Abstract:In order to use the magnetic reluctance torque of the interior permanent magnet synchronous motor (IPMSM), maximum torque per ampere (MTPA) control is generally used to achieve the control effect of maximum torque output per unit stator current. Since the traditional MTPA control strategy usually uses the torque equation to calculate the given value of d-q axis currents directly, it is sensitive to motor parameters, which makes it difficult to operate at the optimal operating point. Therefore, related scholars proposed the virtual signal injection MTPA (VSI-MTPA) control to reduce the sensitivity of motor parameters. However, this control strategy requires complex coordinate transformations to convert the motor d-q axis currents into the current vector is and the current vector angle β. Then, it injects the virtual sinusoidal signals into the current vector angle β. Subsequently, the coordinate changes are performed to obtain the d-q axis currents after injecting the virtual signals ( and ). Conventional band-pass and low-pass filters are also required to extract the virtual signal. The complex coordinate transformation and the use of filters increase the model's complexity, reducing the control rate. Moreover, neglecting high-order terms in the Taylor series expansion of the electromagnetic torque leads to errors in tracking the operating point, which reduces the control accuracy. This paper proposes an improved virtual square wave signal injection MTPA (IVSWSI-MTPA) control strategy. Firstly, the IVSWSI-MTPA strategy injects a specific virtual square wave signal to accelerate the control rate of the VSI-MTPA strategy, which avoids using band-pass and low-pass filters in the virtual signal extraction. Moreover, this control strategy directly injects the virtual square wave signal into the d-q axis currents to obtain the d-q axis currents after the injection of the virtual signal ( and ), avoiding complex coordinate transformations. Thus, the model complexity is reduced, and the control rate is accelerated. Secondly, to improve the control accuracy of the VSI-MTPA control strategy, the torque equation is regarded as a binary function with independent variables id and iq. The torque equation is then expanded in a Taylor series of binary functions. Accordingly, the expansion's second-order and higher partial derivative terms are automatically zero. The error caused by ignoring the higher-order partial derivative terms can be avoided, improving the control accuracy of the system. Finally, the effectiveness of the proposed control strategy is verified using the sector selection calculation method of space vector pulse width modulation (SVPWM). The experimental results demonstrate that the IVSWSI-MTPA strategy has the following advantages. (1) The IVSWSI-MTPA strategy does not need complex coordinate transformations and band-pass and low-pass filters used in the conventional VSI-MTPA strategy. Regarding the suddenly changing state of the motor, the steady state can be reached more quickly. The dynamic response performance of the control system is improved, and the control speed is accelerated. (2) The IVSWSI-MTPA strategy requires a lower current for the same load torque output because it avoids the error caused by ignoring the higher-order partial derivative term in the Taylor expansion of electromagnetic torque. Therefore, it performs better in the tracking accuracy of the current vector angle β. The MTPA operating point can be tracked accurately, improving the system's control accuracy.
王玉彬, 刘瀚文. 改进虚拟方波信号注入的内置式永磁同步电机最大转矩电流比控制策略[J]. 电工技术学报, 2025, 40(20): 6474-6486.
Wang Yubin, Liu Hanwen. Improved Virtual Square Wave Signal Injection MTPA Control of Interior Permanent Magnet Synchronous Motor. Transactions of China Electrotechnical Society, 2025, 40(20): 6474-6486.
