Abstract：The small stator inductance of a high-speed permanent magnet synchronous motor (PMSM) results in significant phase current ripple due to pulse width modulation (PWM). Installing an LC filter at the inverter output can effectively suppress this adverse effect, forming an LC-filtered PMSM drive system (LC-PMSM). However, the LC filter and stator inductance can cause LCL resonance, which significantly affects system stability. Active damping is necessary to suppress resonance and stabilize the system. The filter-based active damping method is widely used due to its simple structure and ease of parameter design. However, there is a lack of criteria for selecting, evaluating, and designing active damping filters. This paper proposes a general graphical method to assess the resonance-suppression performance of active damping filters for inverter-side current feedback in LC-PMSM systems. The robustness to resonance-frequency drift and the stability regions of the traditional notch filter (NF), low-pass filter (LPF), delay filter (DF), and all-pass filter (APF) are compared. Thus, the influence of filter-based active damping on system resonance phenomena is revealed. APF has the widest stability region and does not alter the system's amplitude-frequency characteristics, making it the most suitable for inverter-side current feedback control. Accordingly, this paper proposes a resonance suppression method by reshaping the phase-frequency characteristic. Furthermore, using a discrete- domain transfer function model and stability margin indices, a detailed parameter design approach for the APF is presented. Simulations and experiments were conducted. Simulation results show that compared with NF, LPF, and DF active damping, the proposed APF active damping method maintains stability across the whole speed range under parameter variations. Experimental results show that the proposed APF active damping method maintains stability under large-scale speed variations. It exhibits better harmonic current suppression at the resonant frequency than existing filter-based active damping methods, with lower total harmonic distortion (THD) and lower current ripple. Multi-parameter robustness analysis shows that the unstable system rapidly stabilizes after APF active damping and remains stable across the speed range when multiple LC-PMSM parameters are simultaneously varied. The tolerating individual deviations are ±50% in motor inductance and ±20% in LC filter parameters. Moreover, it can simultaneously accommodate combined variations of ±15% in LC filter parameters and (-30% to +50%) in motor inductance parameters. The following conclusions can be drawn. (1) For inverter side current feedback, the proposed general graphical method effectively evaluates the robustness to resonance frequency drift and stability regions of different active damping filters. (2) The proposed resonance suppression method based on APF phase-frequency characteristic reshaping requires no additional sensors and effectively suppresses LCL resonance by adjusting the APF parameters only. (3) At the whole speed range, the proposed method exhibits good parameter robustness, tolerating simultaneous variations in multiple system parameters.
[1] 罗力岩, 樊启高. 一种改进型永磁同步电机无模型预测电流控制策略[J]. 电工技术学报, 2025, 40(4): 1034-1045. Luo Liyan, Fan Qigao.An improved model-free predictive current control strategy for permanent magnet synchronous motors[J]. Transactions of China Electrotechnical Society, 2025, 40(4): 1034-1045. [2] 徐海, 米彦青, 王艳阳, 等. 带有参数在线辨识的永磁同步电机模型预测控制研究[J]. 电气传动, 2025, 55(2): 3-12. Xu Hai, Mi Yanqing, Wang Yanyang, et al.Model predictive control study of permanent magnet synchronous motor with parameters online identi- fication[J]. Electric Drive, 2025, 55(2): 3-12. [3] 陈瑞, 吴悠, 杜荣华, 等. 一种基于特征模型的永磁同步电机协调控制策略[J]. 电气工程学报, 2025, 20(1): 54-64. Chen Rui, Wu You, Du Ronghua, et al.A coordinated control strategy for the permanent magnet syn- chronous motor based on the characteristic model[J]. Journal of Electrical Engineering, 2025, 20(1): 54-64. [4] 刘刚, 张婧, 郑世强, 等. 基于参数在线辨识的高速永磁电机无差拍电流预测控制[J]. 电机与控制学报, 2023, 27(9): 98-108. Liu Gang, Zhang Jing, Zheng Shiqiang, et al.Deadbeat predictive current control of high speed permanent magnet motor based on online parameter identification[J]. Electric Machines and Control, 2023, 27(9): 98-108. [5] 佟文明, 杨先凯, 鹿吉文, 等. 双层永磁体结构高速永磁电机转子涡流损耗解析模型[J]. 