Abstract：The linear phase-shifting transformer is a new type with the advantages of a simple winding structure, easy modularity, and shift phase ability at any angle. However, the linear structure can cause the end effect, distorting the air gap magnetic field of the linear phase-shifting transformer. Therefore, this paper analyzes the magnetic field of the linear phase-shifting transformer, establishes an equivalent circuit model to account for the end effect, and calculates the correction factor when the end effect is considered. Firstly, the end effect of the linear phase-shifting transformer is mainly considered: magnetic distortion in the air gap due to magnetic circuit asymmetry and magnetic circuit breaking. The end effect mainly affects the compound power transferred from the primary side to the air gap and the secondary side of the linear phase-shifting transformer, which can be reflected as a change in the equivalent impedance in the equivalent circuit model. Then, this paper calculates such end effect. Besides, the primary side of the T-type equivalent circuit is unaffected by the end effect, and the primary side’s equivalent resistance and equivalent reactance can be calculated according to the transformer's parameters. Based on the solved expressions for each parameter, the equivalent circuit model of the linear phase-shifting transformer, considering the end effect, can be established. Finally, a two-dimensional model of the linear phase-shifting transformer prototype is built based on Ansys Maxwell finite element simulation software, and an experimental platform with the same parameters as the simulation model is established. The accuracy of the equivalent circuit model is verified under five operating conditions: no load, 30% load, 50% load, 70% load, and rated load. Compared with the mathematical model calculated by the voltage equation of a magnetic chain, the equivalent circuit model has a simpler structure and is easier to calculate, which is more conducive to the subsequent optimization design. However, the equivalent circuit model based on the voltage balance of each phase has certain limitations. The method of the equivalent circuit model is proposed by analyzing the end effect of the linear phase-shifting transformer. This paper provides a reference for the magnetic field analysis, loss calculation, control strategy, and optimization design of the linear phase-shifting transformer. In addition, it is more convenient in the actual calculation and analysis.
赵镜红, 周长朵, 王涵铭, 严思念, 严冬傲. 计及边端效应的直线式移相变压器等效电路分析[J]. 电工技术学报, 2024, 39(6): 1792-1805.
Zhao Jinghong, Zhou Changduo, Wang Hanming, Yan Sinian, Yan Dongao. Equivalent Circuit Analysis of Linear Phase-Shifting Transformer Considering End Effect. Transactions of China Electrotechnical Society, 2024, 39(6): 1792-1805.
[1] 孟凡刚, 满忠诚, 高蕾, 等. 基于电力电子移相变压器的12脉波整流技术[J]. 电工技术学报, 2019, 34(18): 3865-3872. Meng Fangang, Man Zhongcheng, Gao Lei, et al.12-pulse rectification technology based on power electronic phase-shifting transformer[J]. Transactions of China Electrotechnical Society, 2019, 34(18): 3865-3872. [2] 洪乃刚. 电力电子技术基础[M]. 2版. 北京: 清华大学出版社, 2015. [3] 刘凤君. 现代逆变技术及应用[M]. 北京: 电子工业出版社, 2006. [4] 熊欣, 赵镜红, 丁洪兵, 等. 直线式移相变压器边端效应研究[J]. 