[1] Li Xianglin, Shen Fawen, Yu Shiyang, et al.Flux- regulation principle and performance analysis of a novel axial partitioned stator hybrid-excitation flux- switching machine using parallel magnetic circuit[J]. IEEE Transactions on Industrial Electronics, 2021, 68(8): 6560-6573. [2] 王玉彬, 孙建鑫. 分数槽集中绕组嵌入式永磁同步电机设计[J]. 电工技术学报, 2014, 29(5): 70-76. Wang Yubin, Sun Jianxin.Design of interior per- manent magnet synchronous machines with fractional- slot concentrated windings[J]. Transactions of China Electrotechnical Society, 2014, 29(5): 70-76. [3] Li Ke, Wang Yi.Maximum torque per ampere (MTPA) control for IPMSM drives based on a variable- equivalent-parameter MTPA control law[J]. IEEE Transactions on Power Electronics, 2019, 34(7): 7092-7102. [4] 李桂丹, 任宗芹, 李斌, 等. 多单元永磁同步电机功率分配最大转矩电流比控制[J]. 中国电机工程学报, 2022, 42(22): 8352-8363. Li Guidan, Ren Zongqin, Li Bin, et al.Maximum torque per ampere control of multi-unit permanent magnet synchronous motor under power sharing[J]. Proceedings of the CSEE, 2022, 42(22): 8352-8363. [5] 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. [6] Dianov A, Tinazzi F, Calligaro S, et al.Review and classification of MTPA control algorithms for synchronous motors[J]. IEEE Transactions on Power Electronics, 2022, 37(4): 3990-4007. [7] 吴润秋, 徐磊, 朱孝勇, 等. 基于多变运行工况的漏磁可控型永磁电机变参数最大转矩电流比控制[J/OL]. 中国电机工程学报, 2024: 1-13. (2024-03-19). http://kns.cnki.net/KCMS/detail/detail.aspx?filename=ZGDC20240313001&dbname=CJFD&dbcode=CJFQ. Wu Runqiu, Xu Lei, Zhu Xiaoyong, et al. Variable parameter maximum torque-current ratio control of flux leakage controllable permanent magnet motor based on variable operating conditions[J/OL]. China Industrial Economics, 2024: 1-13. (2024-03-19). http://kns.cnki.net/KCMS/detail/detail.aspx?filename=ZGDC20240313001&dbname=CJFD&dbcode=CJFQ. [8] 刘国海, 张嘉皓, 陈前. 基于空间电压矢量注入的频率可变型五相永磁同步电机最大转矩电流比控制[J]. 电工技术学报, 2020, 35(20): 4287-4295. Liu Guohai, Zhang Jiahao, Chen Qian.Variable frequency maximum-torque-per-ampere control for five-phase permanent-magnet motor based on space voltage vector injection[J]. Transactions of China Electrotechnical Society, 2020, 35(20): 4287-4295. [9] 黄科元, 周佳新, 刘思美, 等. 考虑逆变器非线性永磁同步电机高频注入电感辨识方法[J]. 电工技术学报, 2021, 36(8): 1607-1616. Huang Keyuan, Zhou Jiaxin, Liu Simei, et al.Inductance identification method of permanent magnet synchronous motor considering inverter nonlinearity based on high-frequency injection[J]. Transactions of China Electrotechnical Society, 2021, 36(8): 1607-1616. [10] 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]. Transactions of China Electrotechnical Society, 2025, 40(2): 439-451. [11] 马铱林, 袁浩, 尹威, 等. 考虑等效电磁损耗电阻偏移的永磁同步电机直流信号注入在线参数辨识方法[J]. 电工技术学报, 2023, 38(22): 6015-6026. Ma Yilin, Yuan Hao, Yin Wei, et al.DC-signal- injection-based online parameters identification for permanent magnet synchronous machine considering variation of equivalent electromagnetic loss resi- stance[J]. Transactions of China Electrotechnical Society, 2023, 38(22): 6015-6026. [12] 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.Model reference adaptive identification based MTPA control method for interior PM synchronous motor[J]. Electric Machines and Control, 2020, 24(7): 90-101. [13] 许爱德, 刘鑫, 李新宇, 等. 基于参数辨识的永磁辅助同步磁阻电机电流无差拍控制[J]. 电工技术学报, 2024, 39(18): 5626-5638. Xu Aide, Liu Xin, Li Xinyu, et al.Current deadbeat control of permanent magnet-assisted synchronous reluctance motor based on parameter identification[J]. Transactions of China Electrotechnical Society, 2024, 39(18): 5626-5638. [14] 谢文超, 赵延明, 方紫微, 等. 带可变遗忘因子递推最小二乘法的超级电容模组等效模型参数辨识方法[J]. 