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## Modeling and analysis of eddy-current loss of underwater contact-less power transmission system based on magnetic coupled resonance

Zhang Ke-Han, Yan Long-Bin, Yan Zheng-Chao, Wen Hai-Bing, Song Bao-Wei
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• #### 摘要

文章对基于磁共振的水下非接触式电能传输系统在海水中的传输机理以及电涡流损耗进行了分析. 首先基于互感模型, 建立了空气中磁共振非接触式电能传输系统的数学模型, 分析了系统的频率特性, 从理论上对频率分裂现象进行了解释. 然后针对海水环境, 通过麦克斯韦方程组建立系统的数学模型, 通过级数展开, 略去高阶项, 得到计算电涡流损耗的近似公式, 分析了电涡流损耗与线圈半径、谐振频率、传输距离、磁感应强度的关系, 为水下非接触式电能传输系统的总体设计提供了理论依据. 最后通过实验验证了在空气中和海水中进行非接触式电能传输的异同, 以及电涡流损耗与各项参数的关系. 实验表明: 在空气中当传输距离为50 mm、传输功率为100 W时, 效率在80%以上; 在海水中当传输距离为50 mm、传输功率为100 W时, 效率约为67%, 说明基于磁共振的水下非接触式电能传输系统在海水中也有很好的应用前景.

#### Abstract

In this paper, we investigate the transmission mechanism and eddy-current loss of the contact-less power transmission (CPT) system in seawater environment. Contact-less power transfer could be achieved in the three following ways: magnetic coupling, magnetic resonance coupling, and microwave radiation. When the primary and secondary coils are in resonance, a channel of low resistance in the magnetic resonance coupling system is formed. Therefore, it is used for medium-distance power transmission and it has less restrictions on orientation, which means that it has wide applications in many scenarios. Moreover, contact-less power transfer is safer and more concealed than traditional plug power supply, especially in underwater vehicles. Firstly, the mathematical model based on the mutual inductance model is proposed for the CPT system in the air, then the frequency analysis of the CPT model as well as theoretical explanation of the splitting phenomenon is conducted, after that we consider the seawater effect on the mutual inductance coefficient. Secondly, we build a mathematical model of the eddy-current loss in seawater circumstance according to the Maxwell's equations, where we introduce an average magnetic induction in cross section, then derive an approximate formula through Taylor expansion, and analyze the relations between eddy-current loss and the physical parameters including coil radius, resonance frequency, transmission distance, and magnetic induction. According to the theoretical results, we optimize these physical parameters and then design a 754 kHz CPT system, thereafter we validate the CPT system both in the air and in seawater and find the difference between these two circumstances, and verify the relations between eddy-current loss and the physical parameters which are proposed in our theory. It can be learned from the experiment that when transmission distance is 50 mm and transmission power is 100 W in the air, the transmission efficiency is over 80%, and when transmission distance is 50 mm and transmission power is 100 W in seawater, the transmission efficiency is over 67%. Apparently, our magnetic-resonance-coupling-based CPT system has potentials serving as an underwater vehicle.

#### 参考文献

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#### 施引文献

•  [1] Ho Y L, McCormick D, Budgett D, Hu A P 2013 IEEE International Symposium on Circuits and Systems Beijing, China, May 19-23, 2013 p2787 [2] Sibue J R, Meunier G, Ferrieux J P, Roudet J, Periot R 2013 IEEE Trans. Magn. 49 586 [3] Ping S 2008 Ph. D. Dissertation (Auckland: The University of Auckland) [4] Yang Z, Liu W T, Basham E 2007 IEEE Trans. Magn. 43 3851 [5] Covic G A, Boys J T, Lu H G 2006 Proceedings of the 1st IEEE Conference on Industrial Electronics and Applications Singapore, May 24-26, 2006 p466 [6] Dehennis A D, Wise K D 2005 J. Microelectromech. Syst. 14 12 [7] Kurs A, Karalis A, Moffatt R, Joannopoulos J D, Fisher P, Soljacic M 2007 Science 317 83 [8] Teck C B, Kato M, Imura T, Sehoon O, Hori Y 2013 IEEE Trans. Ind. Electron. 60 3689 [9] Juseop L, Lim Y S, Yang W J, Lim S O 2014 IEEE Trans. Antennas Propag. 62 889 [10] Lim Y, Tang H, Lim S, Park J 2014 IEEE Trans. Power Electron. 29 4403 [11] Fukuda H, Kobayashi N, Shizuno K, Yoshida S, Tanomura M, Hama Y 2013 IEEE International Underwater Technology Symposium Tokyo, Japan March 5-8, 2013 p1 [12] Shizuno K, Yoshida S, Tanomura M, Hama Y 2014 IEEE Oceans Newfoundland Labrador, Canada, September 14-19, 2014 p1 [13] Itoh R, Sawahara Y, Ishizaki T, Awai I 2014 IEEE 3rd Global Conference on Consumer Electronics Tokyo, Japan October 7-10, 2014 p459 [14] Zhou J, Li D J, Chen Y 2013 J. Ocean Eng. 60 175 [15] Chen X L, Lei Y Z 2015 Chin. Phys. B 24 030301 [16] Li Y, Li Z, Shen Y, Ren M 2011 Third International Conference on Measuring Technology and Mechatronics Automation Shanghai, China, Jan. 6-7, 2011 p490 [17] Zhu Q W, Wang L F, Liao C L, Guo Y J 2014 IEEE Conference and Expo Transportation Electrification Asia-Pacific Beijing, China, August 31-September 3, 2014 p1 [18] Su Y G, Tang C S, Wu S P, Sun Y 2006 Proceedings of the International Conference on Power System Technology Chongqing, China, October 22-26, 2006 p794 [19] Sun Y, Xia C Y, Zhao Z B, Zhai Y, Yang F X 2011 Adv. Technol. Electr. Eng. Energy 30 9 (in Chinese) [孙跃, 夏晨阳, 赵志斌, 翟渊, 杨芳勋 2011 电工电能新技术 30 9] [20] Karalis A, Joannopoulos J D, Soljacic M 2008 Ann. Phys. 323 34 [21] Lei Y Z 2000 The Analysis Method of the Time-varying Electromagnetic Field (Beijing: Science Press) p96 (in Chinese) [雷银照 2000 时谐电磁场解析方法 (北京: 科学出版社) 第96页] [22] Wu J S, Wu C Y, Zhang R G 2014 Eddy Current Technology and Application (Changsha: Central South University Press) p209 (in Chinese) [吴桔生, 吴承燕, 张荣刚 2014 电涡流技术与应用 (长沙: 中南大学出版社) 第209页] [23] Yan J C 2013 The Theory of Electromagnetic (Hefei: Universityof Science and Technology of China) p304 (in Chinese) [严济慈 2013 电磁学 (合肥: 中国科技大学出版社) 第304页] [24] Li Y 2012 Ph. D. Dissertation (Hebei: Hebei University of Technology) (in Chinese) [李阳 2012 博士学位论文(河北: 河北工业大学)]
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##### 出版历程
• 收稿日期:  2015-09-11
• 修回日期:  2015-12-14
• 刊出日期:  2016-02-05

## 基于磁共振的水下非接触式电能传输系统建模与损耗分析

• 1. 西北工业大学航海学院, 西安 710072

/