Compensation Strategy for Static End Effect in Nest-Loop Secondary Linear Doubly-Fed Machine
Bao Zhen1, Ge Jian1, Xu Wei1, Zhang Yaping1, Li Weiye2, Lin Guobin3, Su Shihu4, Liu Zhicheng5, Yuan Wenye6
1. State Key Laboratory of Advanced Electromagnetic Technology Huazhong University of Science and Technology Wuhan 430074 China; 2. Xiangyang CRRC Motor Technology Co. Ltd Xiangyang 441047 China; 3. Maglev Transportation Engineering R&D Center Tongji University Shanghai 201804 China; 4. CRRC Zhuzhou Motor Co. Ltd Zhuzhou 412001 China; 5. Guangzhou Metro Group Co. Ltd Guangzhou 510330 China; 6. Zhuzhou CRRC Times Electric Co. Ltd Zhuzhou 412001 China
Abstract:At present, linear induction machines (LIMs) and linear synchronous machines (LSMs) are mainly used for linear traction system adopted to urban rail transit. As a new type of linear machine, the nest-loop secondary linear doubly-fed machine (NLS-LDFM) and its drive system have gradually attracted the attention of scholars for its advantages of adjustable power factor and flexible operation mode. However, the static end effect exists in NLS-LDFM due to the cut-open primary iron core. It generates the pulsating magnetic field which is evenly distributed along the direction of motion. The phenomenon not only leads to two sets of asymmetrical three-phase windings but also direct-coupling between them. Therefore, the static end effect can produce both negative-sequence current and direct-coupling current in the primary windings. Therein, the negative-sequence current can produce negative thrust, which can weaken the average thrust. And the direct-coupling current does not produce effective thrust or active power. Thus, the static end effect will lead to the reduction of power factor and efficiency in the NLS-LDFM. Firstly, based on the law of static end effect and the working principle of NLS-LDFM, the main components of harmonic current generated by static end effect are analyzed. Most of the harmonic currents generated by the static end effect can be compensated by suppressing the fundamental negative-sequence current and direct-coupling current. Secondly, based on the analysis of static end effect pulsating inductance matrix and direct-coupling mutual inductance matrix, the expression of pulsating electromotive force is derived. It can be compensated to the primary windings as feedforward voltage to suppress the negative-sequence current and direct-coupling current. Thirdly, a mixed second- and third-order generalized integrator (MSTOGI) is used to extract fundamental current and direct-coupling current to improve the compensation accuracy. The corresponding positive- and negative-sequence components are obtained by using instantaneous symmetric component method. Finally, the effectiveness of proposed compensation strategy is verified by simulation and experiment. The simulation results show that when the static end effect compensation strategy is not adopted, the three-phase current is very asymmetrical, indicating that the negative-sequence current is of high content. After applying the static end effect compensation strategy, the negative sequence current is effectively suppressed and the three-phase current becomes more symmetrical. By fast Fourier transform analysis of C-phase current of power winding, the current content of direct-coupling decreases from 12.0% to 3.1% after compensation. In experiments, the asymmetry of three-phase current in the power winding decreases from 27.7% to 3.9%, and the content of direct-coupling current decreases from 11.4% to 5.8%. The following conclusions can be drawn from the simulation and experiment analysis: (1) The static end effect of NLS-LDFM will generate harmonic current and negative-sequence current of various frequencies, of which the fundamental negative-sequence current and direct-coupling current are the main components. (2) The proposed current control process based MSTOGI and pulsating voltage feedforward can suppress the fundamental negative-sequence current and direct-coupling current, which can effectively compensate the static end effect in NLS-LDFM.
包振, 葛健, 徐伟, 张娅平, 李伟业, 林国斌, 苏诗湖, 刘智成, 袁文烨. 同心笼次级直线双馈电机静态端部效应补偿策略[J]. 电工技术学报, 2023, 38(17): 4621-4632.
Bao Zhen, Ge Jian, Xu Wei, Zhang Yaping, Li Weiye, Lin Guobin, Su Shihu, Liu Zhicheng, Yuan Wenye. Compensation Strategy for Static End Effect in Nest-Loop Secondary Linear Doubly-Fed Machine. Transactions of China Electrotechnical Society, 2023, 38(17): 4621-4632.