电工技术学报, 2021, 36(5): 996-1005. Xie Wenchao, Zhao Yanming, Fang Ziwei, et al.Variable forgetting factor recursive least squales based parameter identification method for the equivalent circuit model of the supercapacitor cell module[J]. Transactions of China Electrotechnical Society, 2021, 36(5): 996-1005. [15] 李洪凤, 徐浩博, 徐越. 扩展卡尔曼滤波参数辨识下永磁同步电机模型预测转矩控制[J]. 电机与控制学报, 2023, 27(9): 19-30. Li Hongfeng, Xu Haobo, Xu Yue.Model prediction torque control of PMSM based on extended Kalman filter parameter identification[J]. Electric Machines and Control, 2023, 27(9): 19-30. [16] 赵强, 王昊洁, 谢春丽. 基于改进蜣螂优化算法的永磁同步电机参数辨识[J]. 重庆交通大学学报(自然科学版), 2024, 43(6): 102-108. Zhao Qiang, Wang Haojie, Xie Chunli.Parameter identification of permanent magnet synchronous motor based on improved dung beetle optimization algorithm[J]. Journal of Chongqing Jiaotong University (Natural Science), 2024, 43(6): 102-108. [17] 李婕, 杨淑英, 谢震, 等. 基于有效信息迭代快速粒子群优化算法的永磁同步电机参数在线辨识[J]. 电工技术学报, 2022, 37(18): 4604-4613. Li Jie, Yang Shuying, Xie Zhen, et al.Online parameter identification of permanent magnet syn- chronous motor based on fast particle swarm optimization algorithm with effective information iterated[J]. Transactions of China Electrotechnical Society, 2022, 37(18): 4604-4613. [18] 高森, 王康, 姜宏昌, 等. 基于改进花授粉算法的永磁同步电机参数辨识[J]. 电机与控制应用, 2024, 51(1): 97-105. Gao Sen, Wang Kang, Jiang Hongchang, et al.Parameters identification of PMSM based on improved flower pollination algorithm[J]. Electric Machines & Control Application, 2024, 51(1): 97-105. [19] 张雨馨, 王云冲, 史丹, 等. 自寻优最大转矩电流比矢量控制连载之二: 同步磁阻电机虚拟双极性信号注入法控制[J]. 微特电机, 2022, 50(10): 1-8. Zhang Yuxin, Wang Yunchong, Shi Dan, et al.Self- optimizing MTPA vector control part 2: virtual bipolar signal injection method for synchronous reluctance motor control[J]. Small & Special Elec- trical Machines, 2022, 50(10): 1-8. [20] 邱建琪, 宋攀, 陈卓易, 等. 改进虚拟信号注入永磁同步电机MTPA控制[J]. 电机与控制学报, 2022, 26(9): 1-8. Qiu Jianqi, Song Pan, Chen Zhuoyi, et al.Improved virtual signal injection control for MTPA operation of permanent magnet synchronous motor[J]. Electric Machines and Control, 2022, 26(9): 1-8. [21] 孙天夫, 杨日阳, 梁嘉宁, 等. 考虑电机参数偏导项的同步磁阻电机虚拟信号注入MTPA控制[J]. 中国电机工程学报, 2021, 41(24): 8326-8334. Sun Tianfu, Yang Riyang, Liang Jianing, et al.MTPA control of synchronous reluctance motors based on virtual signal injection control considering derivative terms[J]. Proceedings of the CSEE, 2021, 41(24): 8326-8334. [22] Zhang Jiahao, Liu Guohai, Chen Qian.MTPA control of sensorless IPMSM drive system based on virtual and actual high-frequency signal injection[J]. IEEE Transactions on Transportation Electrification, 2021, 7(3): 1516-1526. [23] Chen Zhiwei, Yan Yan, Shi Tingna, et al.An accurate virtual signal injection control for IPMSM with improved torque output and widen speed region[J]. IEEE Transactions on Power Electronics, 2021, 36(2): 1941-1953. [24] Wang Jun, Huang Xiaoyan, Yu Dong, et al.An accurate virtual signal injection control of MTPA for an IPMSM with fast dynamic response[J]. IEEE Transactions on Power Electronics, 2018, 33(9): 7916-7926. [25] 赵文祥, 刘桓, 陶涛, 等. 基于虚拟信号和高频脉振信号注入的无位置传感器内置式永磁同步电机MTPA控制[J]. 电工技术学报, 2021, 36(24): 5092-5100. Zhao Wenxiang, Liu Huan, Chen Tao, et al.MTPA control of sensorless IPMSM based on virtual signal and high-frequency pulsating signal injection[J]. Transactions of China Electrotechnical Society, 2021, 36(24): 5092-5100. [26] Jiang Lin, Wu Yunchuan, Qin Haoran, et al.An improved virtual constant signal injection MTPA control for PMa-SynRM drives[C]//2022 5th Inter- national Conference on Power and Energy Appli- cations (ICPEA), Guangzhou, China, 2022: 144-149.