Abstract：The doubly salient electro-magnetic machine (DSEM) has been proposed by introducing additional field windings on the stator of the switched reluctance motor (SRM). Therefore, the DSEM has a simple and reliable structure and flexible flux-regulation ability, suitable for wide-speed range operation. However, due to the non-sinusoidal back electromotive force (EMF) of DSEM, the phase current has significant 2nd and 4th current harmonics under the conventional sinusoidal current control method. The 2nd and 4th current harmonics will deteriorate the torque capability of the DSEM. Meanwhile, the high harmonic frequency of the DSEM makes the conventional quasi-proportional resonant (PR) controller have considerable resonance frequency deviation under the conventional discretization method. Thus, this paper proposes an improved quasi-PR control based on the discretization method with zero resonance frequency deviation. Firstly, the production mechanism of the current harmonics is analyzed with the help of the back-EMF characteristics of DSEM. Then, the average torque model of the DSEM, considering the current and back-EMF harmonics, is derived. Secondly, the operation principle of quasi-PR control is introduced, and the influence of the control parameter is analyzed through a bode diagram. Then, the equation of resonance frequency deviation under the conventional bilinear transform is derived. The discretization method with zero resonance frequency deviation is proposed by introducing the compensation coefficient based on the bilinear transform. Furthermore, the improved discretization equation is simplified by replacing the tangent function with a polynomial function. The amplitude-frequency response shows that the improved quasi-PR controller can effectively compensate for the resonance frequency deviation. Finally, the current harmonics suppression method of DSEM based on improved quasi-PR control is introduced, and the simulation and experiments are carried out to verify the performance. The performance of improved quasi-PR control is compared with the performance of PI control and conventional quasi-PR control through simulation and experimental results. Firstly, the simulation and experimental results at rated speed show that the phase current has nonnegligible 2nd and 4th harmonics under PI control. The conventional quasi-PR control can reduce the phase current harmonics to some extent. However, due to resonance frequency deviation, there is still considerable phase current harmonics under conventional quasi-PR control. The improved quasi-PR control can effectively suppress the phase current harmonics by compensating the resonance frequency deviation. Secondly, the simulation and experimental results at different speeds show that the improved quasi-PR control proposed in this paper can obtain much lower phase current harmonics than PI control and conventional quasi-PR control. Finally, based on the torque model, the influence of current harmonics on average torque is analyzed. The results show that the uncontrollable current harmonics under PI control contribute to the negative average torque. The improved quasi-PR control can eliminate the negative average torque by suppressing the current harmonics. Therefore, the improved quasi-PR control can suppress the current harmonics and enhance the torque capability of DSEM. The following conclusions can be drawn from the simulation and experimental results: (1) The high fundamental frequency of DSEM leads to significant resonance frequency deviation and deteriorates the current harmonics suppression performance of conventional quasi-PR control. (2) The improved quasi-PR control proposed in this paper can compensate for the resonance frequency deviation and suppress current harmonics. The 2nd and 4th harmonics contents under PI control are 23.50 % and 14.16 %. The 2nd and 4th harmonic contents under improved quasi-PR control are 1.76 % and 3.31 %. (3) The uncontrollable current harmonics under PI control contribute negative average torque. The improved quasi-PR control can effectively suppress the current harmonics, and the torque ampere ratio of DSEM can be enhanced by 10.6 %.