[1] 范瑜, 李文球, 杨中平. 国外直线电机轮轨交通[M]. 北京: 中国科学技术出版社, 2010. [2] 曹瑞武, 苏恩超, 张学. 轨道交通用次级分段型直线磁通切换永磁电机研究[J]. 电工技术学报, 2020, 35(5): 1001-1012. Cao Ruiwu, Su Enchao, Zhang Xue.Investigation of linear flux-switching permanent magnet motor with segmented secondary for rail transit[J]. Transactions of China Electrotechnical Society, 2020, 35(5): 1001-1012. [3] Xu Wei, Sun Guangyong, Wen Guilin, et al.Equivalent circuit derivation and performance analysis of a single-sided linear induction motor based on the winding function theory[J]. IEEE Transactions on Vehicular Technology, 2012, 61(4): 1515-1525. [4] 吕刚. 直线电机在轨道交通中的应用与关键技术综述[J]. 中国电机工程学报, 2020, 40(17): 5665-5674. Lü Gang.Review of the application and key technology in the linear motor for the rail transit[J]. Proceedings of the CSEE, 2020, 40(17): 5665-5674. [5] 徐伟, 肖新宇, 董定昊, 等. 直线感应电机效率优化控制技术综述[J]. 电工技术学报, 2021, 36(5): 902-915, 934. Xu Wei, Xiao Xinyu, Dong Dinghao, et al.Review on efficiency optimization control strategies of linear induction machines[J]. Transactions of China Electrotechnical Society, 2021, 36(5): 902-915, 934. [6] Lü Gang, Zhang Zhixuan, Li Xiaodong.Three-dimensional electromagnetic characteristics analysis of novel linear synchronous motor under lateral and yaw conditions of MAGLEV[J]. CES Transactions on Electrical Machines and Systems, 2022, 6(1): 29-36. [7] Kang Jinsong, Mu Siyuan, Ding Hao.Long stator linear doubly-fed motor for high-speed maglev integrated suspension, propulsion and contactless power supply[C]//2021 13th International Symposium on Linear Drives for Industry Applications (LDIA), Wuhan, China, 2021: 1-5. [8] 曾志凌. 城轨列车双馈直线驱动电机电磁计算与设计[D]. 成都: 西南交通大学, 2015. [9] Yang Bo, Henke M, Grotstollen H.Pitch analysis and control design for the linear motor of a railway carriage[C]//Conference Record of the 2001 IEEE Industry Applications Conference. 36th IAS Annual Meeting (Cat. No.01CH37248), Chicago, IL, USA, 2002: 2360-2365. [10] Seifkhani F.Investigation, analysis and design of the linear brushless doubly-fed machine[D]. Corvallis: Oregon State University, 1991. [11] Saifkhani F, Wallace A K.A linear brushless doubly-fed machine drive for traction applications[C]//1993 Fifth European Conference on Power Electronics and Applications, Brighton, UK, 2002: 344-348. [12] 葛健. 同心笼次级直线双馈电机端部效应及运行特性分析[D]. 武汉: 华中科技大学, 2019. [13] 刘慧娟, 马杰芳, 张千, 李雨蔓. 双边型长初级直线感应电机电磁推力特性研究[J]. 中国电机工程学报, 2019, 39(增刊1): 268-277. Liu Huijuan, Ma Jiefang, Zhang Qian, Li Yuman.Research on electromagnetic thrust characteristic of double sided long primary linear induction motor[J]. Proceedings of the CSEE, 2019, 39(S1): 268-277. [14] Liu Gang, Chen Baodong, Wang Kun, et al.Selective Current harmonic suppression for high-speed PMSM based on high-precision harmonic detection method[J]. IEEE Transactions on Industrial Informatics, 2019, 15(6): 3457-3468. [15] 张海洋, 许海平, 方程, 等. 基于比例积分-准谐振控制器的直驱式永磁同步电机转矩脉动抑制方法[J]. 电工技术学报, 2017, 32(19): 41-51. Zhang Haiyang, Xu Haiping, Fang Cheng, et al.Torque ripple suppression method of direct-drive permanent magnet synchronous motor based on proportional-integral and quasi resonant controller[J]. Transactions of China Electrotechnical Society, 2017, 32(19): 41-51. [16] 钟再敏, 江尚, 康劲松, 等. 永磁同步电机谐波电压与电流的耦合模型及前馈控制[J]. 电工技术学报, 2017, 32(18): 131-142. Zhong Zaimin, Jiang Shang, Kang Jinsong, et al.A harmonic voltage and current coupling permanent magnet synchronous motor model and feedforward control[J]. Transactions of China Electrotechnical Society, 2017, 32(18): 131-142. [17] 郭小强. 光伏并网逆变器通用比例复数积分控制策略[J]. 中国电机工程学报, 2015, 35(13): 3393-3399. Guo Xiaoqiang.Generalized proportional complex integral control scheme for PV grid-connected inverters[J]. Proceedings of the CSEE, 2015, 35(13): 3393-3399. [18] 武永燎, 李红, 宋欣达, 等. 基于改进型重复控制器的永磁同步电机电流谐波抑制方法研究[J]. 电工技术学报, 2019, 34(11): 2277-2286. Wu Yongliao, Li Hong, Song Xinda, et al.Suppression of harmonic current in permanent magnet synchronous motors using improved repetitive controller[J]. Transactions of China Electrotechnical Society, 2019, 34(11): 2277-2286. [19] Ge Jian, Xu Wei, Liu Yi, et al.Investigation on winding theory for short primary linear machines[J]. IEEE Transactions on Vehicular Technology, 2021, 70(8): 7400-7412. [20] 闫光亚, 艾武, 陈冰, 等. 永磁直线同步电机ADRC控制系统[J]. 电工技术学报, 2011, 26(9): 60-66. Yan Guangya, Ai Wu, Chen Bing, et al.PMLSM active disturbance rejection control[J]. Transactions of China Electrotechnical Society, 2011, 26(9): 60-66. [21] Zhao Rende, Xin Zhen, Loh P C, et al.A novel flux estimator based on multiple second-order generalized integrators and frequency-locked loop for induction motor drives[J]. IEEE Transactions on Power Electronics, 2017, 32(8): 6286-6296. [22] Zhang Chunjiang, Zhao Xiaojun, Wang Xiaohuan, et al.A grid synchronization PLL method based on mixed second- and third-order generalized integrator for DC offset elimination and frequency adaptability[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2018, 6(3): 1517-1526. [23] Rodríguez P, Luna A, Muñoz-Aguilar R S, et al. A stationary reference frame grid synchronization system for three-phase grid-connected power converters under adverse grid conditions[J]. IEEE Transactions on Power Electronics, 2012, 27(1): 99-112. [24] Xu Wei, Yu Kailiang, Liu Yi, et al.Improved coordinated control of standalone brushless doubly fed induction generator supplying nonlinear loads[J]. IEEE Transactions on Industrial Electronics, 2019, 66(11): 8382-8393.