. source in series with magnetic reluctance. )e voltage source Each core section is modelled as magnetic reluctance, while corresponds to the number of turns and current excitation in core section with excitation winding is modelled as a voltage the winding, represented by α · i in Figure 5. p Wireless Power Transfer 3 ϕ ϕ ϕ r2 r1 r2 R R R R R R R C C C C C C C R R R R m2 m1 m4 m5 R R m1 m1 L2 ϕ ϕ m1 m1 l11 L1 l11 +- +- +- +- +- ϕ ϕ ϕ ϕ ϕ ϕ 2 2 1 3 4 4 3 R R R R R R R a·j a·j C a·j C a·j C a·j C C C C P P P P P L3 l12 ϕ ϕ lb1 lb1 l12 L4 lb1 Figure 6: Lumped magnetic reluctance model. in Internal flux a·i Leakage flux out (4) P � k · f · B , Mutual flux where B is the peak induction of a sinusoidal excitation with Figure 5: Equivalent magnetic reluctance network. frequency f, P is the time-average power loss per unit volume, and k and α are material parameters which can be A lumped magnetic reluctance model was built in obtained from the material datasheet. Figure 6, concerning voltage source and reluctance inside By substituting (3) into (4), the magnetic loss in each the core and in the air. section can be calculated. Generally, the highest flux density In the situation of uneven flux distribution, values of is designed well under saturation; thus, the ferrite usually parameters {R , R , R , R } and {R , R , R , R } l1 l2 l3 l4 m1 m2 m3 m4 works in the linear region and the overall magnetic loss can cannot be derived using the empirical equation. FEM be summed. simulation is applied once to obtain flux distribution {ϕ , ϕ , 1 2 ϕ , ϕ }. Substitute the flux values into the model in Figure 6; 3 4 3. Influence of Winding Parameters the magnetic reluctance values can be derived according to Kirchhoff’s voltage law. To investigate the influence of winding parameters, we In addition, the magnetic reluctance R can be calculated as constructed two coupled coils, each with the same number of turns in total and different winding spaces between each R � , (1) turn. )e receiver coil is designed to be homogeneous μ μ A 0 r c winding, while the transmitter coil was constructed with where l is the length of each individual core, μ is the c 0 different spaces between each turn. vacuum permeability, and μ is the relative permeability of r It would be desirable to reduce the magnetic loss while cores. maintaining tight and compact windings. In this paper, )e total flux density along y-axis is different coil winding width ratio combinations were in- vestigated and compared, in terms of coupling coefficient B � , (2) and magnetic loss. )e system configurations are as follows. )e magnetic where A is the cross-sectional area of the core in the x-z c core is made of ultra-low-loss soft magnetic material plane. DMR47. )e overall dimension of the core is After obtaining all of the parameters in the lumped 500∗ 380∗12 mm, which is formed by small magnetic cubes magnetic reluctance model, the magnetic flux density under (50∗ 38∗ 6 mm). )e number of primary and secondary coil different working conditions can be acquired: turns is both 45 turns. )e air gap between primary and − 1 secondary coils is 200 mm. )e system works at its resonant A U (3) B � , frequency 50 kHz. )e input voltage is 160V and the load of the system is 50 Ω. where U is the magnetic motive force (MMF) matrix and A is )e coils were equally divided into 5 portions. )e number of portions determines the number of combination the magnetic reluctance coefficient. It is worth noting that the flux density in the primary possibilities of winding density. With more portions, we can core is excited not only by the primary winding but also by obtain a much more accurate result, but the calculation the secondary winding. By combining the results generated complexity will increase dramatically. )e discretization by primary and secondary excitations, the flux density number is a trade-off between precision and complexity. )e distribution in the primary core can be calculated. current in each section α · i corresponds to the number of As a result, for cores under sinusoidal current excitation, turns. Serially connect the 5 portions, and calculate the the magnetic loss can be