[1] Liu Chuang, Zhou Bo, Yan Yangguang.Imple- mentation and study of a novel doubly salient structure starter/generator system[J]. Chinese Journal of Aeronautics, 2002, 15(3): 150-155. [2] Yu Li, Zhang Zhuoran, Chen Zhihui, et al.Analysis and verification of the doubly salient brushless DC generator for automobile auxiliary power unit appli- cation[J]. IEEE Transactions on Industrial Electronics, 2014, 61(12): 6655-6663. [3] Benzaquen J, He Jiangbiao, Mirafzal B.Toward more electric powertrains in aircraft: technical challenges and advancements[J]. CES Transactions on Electrical Machines and Systems, 2021, 5(3): 177-193. [4] Jia Wanying, Xiao Lan, Wang Chuyang, et al.Self- tuning control of advanced angles for doubly salient motor drive system[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2020, 8(2): 1236-1247. [5] Wang Yin, Zhang Zhuoran, Liang Rui, et al.Torque density improvement of doubly salient electro- magnetic machine with asymmetric current control[J]. IEEE Transactions on Industrial Electronics, 2016, 63(12): 7434-7443. [6] Bian Zhangming, Zhang Zhuoran, Yu Li.Syn- chronous commutation control of doubly salient motor drive with adaptive angle optimization[J]. IEEE Transactions on Power Electronics, 2020, 35(6): 6070-6081. [7] Zhang Jian, Xia Yiwen, Zhang Zhuoran, et al.Influence of driving mode on loss characteristics of doubly salient brushless motor with rectangular wire armature winding[J]. IEEE Transactions on Magnetics, 2022, 58(2): 1-6. [8] Yu Zixiang, Li Dawei, Kong Wubin, et al.New optimal current control strategy for six-phase DC- biased vernier reluctance machines considering distorted EMF[J]. IEEE Transactions on Power Electronics, 2018, 33(12): 10633-10645. [9] 肖阳, 宋金元, 屈仁浩, 等. 变频谐波对电机振动噪声特性的影响规律[J]. 电工技术学报, 2021, 36(12): 2607-2615. Xiao Yang, Song Jinyuan, Qu Renhao, et al.The effect of harmonics on electromagnetic vibration and noise characteristic in inverter-duty motor[J]. Transa- ctions of China Electrotechnical Society, 2021, 36(12): 2607-2615. [10] 陈少先, 丁树业, 申淑锋, 等. 船舶用表贴式永磁同步电机的电磁振动分析与抑制[J]. 电工技术学报, 2023, 37(5): 1275-1286, 1298. Chen Shaoxian, Ding Shuye, Shen Shufeng, et al.Analysis and suppression of electromagnetic vibration of surface mounted permanent magnet synchronous motor for ships[J]. Transactions of China Electro- technical Society, 2023, 37(5): 1275-1286, 1298. [11] 石恒星, 陈世元. 转子斜槽电磁式双凸极电机的有限元分析[J]. 微电机, 2013, 46(2): 16-19. Shi Hengxing, Chen Shiyuan.Finite element analysis of doubly salient electro-magnetic motor based on rotor skewing[J]. Micromotors, 2013, 46(2): 16-19. [12] Kong Wubin, Yu Zixiang, Li Dawei, et al.Com- parative study of harmonic current suppression control strategies for six-phase DC-biased vernier reluctance machines[J]. IEEE Transactions on Indu- stry Applications, 2018, 54(6): 5843-5855. [13] 李帅, 孙立志, 刘兴亚, 等. 永磁同步电机电流谐波抑制策略[J]. 电工技术学报, 2019, 34(增刊1): 87-96. Li Shuai, Sun Lizhi, Liu Xingya, et al.Current harmonics suppression strategies of permanent mag- net synchronous motor[J]. Transactions of China Electrotechnical Society, 2019, 34(S1): 87-96. [14] 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 syn- chronous motors using improved repetitive con- troller[J]. Transactions of China Electrotechnical Society, 2019, 34(11): 2277-2286. [15] 王贺超, 夏长亮, 阎彦, 等. 基于谐振控制的表贴式永磁同步电机弱磁区电流谐波抑制[J]. 