Abstract：The maximum torque per ampere (MTPA) control strategy can fully use the reluctance torque to output the maximum torque per unit stator current and improve the operating efficiency of interior permanent magnet synchronous motors (IPMSMs). Still, the traditional formula method or the high-frequency signal injection method requires the installation of at least two phase-current sensors to obtain the current information of the motor. Once the current sensor fails, the closed-loop control of the system will fail and cause unpredictable damage. The paper proposes an MTPA control strategy for IPMSM without current sensors. The strategy can accurately realize the MTPA control of the permanent magnet synchronous motor by calculating the optimal voltage control instruction only from the rotational speed information and the mathematical model of the system. Firstly, the relationship between the control voltage command and the rotational speed is calculated using the formula method according to the mathematical model of the IPMSM and the conditions of the MTPA control. Secondly, inverter nonlinearity can cause the inverter output voltage to deviate from the commanded voltage, resulting in the motor deviating from the MTPA operating point. Therefore, the mean value compensation method is proposed to compensate the command voltage for the nonlinearity. Thirdly, the effect of current estimation error on the calculated voltage compensation value is analyzed. The analysis shows that even if the current estimation error exists, the average error of the voltage compensation value based on the estimated current is still 0. Finally, the effect of parameter deviation on the control strategy is analyzed, and the influence of parameter deviation on the optimal voltage command amplitude and the response current is given. The experimental results for steady-state conditions show that the A-phase current fundamental wave amplitude of the motor with the proposed strategy is smaller than that with the traditional strategy. The effectiveness of the proposed method is verified. The experimental results at the same load torque under different speeds show that the current vector amplitude error of the MTPA control with the proposed method is small. Its maximum error does not exceeding 0.5%, while the traditional method is 14%~30%. The experimental results at the same speed with different load torques show that the current vector magnitude error of MTPA control with the proposed method is small, with the maximum error not exceeding 1%. In contrast, the traditional method’s maximum error is in the range of 2%~37%. The experimental results of dynamic operation and loaded starting conditions show that the proposed control strategy is robust to parameter deviations and has good dynamic performance. The following conclusions can be drawn. (1) The proposed method can realize MTPA control of IPMSM without current sensors, which is of great significance to the fault-tolerant control capability of current sensor failures in the IPMSM drive system. (2) The proposed method has good dynamic performance and is robust in the variation of motor parameters. (3) The proposed MTPA control strategy considers the effect of VSI nonlinearity, and the control voltages are compensated, effectively improving the running accuracy in MTPA.
[1] 肖飞, 许观达, 连传强, 等. 永磁同步电机单电流传感器系统的三相电流重构策略[J]. 电工技术学报, 2022, 37(7): 1609-1617. Xiao Fei, Xu Guanda, Lian Chuanqiang, et al.Three- phase current reconstruction strategy of permanent magnet synchronous machine drives using a single current sensor[J]. Transactions of China Electro- technical Society, 2022, 37(7): 1609-1617. [2] 王柄东, 王道涵, 王晓姬, 等. 交流调磁型永磁同步电机磁通协同调控最大转矩铜耗比控制[J]. 电工技术学报, 2024, 39(12): 3630-3645. Wang Bingdong, Wang Daohan, Wang Xiaoji, et al.A maximum torque per copper loss control for AC flux-regulation permanent magnet synchronous motor with magnetic flux co-regulation[J]. Transactions of China Electrotechnical Society, 2024, 39(12): 3630-3645. [3] Shakib S M S I, Xiao Dan, Dutta R, et al. An optimal maximum torque per active flux and field weakening operation for deadbeat direct torque control based IPMSM drive[J]. IEEE Transactions on Industry Applications, 2024, 60(2): 3210-3220. [4] Naganathan P, Srinivas S.MTPA associated DTC methodologies for enhanced performance and energy savings in electric vehicle mobility with induction motor drive[J]. IEEE Transactions on Transportation Electrification, 2022, 8(2): 1853-1862. [5] 许水清, 许晓凡, 何怡刚, 等. 