calculated using the Steinmetz coupling coefficient of the receiver side with the transmitter equation: side. Apply different current in each portion to realize the 4 Wireless Power Transfer B [tesla] B [tesla] 1.0750E-02 1.0750E-02 1.0099E-02 1.0099E-02 9.4476E-03 9.4476E-03 8.7963E-03 8.7963E-03 8.1451E-03 8.1451E-03 7.4939E-03 7.4939E-03 6.8427E-03 6.8427E-03 6.1915E-03 6.1915E-03 5.5402E-03 5.5402E-03 4.8890E-03 4.8890E-03 4.2378E-03 4.2378E-03 3.5866E-03 3.5866E-03 2.9353E-03 2.9353E-03 2.2841E-03 2.2841E-03 1.6329E-03 1.6329E-03 9.8168E-04 9.8168E-04 (a) (b) B [tesla] 1.0750E-02 1.0099E-02 9.4476E-03 8.7963E-03 8.1451E-03 7.4939E-03 6.8427E-03 6.1915E-03 5.5402E-03 4.8890E-03 4.2378E-03 3.5866E-03 2.9353E-03 2.2841E-03 1.6329E-03 9.8168E-04 (c) Figure 7: Magnetic field distributions in core with different winding parameters. (a) Homogeneous winding (9 : 9 : 9 : 9 : 9). (b) Winding parameters (10 :10 : 5 :10 :10). (c) Winding parameters (17 : 4 : 3 : 4 :17). effects of inhomogeneous winding. A one-row five-column Table 1: Comparison of core loss in theoretical and simulation results. array indicates the current value in 5 portions. As seen in Figure 7, (9 : 9 : 9 : 9 : 9) indicates 9 turns in each portion. Winding parameters )eoretical loss (W) Simulation loss (W) )e receiver coil remains homogeneous winding, while (9 : 9 : 9 : 9 : 9) 16.05 16.08 different winding parameters of the transmitter coil were (10 :10 : 5 :10 :10) 15.55 15.58 studied to seek for the optimal combination. Typical the- (17 : 4 : 3 : 4 :17) 15.10 15.12 oretical results were compared with simulations in ANSYS Maxwell; the effects of inhomogeneous winding were shown in Figures 7(a)–7(c) under the same magnetic induction winding parameters, relative low magnetic field density in intensity scale. )e simulation results agree well with the- the core center helps to reduce the overall core loss. oretical analysis, as shown in Table 1. In order to illustrate the effects of inhomogeneous 4. Experimental Result and Discussion winding on magnetic loss, the variations of coupling coef- ficient and core loss are depicted with different winding Measurements for wireless power transfer system under parameters, as shown in Figure 8. inhomogeneous winding were obtained to evaluate whether )e horizontal axis represents the coupling coefficient, the power loss reduction found for inhomogeneous winding while the vertical axis is 1/core loss. )e desired winding translated to improve power efficiency well. parameters are with high coupling coefficients and low core Primary coil turns are winded around the core with losses, so points positioned in the top right region are preferred. different spaces between each turn. )e total number of As seen from Figure 8, the range of coupling coefficient is turns remains constant, and the working frequency is un- limited between 0.118 and 0.122. Homogeneous winding (9, changed, so the copper loss is assumed to be the same, and so 9, 9, 9, 9) has the worst performance, with the lowest is the eddy-current loss. )e circuit always works at the soft coupling coefficient and highest core loss, compared with switching mode, so the switching loss remain unchanged. other cases with coarse winding in center. Inhomogeneous )erefore, with different winding parameters, the variation winding effectively reduced the magnetic loss in the ferrite in core loss results in the change in system efficiency. )e core. )e optimal situation within consideration range, with overview of the experiment system is shown in Figure 9. winding parameter (17, 4, 3, 4, 17), reduced the core loss by )e diagram of setups for measuring is shown in Fig- 5.6% compared with the homogeneous case, while the ure 10. Test waveforms of the system are shown in Figure 11, coupling coefficient increased by 1.9%. When designing the including the primary current i , secondary current i , and p s Wireless Power Transfer 5 0.066 Coupling coefficient/Core loss 0.078 (17,4,3,4,17) 0.0655 0.065 0.077 (14,6,5,6,14) (12,9,3,9,12) 0.0645 (13,7,5,7,13) 0.064 0.0635 (11,8,7,8,11) (9,11,5,11,9) 0.063 (9,9,9,9,9) 0.0625 0.118 0.1185 0.119 0.1195 0.12 0.1205 0.121 0.1215 0.122 Coupling Coefficient Figure 8: Variation of core loss and coupling coefficient with different winding parameters. Figure 11: Test waveforms of the system. 