电工技术学报, 2014, 29(9): 83-91. Wang Hechao, Xia Changliang, Yan Yan, et al.Current harmonic suppression in the flux-weakening control of surface permanent magnet synchronous motors using resonant controllers[J]. Transactions of China Electrotechnical Society, 2014, 29(9): 83-91. [16] Hu Mingjin, Hua Wei, Wang Zuo, et al.Selective periodic disturbance elimination using extended harmonic state observer for smooth speed control in PMSM drives[J]. IEEE Transactions on Power Electronics, 2022, 37(11): 13288-13298. [17] 徐卿瀚, 蒙显辉, 杨苓, 等. 直流微电网储能系统的NF+QPR+LPF双闭环2次谐波电流抑制方法[J]. 电工技术学报, 2022, 37(20): 5188-5200. Xu Qinghan, Meng Xianhui, Yang Ling, et al.NF+ QPR+LPF double closed loop second harmonic current suppression method for DC microgrid energy storage system[J]. Transactions of China Electro- technical Society, 2022, 37(20): 5188-5200. [18] 麦志勤, 肖飞, 刘计龙, 等. 基于准比例谐振级联PI的双三相永磁同步电机谐波电流抑制策略[J]. 电工技术学报, 2018, 33(24): 5751-5759. Mai Zhiqin, Xiao Fei, Liu Jilong, et al.Harmonic Current suppression strategy of dual three-phase permanent magnet synchronous motor based on quasi proportional resonant cascading PI[J]. Transactions of China Electrotechnical Society, 2018, 33(24): 5751-5759. [19] 杨才伟, 王剑, 游小杰, 等. 二阶广义积分器锁频环数字实现准确性对比[J]. 电工技术学报, 2019, 34(12): 2584-2596. Yang Caiwei, Wang Jian, You Xiaojie, et al.Accuracy comparison of digital implementation on the second-order generalized integrator frequency- locked loop[J]. Transactions of China Electro- technical Society, 2019, 34(12): 2584-2596. [20] 刘亚静, 段超. 全数字自适应滤波器不同离散结构的性能对比分析[J]. 电工技术学报, 2021, 36(20): 4339-4349. Liu Yajing, Duan Chao.Performance comparison and analysis of all-digital adaptive filter with different discrete methods[J]. Transactions of China Electro- technical Society, 2021, 36(20): 4339-4349. [21] 曾君, 岑德海, 陈润, 等. 针对直流偏移和谐波干扰的单相锁相环[J]. 电工技术学报, 2021, 36(16): 3504-3515. Zeng Jun, Cen Dehai, Chen Run, et al.Single-phase phase-locked loop for DC offset and harmonic inter- ference[J]. Transactions of China Electrotechnical Society, 2021, 36(16): 3504-3515. [22] 魏艺涵, 罗响, 朱莉, 等. 基于比例谐振控制器的高凸极率永磁同步电机电流谐波抑制策略研究[J]. 中国电机工程学报, 2021, 41(7): 2526-2538. Wei Yihan, Luo Xiang, Zhu Li, et al.Research on current harmonic suppression strategy of high saliency ratio permanent magnet synchronous motor based on proportional resonance controller[J]. Pro- ceedings of the CSEE, 2021, 41(7): 2526-2538. [23] 王恩德, 黄声华. 表贴式永磁同步电机伺服系统电流环设计[J]. 中国电机工程学报, 2012, 32(33): 82-88, 179. Wang Ende, Huang Shenghua.Current regulator design for surface permanent magnet synchronous motor servo systems[J]. Proceedings of the CSEE, 2012, 32(33): 82-88, 179. [24] 杨淑英, 刘世园, 李浩源, 等. 永磁同步电机无位置传感器控制谐波抑制策略研究[J]. 中国电机工程学报, 2019, 39(20): 6075-6084, 6188. Yang Shuying, Liu Shiyuan, Li Haoyuan, et al.Research on harmonic suppression strategy of position sensorless control for permanent magnet synchronous motor[J]. Proceedings of the CSEE, 2019, 39(20): 6075-6084, 6188. [25] Huang Mingfei, Deng Yongting, Li Hongwen, et al.Torque ripple suppression of PMSM using fractional- order vector resonant and robust internal model control[J]. IEEE Transactions on Transportation Electrification, 2021, 7(3): 1437-1453. [26] Hu Mingjin, Hua Wei, Ma Guangtong, et al.Improved current dynamics of proportional-integral-resonant controller for a dual three-phase FSPM machine[J]. IEEE Transactions on Industrial Electronics, 2021, 68(12): 11719-11730.
2023, Vol. 38 