电工技术学报, 2024, 39(20): 6293-6304. Tong Wenming, Yang Xiankai, Lu Jiwen, et al.Rotor eddy current loss analytical model for high-speed permanent magnet motor based on double layer permanent magnet structure[J]. Transactions of China Electrotechnical Society, 2024, 39(20): 6293-6304. [6] 郑长明, 董萱萱, 肖子语, 等. 基于虚拟电阻有源阻尼的LC滤波型永磁同步电机系统预测电流控制[J]. 电工技术学报, 2023, 38(22): 6059-6069. Zheng Changming, Dong Xuanxuan, Xiao Ziyu, et al.Virtual resistance active damping based predictive current control of LC-filtered permanent magnet synchronous motor system[J]. Transactions of China Electrotechnical Society, 2023, 38(22): 6059-6069. [7] 吕立傲, 胡存刚, 芮涛, 等. 基于无模型预测与无参数参考的LC型滤波逆变器三矢量预测控制方法[J]. 电工技术学报, 2025, 40(16): 5306-5316. Lü Li’ao, Hu Cungang, Rui Tao, et al.Model-free prediction and parameter-less reference based on LC- filtered voltage source inverter triple-vector predi- ctive control[J]. Transactions of China Electrotech- nical Society, 2025, 40(16): 5306-5316. [8] 李耀华, 王孝宇, 吴庭旭, 等. 带LC滤波器的永磁同步电机多步模型预测电流控制[J]. 电机与控制应用, 2024, 51(11): 21-31. Li Yaohua, Wang Xiaoyu, Wu Tingxu, et al.Multi- step model predictive current control of permanent magnet synchronous motor with LC filter[J]. Electric Machines & Control Application, 2024, 51(11): 21-31. [9] Kukkola J, Hinkkanen M, Kai Zenger.Observer- based state-space current controller for a grid con- verter equipped with an LCL filter: analytical method for direct discrete-time design[J]. IEEE Transactions on Industry Applications, 2015, 51(5): 4079-4090. [10] Parker S G, McGrath B P, Holmes D G. Regions of active damping control for LCL filters[J]. IEEE Transactions on Industry Applications, 2014, 50(1): 424-432. [11] 吴翔, 李超, 刘志恒, 等. 带有LC正弦波滤波器的内置式永磁同步电机电流控制器谐振抑制参数设计[J]. 电工技术学报, 2023, 38(22): 6082-6093. Wu Xiang, Li Chao, Liu Zhiheng, et al.Parameter design of the current controller for interior permanent magnet synchronous motor with LC sinusoidal filter to suppress resonance[J]. Transactions of China Electrotechnical Society, 2023, 38(22): 6082-6093. [12] 周佳新, 姚宇, 彭飞, 等. 带LLCL滤波器的高速永磁同步电机低载波比电流阻尼控制器设计[J]. 中国电机工程学报, 2025, 45(19): 7743-7755. Zhou Jiaxin, Yao Yu, Peng Fei, et al.Current damping controller for high-speed permanent magnet synchronous motor with LLCL filter in conditions with low carrier ratio[J]. Proceedings of the CSEE, 2025, 45(19): 7743-7755. [13] Yao Wenli, Yang Yongheng, Zhang Xiaobin, et al.Design and analysis of robust active damping for LCL filters using digital Notch filters[J]. IEEE Transa- ctions on Power Electronics, 2017, 32(3): 2360-2375. [14] Yang Ming, Lü Zekai, Xu Donglin, et al.Resonance suppression and EMI reduction of GaN-based motor drive with sine wave filter[J]. IEEE Transactions on Industry Applications, 2020, 56(3): 2741-2751. [15] Lü Zekai, Wu Lijian.Resonant frequency deviation analysis and modified Notch filter-based active damping for SiC-based PMSM drive with sine wave filter[J]. IEEE Transactions on Energy Conversion, 2023, 38(1): 417-427. [16] Yao Wenli, Yang Yongheng, Xu Yan, et al.Phase reshaping via all-pass filters for robust LCL-filter active damping[J]. IEEE Transactions on Power Electronics, 2020, 35(3): 3114-3126. [17] Mahafugur Rahman F M, Pirsto V, Kukkola J, et al. State-space control for LCL filters: converter versus grid current measurement[J]. IEEE Transactions on Industry Applications, 2020, 56(6): 6608-6618. [18] Antivachis M, Niklaus P S, Bortis D, et al.Input/ output EMI filter design for three-phase ultra-high speed motor drive Gan inverter stage[J]. CPSS Transactions on Power Electronics and Applications, 2021, 6(1): 74-92. [19] Bae B H, Sul S K.A compensation method for time delay of full-digital synchronous frame current regulator of PWM AC drives[J]. IEEE Transactions on Industry Applications, 2003, 39(3): 802-810. [20] 胡寿松. 自动控制原理[M]. 7版. 北京: 科学出版社, 2019. [21] 王奇维, 李斌兴, 潘冠丞, 等. 基于转子位置误差解耦阻抗建模的永磁同步电机电感在线辨识方法[J]. 电工技术学报, 2025, 40(2): 439-451. Wang Qiwei, Li Binxing, Pan Guancheng, et al.Impedance model based online inductance identi- fication method of permanent magnet synchronous motor decoupled from rotor position error[J]. Transa- ctions of China Electrotechnical Society, 2025, 40(2): 439-451. [22] Yao Yu, Xu Dingkuan, Chen Yansong, et al.Robust Notch filter-based active damping design for LCL- equipped high-speed PMSMs considering dual reso- nance problem[J]. IEEE Transactions on Industrial Electronics, 2024, 71(11): 13845-13854.
2026, Vol. 41 