16.4 Figure 9: Experimental setup for wireless power transfer under inhomogeneous winding. 15.6 15.2 i i 14.8 p s C R 14.4 o o C u C U i p s o (9:9:9:9:9) (10:10:5:10:10) (14:7:3:7:14) (17:4:3:4:17) Calculation results Experimental results Figure 12: Variation of core loss with different winding parameters. Figure 10: )e diagram of the setups for measuring. output voltage of the inverter u . u represent the gate winding losses by using a LCR meter, the switching device p g driving signal for MOSFET in the inverter bridge. )e losses, and the diode losses by integrating the voltage and system works under ZVS condition, as not much of a voltage current waveforms using a HDO4034 oscilloscope. )e spike is observed in the waveform. variation of measured core loss agrees well with the cal- )e experimental and calculation results are compared culated results, assuming the winding loss and switching loss in Figure 12. Since it is difficult to directly obtain the core remain unchanged under the same frequency. )e system loss, the experimental core losses were obtained by sub- power loss significantly reduces as coils are wound relatively tracting the measured total losses with the measured coarsely in the center and tightly at two ends. -1 1/Core Loss (W ) Core loss (W) 6 Wireless Power Transfer wireless electric vehicle charging,” IEEE Sensors Journal, 5. Conclusions vol. 19, no. 5, pp. 1683–1692, 2019. [8] T. Gonda, S. Mototani, K. Doki, and A. Torii, “Effect of air A novel inhomogeneous winding method for loosely cou- space in waterproof sealed case containing transmitter and pled transformers is proposed in the paper. A magnetic receiver of wireless power transfer in sea water,” Electrical reluctance model for solenoid structure is built to calculate Engineering in Japan, vol. 206, pp. 24–31, 2019. the core loss under inhomogeneous winding. Sweeping [9] J. Muhlethaler, J. Biela, J. W. Kolar, and A. Ecklebe, “Core maps with different primary winding parameters were losses under the DC bias condition basedon steinmetz pa- provided to investigate the optimal combination. )e ob- rameters,” IEEE Transactions on Power Electronics, vol. 27, tained experimental results show great agreement with the no. 2, pp. 953–963, 2012. presented optimization. Compared with traditional homo- [10] S. C. Tang and N. J. McDannold, “Power Loss analysis and geneous winding, the new inhomogeneous winding method comparison of segmented and unsegmented energy coupling effectively reduces magnetic loss in the ferrite core, while coils for wireless energy transfer,” IEEE Journal of Emerging maintaining tight coupling between primary and secondary and Selected Topics in Power Electronics, vol. 3, no. 1, pp. 215–225, 2015. coils. [11] K. E. I. Elnail, X. L. Huang, X. Chen, L. L. Tan, and H. Z. 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Cho et al., “Low leakage electromagnetic field level and high efficiency using a novel hybrid loop-array design for wireless high power transfer system,” IEEE Transactions on Industrial Electronics, vol. 66, no. 6, pp. 4356–4367, 2019. [2] M. Y. Li, X. Y. Chen, H. Y. Gou et al., “Conceptual design and characteristic analysis of a sliding-type superconducting wireless power transfer system using ReBCO primary at 50Hz,” IEEE Transactions on Applied Superconductivity, vol. 29, no. 2, Article ID 5501304, 2019. [3] Z. H. Ye, Y. Sun, X. Dai, and C. Tang, “Energy efficiency analysis of U-coil wireless power transfer system,” IEEE Transactions on Power Electonics, vol. 31, no. 7, pp. 4809–4817, [4] Z. Yan, Y. Li, C. Zhang, and Q. Yang, “Influence factors analysis and improvement method on efficiency of wireless power transfer via coupled magnetic resonance,” IEEE Transactions on Magnetics, vol. 50, no. 4, Article ID 4004204, [5] J. Liu, Q. Deng, D. Czarkowski, M. K. Kazimierczuk, H. 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Wireless Power TransferHindawi Publishing Corporation

Published: Oct 5, 2021

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