西安交通大学学报, 2017, 51(8): 110-115. Xiong Xin, Zhao Jinghong, Ding Hongbing, et al.Reducing end effect impact on linear phase-shifting transformer[J]. Journal of Xi’an Jiaotong University, 2017, 51(8): 110-115. [5] 赵镜红, 许浩, 郭国强. 12/3相直线式移相变压器设计[J]. 海军工程大学学报, 2021, 33(4): 1-6. Zhao Jinghong, Xu Hao, Guo Guoqiang.Design of 12/3 phase linear phase-shifting transformer[J]. Journal of Naval University of Engineering, 2021, 33(4): 1-6. [6] 王铁军, 饶翔, 姜小弋, 等. 用于多重化逆变的移相变压器[J]. 电工技术学报, 2012, 27(6): 32-37. Wang Tiejun, Rao Xiang, Jiang Xiaoyi, et al.A phase-shift transformer applied in multi-module inverters[J]. Transactions of China Electrotechnical Society, 2012, 27(6): 32-37. [7] 王众, 赵镜红, 孙盼, 等. 平板式移相变压器的磁场分析[J]. 船电技术, 2014, 34(12): 35-38. Wang Zhong, Zhao Jinghong, Sun Pan, et al.Field analysis of flat phase-shifting transformer[J]. Marine Electric & electronic Engineering, 2014, 34(12): 35-38. [8] 葛健, 徐伟, 刘毅, 等. 考虑端部效应的同心笼次级直线双馈电机等效电路[J]. 电工技术学报, 2022, 37(19): 4957-4968. Ge Jian, Xu Wei, Liu Yi, et al.Equivalent circuit for nested-Loop secondary linear doubly-fed machine considering end effect[J]. Transactions of China Electrotechnical Society, 2022, 37(19): 4957-4968. [9] 赵镜红, 许浩, 孙盼, 等. 直线式移相变压器两类纵向边端效应分析[J]. 电工技术学报, 2021, 36(5): 984-995. Zhao Jinghong, Xu Hao, Sun Pan, et al.Research on two kinds of longitudinal side effects of linear phase-shifting transformer[J]. Transactions of China Electrotechnical Society, 2021, 36(5): 984-995. [10] 张梓铭, 赵镜红, 马远征, 等. 直线式移相变压器逆变系统的解析法建模[J]. 电气工程学报, 2019, 14(3): 54-60. Zhang Ziming, Zhao Jinghong, Ma Yuanzheng, et al.Analytical modeling of inverter system of linear phase-shift transformer[J]. Journal of Electrical Engineering, 2019, 14(3): 54-60. [11] Zare-Bazghaleh A, Naghashan M R, Khodadoost A.Derivation of equivalent circuit parameters for single- sided linear induction motors[J]. IEEE Transactions on Plasma Science, 2015, 43(10): 3637-3644. [12] Woronowicz K, Safaee A.A novel linear induction motor equivalent-circuit with optimized end effect model[J]. Canadian Journal of Electrical and Com- puter Engineering, 2014, 37(1): 34-41. [13] Amiri E, Mendrela E A.A novel equivalent circuit model of linear induction motors considering static and dynamic end effects[J]. IEEE Transactions on Magnetics, 2014, 50(3): 120-128. [14] Wang Hanming, Zhao Jinghong, Xue Jie, et al.Opti- mal design of a short primary double-sided linear induction motor based on derived Quasi-3D equi- valent circuit model using an improved differential evolution[J]. IET Electric Power Applications, 2022, 16(12): 1521-1541. [15] 龙遐令. 直线感应电动机等值电路的通用推导方法[J]. 电工技术学报, 1993, 8(4): 55-60. Long Xialing.A general method driving the equivalent circuit of linear induction motor[J]. Transactions of China Electrotechnical Society, 1993, 8(4): 55-60. [16] Mirsalim M, Doroudi A, Moghani J S.Obtaining the operating characteristics of linear induction motors: a new approach[J]. IEEE Transactions on Magnetics, 2002, 38(2): 1365-1370. [17] 龙遐令. 直线感应电动机的理论和电磁设计方法[M]. 北京: 科学出版社, 2006. [18] 吕刚, 罗志昆, 曾迪晖, 等. 次级断续时直线感应牵引电机的分段式等效电路与特性分析[J]. 电工技术学报, 2021, 36(5): 944-953. Lü Gang, Luo Zhikun, Zeng Dihui, et al.A piecewise equivalent circuit and characteristic analysis of linear induction traction motor when the secondary is discontinuous[J]. Transactions of China Electro- technical Society, 2021, 36(5): 944-953. [19] Gieras J F.Linear induction drives[M]. New York: Oxford University Press, 1994.
2024, Vol. 39 
