Torque Calculation Method of Fractional Slot Permanent Magnet Synchronous Motor

doi:10.11985/2021.03.001

Abstract

Abstract:

In order to accurately calculate the torque of the fractional slot permanent magnet synchronous motor, a new mathematical model of the fractional slot permanent magnet synchronous motor is established. By analyzing the no-load back EMF and stator flux linkage of the motor, considering the flux linkage harmonics and the cross-inductance between d-q axis, the permanent magnet torque, permanent magnet torque ripple, reluctance torque, and reluctance torque ripple of the motor are calculated. The mechanism of torque ripple is also revealed: permanent magnet torque ripple is mainly 6k harmonics, the largest proportion of the permanent magnet torque ripple is the 12th harmonic torque generated by the rotor flux linkage and the permanent magnet. The reluctance torque ripple is mainly caused by the 6k self-inductance harmonics and cross mutual inductance harmonics of the stator winding on the d-q axis, the largest proportion of reluctance torque ripple is the 6th harmonic torque generated by the 6th d-q axis mutual inductance. Regardless of permanent magnet torque and reluctance torque, the largest proportion of the 6th harmonic torque is the harmonic torque generated by the q-axis current. Finally, the correctness of the model is verified.

Key words: Fractional slot permanent magnet synchronous motor, back-EMF constant, d-q mutual inductance, harmonic torque

CLC Number:

TM561

LUO Xiaoyi, ZHANG Fengge. Torque Calculation Method of Fractional Slot Permanent Magnet Synchronous Motor[J]. Journal of Electrical Engineering, 2021, 16(3): 1-8.

Figures/Tables 25

References 15

[1]	MOGHADDAM R R, MAGNUSSEN F, SADARANGANI C. Theoretical and experimental revaluation of synchronous reluctance machine[J]. IEEE Trans. Ind. Electron., 2010, 57(1):6-13. doi: 10.1109/TIE.2009.2025286
[2]	IM J, KIM W, KIM K, et al. Inductance calculation method of synchronous reluctance motor including iron loss and cross magnetic saturation[J]. IEEE Trans. Magn., 2009, 45(6):2803-2806. doi: 10.1109/TMAG.2009.2018663
[3]	ARMANDO E, BOJOI R I, GUGLIELMI P, et al. Experimental identification of the magnetic model of synchronous machines[J]. IEEE Trans. Ind. Appl., 2013, 49(5):2116-2165. doi: 10.1109/TIA.2013.2258876
[4]	HU D, ALSMADI Y, XU L. High fidelity nonlinear IPM modeling based on measured stator winding flux linkage[J]. IEEE Energy Conversion Congress and Exposition, 2014:3199-3205.
[5]	于圣龙. 负载对分数槽永磁电机转矩波动的影响[J]. 仪器仪表学报, 2015, 29(12):1781-1789.
	YU Shenglong. Influence of load on torque ripple of fractional slot permanent magnet motor[J]. Journal of Instrumentation, 2015, 29(12):1781-1789.
[6]	BARCARO M, BIANCHI N, MAGNUSSEN F. Remarks on torque estimation accuracy in fractional-slot permanent-magnet motors[J]. IEEE Trans. Ind. Electron., 2012, 59(6):2565-2572. doi: 10.1109/TIE.2011.2160517
[7]	李玉猛, 赵静, 陈振, 等. 五相容错永磁同步电机磁动势与转矩研究[J]. 电机与控制学报, 2015, 19(12):24-32.
	LI Yumeng, ZHAO Jing, CHEN Zhen, et al. Research on magnetomotive force and torque of five compatible error permanent magnet synchronous motor[J]. Journal of Electrical Engineering and Control, 2015, 19(12):24-32.
[8]	白海军, 张凤阁. 外永磁转子爪极电机转矩研究[J]. 电机与控制学报, 2011, 15(5):78-82,88.
	BAI Haijun, ZHANG Fengge. Research on torque of external permanent magnet rotor claw pole motor[J]. Journal of Electrical Engineering and Control, 2015, 15(5):78-82,88.
[9]	刘金海. 基于参数化dq0坐标变换的PMSM建模与矢量控制[J]. 电气工程学报, 2017, 12(11):28-34.
	LIU Jinhai. PMSM modeling and vector control based on parameterized dq0 coordinate transformation[J]. Journal of Electrical Engineering, 2017, 12(11):28-34.
[10]	MEIER F, SOULARD SOULARD. dq theory applied to a permanent magnet synchronous machine with concentrated windings[C]// Proc. 4th IET Conf. PEMD,York,UK, Apr. 2-8, 2008:2-8.
[11]	YAMAZAKI K, ISHIGAMI H. Rotor-shape optimization of interior permanent-magnet motors to reduce harmonic iron losses[J]. IEEE Trans. Ind. Electron., 2010, 57(1):61-69. doi: 10.1109/TIE.2009.2025285
[12]	SOCK de H W, RIX A J, KAMPER M J. Optimal torque control of synchronous machines based on finite-element analysis[J]. IEEE Trans. Ind. Electron., 2010, 57(1):413-419. doi: 10.1109/TIE.2009.2030209
[13]	钟锐, 曹彦萍, 徐宇柘, 等. 三角函数的开关磁阻电机磁链解析模型[J]. 电机与控制学报, 2013, 17(1):13-19.
	ZHONG Rui, CAO Yanping, XU Yutuo, et al. Analytical model of switched reluctance motor flux linkage based on trigonometric function[J]. Journal of Electrical Engineering and Control, 2013, 17(1):13-19.
[14]	ELREFAIE A M, ZHU Z Q, JAHNS T M, et al. Winding inductances of fractional slot surface-mounted permanent magnet brushless machines[C]// IEEE Industry Applications Society Meeting, 2008:1-8.
[15]	金石, 朱熙, 金无痕, 等. 基于谐波提取器的永磁同步电机谐波抑制方法[J]. 电气工程学报, 2021, 16(1):9-15.
	JIN Shi, ZHU Xi, JIN Wuhen, et al. Harmonic suppression method of permanent magnet synchronous motor based on harmonic extractor[J]. Journal of Electrical Engineering, 2021, 16(1):9-15.

参数	数值
功率P/kW	1.5
转速n/(r/min)	3 000
频率f/Hz	250
线电压U/V	37
定子外径D_o/mm	120
定子内径D_i/mm	75
槽数	12
极数	10

电流有效值I/A	计算值(%)	仿真值(%)
18	7.15	7.46
27	4.68	4.60
36	6.01	6.22
45	6.85	7.11
54	7.45	7.35