Modelling of negative equivalent magnetic reluctance structure and its application in weak-coupling wireless power transmission

Article https://doi.org/10.1038/s41467-024-50492-w Modelling of negative equivalent magnetic reluctance structure and its application in weak-coupling wireless power transmission Received: 30 October 2023 Yuanxi Chen 1 , Shuangxia Niu 1 , Weinong Fu 2 & Hongjian Lin3 Check for updates 1234567890():,; 1234567890():,; Accepted: 9 July 2024 In weak-coupling wireless power transmission, increasing operating frequency, and incorporating metamaterials, resonance structures or ferrite cores have been explored as effective solutions to enhance power efficiency. However, these solutions present significant challenges that need to be addressed. The increased operating frequency boosts ferrite core losses when it exceeds the working frequency range of the material. Existing metamaterial-based solutions present challenges in terms of requiring additional space for slab installation, resulting in increased overall size. In addition, limitations are faced in using Snell’s law for explaining the effects of metamaterial-based solutions outside the transmission path, where the magnetic field can not be reflected or refracted. To address these issues, in this work, the concept of a negative equivalent magnetic reluctance structure is proposed and the metamaterial theory is extended with the proposed magnetic reluctance modelling method. Especially, the negative equivalent magnetic reluctance structure is effectively employed in the weak-coupling wireless power transfer system. The proposed negative equivalent magnetic reluctance structure is verified by the stacked negative equivalent magnetic reluctance structure-based transformer experiments and two-coil mutual inductance experiments. Besides, the transmission gain, power experiments and loss analysis experiments verify the effectiveness of the proposed structure in the weak-coupling wireless power transfer system. Wireless power transfer (WPT) technology1–3 is a fast-growing charging solution for electric vehicles4, sensors5,6, home automation7, and medical and biological applications8–10. The operating frequency of the WPT systems typically ranges from kHz to MHz, largely dependent on the coupling coefficient of the coils. The coupling coefficient of the generalized 85 kHz WPT system11,12 is usually larger than 0.15, to ensure a qualified transfer efficiency of the system. While for the weakcoupling WPT system13–16, the coupling coefficient is much lower than the generalized solution, which cannot operates with high efficiency in the kHz frequency region. Generalized solutions employ the magnetic core or increased operation frequency to enhance efficiency. The magnetic ferrite core with high permeability can reduce the total magnetic reluctance, thereby increasing the mutual inductance and coupling between the coils17. However, the hysteresis loss of the ironoxide ferrite will boost when the system operating frequency exceeds the working frequency range of ferrite materials, leading to a decrease in the efficiency of the weak-coupling WPT system18. Hence, a conventional weak-coupling WPT system cannot effectively incorporate both a generalized ferrite core and operating at high frequencies. To address this issue, researchers have been working on developing specialized core materials and designs for these high-frequency, weak-coupling WPT systems. The designed Ndx Fe1−x Ny material19 as 1 Department of Electrical and Electronic Engineering, The Hong Kong Polytechnic University, 999077 Hong Kong, China. 2Faculty of Computer Science and Control Engineering, Shenzhen University of Advanced Technology, Shenzhen 518107, China. 3Department of Electrical Engineering, City University of Hong e-mail: Kong, 999077 Hong Kong, China. Nature Communications | (2024)15:6135 1 Article the magnetic core in a 13.56 MHz system increases the inductance from 0.69 to 1.15 μH. The cap-shaped back yoke topology20 for the MHz WPT system explores the impact of different core materials, such as Ni-Zn, Fe-Si, and amorphous, on efficiency enhancement. The results show an efficiency improvement ranging from 0.7 to 1.2%. Employing resonance coil21–23 is another widely used solution for efficiency enhancement in weak-coupling WPT systems. A dualintermediate resonant coil21 design achieved an efficiency of 72.4% at 4.63 MHz. A 13.56 MHz WPT system with multiple coupling paths22 also demonstrates increased efficiency. The superconductivity resonance coils23 has been shown to increase the efficiency of the system from 17.5 to 49.7%. Apart from the above-mentioned solutions, metamaterials and metasurfaces have also been investigated to enhance the efficiency of weak-coupling WPT systems24–31 as well as improve the misalignment tolerance32,33. The key is to design and achieve either a negative permeability to refract the electromagnetic field24–29 or nearzero permeability to reflect the electromagnetic field30,31, thereby increasing the flux on the receiver coil and enhancing the overall efficiency. However, for employing unconventional core materials, the effectiveness of efficiency enhancement is limited19,20. Additionally, due to the positive permeability of ferrite materials, the corresponding magnetic reluctance always remains positive, regardless of optimization and design. Consequently, in terms of magnetic reluctance reduction for weak-coupling WPT systems, the ferrite materials are inherently weaker than the metamaterials with negative permeability in efficiency enhancement. Given the reasons above, employing metamaterials is considered a potentially ideal solution for a weakcoupling WPT system. Nevertheless, the application of existing metamaterial-based solutions is not only limited by the low practicability but also the theoretical issue. Firstly, the metamaterials24–31 occupy additional space beyond the coils, which significantly increases the overall size of the weak-coupling WPT systems. A transmitterembedded metasurface34 can solve the space-occupying issue. Secondly, the existing theory based on Snell’s law cannot properly explain the effect of metamaterials outside the transmission path, which cannot reflect or refract the magnetic field generated by the transmitter coil, i.e. the metamaterial is installed in the receiver coil. Besides, the generalized metamaterial/metasurface requires a quantity of units to generate a homogeneous material. This design limits the quality factor of the units, as well as increases the corresponding loss, making the resonator can only effectively operate at relatively high frequency with large size. To address the aforementioned issues, the concept of a negative equivalent magnetic reluctance (NEMR) structure and its modelling method, as well as its application in a weak coupling WPT system are proposed and verified. This design installs the NEMR structure in both the transmitter and receiver coils, aiming to increase the mutual inductance and enhance efficiency by reducing the total magnetic reluctance based on negative permeabi (...truncated)