基于自适应滑模观测器的中点钳位型三电平并网逆变器开关管和电流传感器故障诊断[J]. 电工技术学报, 2024, 39(13): 4066-4078. Xu Shuiqing, Xu Xiaofan, He Yigang, et al.A diagnosis method for power switch and current sensor faults in grid-connected three-level neutral-point clamped inverters based on adaptive sliding mode observer[J]. Transactions of China Electrotechnical Society, 2024, 39(13): 4066-4078. [6] 孙元统, 巩建英, 张震, 等. 基于转矩反馈补偿的永磁同步电机MTPA控制[J]. 微电机, 2023, 56(1): 35-40. Sun Yuantong, Gong Jianying, Zhang Zhen, et al.MTPA control of permanent magnet synchronous motor based on torque feedback compensation[J]. Micromotors, 2023, 56(1): 35-40. [7] Yoo J, Kim H S, Sul S K.MTPA tracking control of sensorless IPMSM based on square-wave voltage signal injection[J]. IEEE Transactions on Power Electronics, 2022, 37(10): 12525-12537. [8] An Xingke, Liu Guohai, Chen Qian, et al.Adjustable model predictive control for IPMSM drives based on online stator inductance identification[J]. IEEE Transactions on Industrial Electronics, 2022, 69(4): 3368-3381. [9] 陈前, 顾理成, 赵文祥, 等. 采用VSIC-MTPA的五相内嵌式永磁容错电机短路容错控制[J]. 中国电机工程学报, 2020, 40(21): 7087-7094. Chen Qian, Gu Licheng, Zhao Wenxiang, et al.A short-circuit fault-tolerant control for five-phase IPMFTM by adopting virtual-signal-injection-based MTPA[J]. Proceedings of the CSEE, 2020, 40(21): 7087-7094. [10] 金宁治, 周凯, Herbert Ho-Ching Iu. 带有自适应参数辨识的IPMSM MTPA控制[J]. 电机与控制学报, 2020, 24(7): 90-101. Jin Ningzhi, Zhou Kai, Iu H H C. Model reference adaptive identification based MTPA control method for interior PM synchronous motor[J]. Electric Machines and Control, 2020, 24(7): 90-101. [11] 李峰, 夏超英. 考虑磁路饱和的IPMSM电感辨识算法及变参数MTPA控制策略[J]. 电工技术学报, 2017, 32(11): 136-144. Li Feng, Xia Chaoying.Inductance identification algorithm and variable-parameters MTPA control strategy for IPMSM considering magnetic circuit saturation[J]. Transactions of China Electrotechnical Society, 2017, 32(11): 136-144. [12] 付兴贺, 陈锐, 殷凯轩, 等. 基于直接判据提取方式的直轴电流补偿型IPMSM最大转矩电流比控制算法[J]. 电工技术学报, 2023, 38(19): 5194-5206. Fu Xinghe, Chen Rui, Yin Kaixuan, et al.Direct axis current compensated MTPA control algorithm of IPMSM based on direct criterion calculation[J]. Transactions of China Electrotechnical Society, 2023, 38(19): 5194-5206. [13] 陈玥轩, 葛兴来, 左运, 等. 一种感应电机无速度传感器系统的电流传感器容错控制策略[J]. 中国电机工程学报, 2022, 42(6): 2346-2356. Chen Yuexuan, Ge Xinglai, Zuo Yun, et al.A current sensor fault-tolerant control strategy for speed- sensorless induction motor system[J]. Proceedings of the CSEE, 2022, 42(6): 2346-2356. [14] Carpaneto M, Fazio P, Marchesoni M, et al.Dynamic performance evaluation of sensorless permanent- magnet synchronous motor drives with reduced current sensors[J]. IEEE Transactions on Industrial Electronics, 2012, 59(12): 4579-4589. [15] 滕青芳, 崔宏伟, 朱建国, 等. 基于无电流传感器的永磁同步电机系统模型预测控制[J]. 电机与控制学报, 2019, 23(5): 119-128. Teng Qingfang, Cui Hongwei, Zhu Jianguo, et al.Current sensorless-based model predictive control for PMSM drive system[J]. Electric Machines and Control, 2019, 23(5): 119-128. [16] Khayamy M, Chaoui H.Current sensorless MTPA operation of interior PMSM drives for vehicular applications[J]. IEEE Transactions on Vehicular Technology, 2018, 67(8): 6872-6881. [17] Li Ze, Feng Guodong, Lai Chunyan, et al.Current injection-based multi-parameter estimation for dual three-phase IPMSM considering VSI nonlinearity[J]. IEEE Transactions on Transportation Electrification, 2019, 5(2): 405-415. [18] 康薇, 肖飞, 任强, 等. 双有源桥DC-DC变换器三移相调制及其死区效应分析和补偿[J]. 电工技术学报, 2024, 39(6): 1907-1922. Kang Wei, Xiao Fei, Ren Qiang, et al.Three-phase- shift modulation and its dead band effect analysis and compensation of dual-active-bridge DC-DC conver- ter[J]. Transactions of China Electrotechnical Society, 2024, 39(6): 1907-1922. [19] 李国华, 苑朝鸣. 低开关频率下五电平逆变器双波段特定谐波消除方法[J]. 电气工程学报, 2023, 18(4): 171-178. Li Guohua, Yuan Zhaoming.Double-band selective harmonic elimination method for five-level inverter with low switching frequency[J]. Journal of Electrical Engineering, 2023, 18(4): 171-178. [20] Liang Donglai, Li Jian, Qu Ronghai, et al.Adaptive second-order sliding-mode observer for PMSM sensorless control considering VSI nonlinearity[J]. IEEE Transactions on Power Electronics, 2018, 33(10): 8994-9004. [21] 龙江, 杨明, 陈扬洋, 等. 基于误差电压精确计算的表贴式永磁同步电机逆变器非线性补偿方法[J]. 中国电机工程学报, 2022, 42(17): 6425-6436. Long Jiang, Yang Ming, Chen Yangyang, et al.Inverter nonlinearity compensation method for SPMSM drives based on accurate voltage error calculation[J]. Proceedings of the CSEE, 2022, 42(17): 6425-6436.
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