A Mathematical Model Based on Coil Sub-Element for Permanent Magnet Synchronous Motor with Health and Stator Winding Short-Circuit Fault
Gao Caixia1, Miao Zhuang1, Chen Hao2, Si Jikai3, Lü Ke4
1. School of Electrical Engineering and Automation Henan Polytechnic University Jiaozuo 454003 China; 2. School of Emergency Management Henan Polytechnic University Jiaozuo 454003 China; 3. School of Electrical Engineering Zhengzhou University Zhengzhou 450001 China; 4. National Key Laboratory for Vessel Integrated Power System Technology Naval University of Engineering Wuhan 430033 China
Abstract To solve the issues existing in the mathematical model of stator winding short-circuit fault of permanent magnet synchronous motor (PMSM) with phase winding as the basic element, such as the influence of fault space location cannot be taken into account, different short-circuit faults need to be remodeled, and the contribution of coil to motor performance under healthy condition cannot be studied. This paper proposes a mathematical model based on coil sub-element for PMSM (APM) with health and stator winding short-circuit fault. Firstly, each coil of PMSM is divided into multiple coil sub-elements, and the matrix equations of physical quantities such as voltage, impedance and no-load back EMF of each sub-element are established respectively. The voltage equations of all sub-elements are established by using Kirchhoff's voltage law, and the electromagnetic power and torque equations of the motor are established. Secondly, the finite element method is used to establish the no-load back EMF matrix of each wire turn considering the spatial position relationship in the slot, and the sub-element no-load back EMF matrix considering the position information is obtained by matrix transformation. Then, the finite element method and fitting method are used to establish the inductance matrix of each wire turn considering the spatial position relationship in the slot, and the sub-element inductance matrix considering the position information is also obtained by matrix transformation. Finally, the simulation model and graphical interface of APM are established in Matlab/Simulink. By modifying the tap number and the connection position of the short-circuit resistance module in the graphical interface, the electromagnetic characteristics of motor health and different types of stator winding short-circuit fault (WSF) are calculated. By comparing the APM calculation results, finite element simulation results and experimental results, the correctness and accuracy of the APM are verified, and the following conclusions are obtained: (1) By modifying the tap number and the connection position of the short-circuit resistance module in the graphical interface, APM can conveniently and quickly calculate the voltage, current, torque and other electromagnetic characteristics of the motor health and different types of WSF. (2) Considering the influence of the motor winding structure, APM can subtly analyze the contribution of coils to motor performance under different operating conditions when PMSM is in a healthy state. Using APM to analyze coils at different positions, it can be found that the coils at different positions of the same branch have different voltages, different powers, and different loads. Due to the different voltages of different coils in the same branch, the fault probability of different coils in the same branch is different under the same coil insulation level. In the design of coil insulation, coils at different positions of the same branch can adopt different insulation levels to reduce motor manufacturing costs. (3) Without changing the internal structure, APM can efficiently, accurately and subtly analyze the motor performance under different types of WSF such as interturn short-circuit fault and interphase short-circuit fault. (4) Considering the influence of fault space position, APM can accurately analyze the influence of short-circuit fault at different positions of the coil in the PMSM slot on motor performance. It is found that when the short-circuit turns (Rf) and short-circuit resistance (Nf) are the same, the short-circuit current and average torque are different under ISF at different positions in the slot, which reveals the limitation of Nf and Rf as the criterion of fault severity.
[1] 李晓华, 赵容健, 田晓彤, 等. 逆变器供电对电动汽车内置式永磁同步电机振动噪声特性影响研究[J]. 电工技术学报, 2020, 35(21): 4455-4464. Li Xiaohua, Zhao Rongjian, Tian Xiaotong, et al.Study on vibration and noise characteristics of interior permanent magnet synchronous machine for electric vehicles by inverter[J]. Transactions of China Electrotechnical Society, 2020, 35(21): 4455-4464. [2] 张伟伟, 肖飞, 刘计龙, 等. 轨道交通车辆永磁同步牵引系统断电区穿越控制策略[J]. 电工技术学报, 2021, 36(16): 3483-3492. Zhang Weiwei, Xiao Fei, Liu Jilong, et al.Power-off area traversing control strategy of permanent magnet synchronous motor traction system in rail transit vehicle[J]. Transactions of China Electrotechnical Society, 2021, 36(16): 3483-3492. [3] 崔淑梅, 匡志, 杜博超, 等. 基于自抗扰控制原理的全电飞机用永磁同步电机转速闭环控制[J]. 电工技术学报, 2017, 32(增刊1): 107-115. Cui Shumei, Kuang Zhi, Du Bochao, et al.Speed closed-loop control of permanent magnet synchronous motor for all-electric aircraft applications based on active disturbance rejection controller[J]. Transa-ctions of China Electrotechnical Society, 2017, 32(S1): 107-115. [4] 郑大勇, 张品佳. 交流电机定子绝缘故障诊断与在线监测技术综述[J]. 中国电机工程学报, 2019, 39(2): 395-406, 637. Zheng Dayong, Zhang Pinjia.A review of fault diagnosis and online condition monitoring of stator insulation in AC electrical machine[J]. Proceedings of the CSEE, 2019, 39(2): 395-406, 637. [5] Zafarani M, Bostanci E, Qi Yuan, et al.Interturn short-circuit faults in permanent magnet synchronous machines: an extended review and comprehensive analysis[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2018, 6(4): 2173-2191. [6] Hang Jun, Ding Shichuan, Zhang Jianzhong, et al.Detection of interturn short-circuit fault for PMSM with simple fault indicator[J]. IEEE Transactions on Energy Conversion, 2016, 31(4): 1697-1699. [7] 谢颖, 胡圣明, 陈鹏, 等. 永磁同步电机匝间短路故障温度场分析[J]. 电工技术学报, 2022, 37(2): 322-331. Xie Ying, Hu Shengming, Chen Peng, et al.Thermal field analysis on inter-turn short circuit fault of permanent magnet synchronous motor[J]. Transa-ctions of China Electrotechnical Society, 2022, 37(2): 322-331. [8] Qi Yuan, Bostanci E, Gurusamy V, et al.A com-prehensive analysis of short-circuit current behavior in PMSM interturn short-circuit faults[J]. IEEE Transactions on Power Electronics, 2018, 33(12): 10784-10793. [9] Choi G, Jahns T M.PM synchronous machine drive response to asymmetrical short-circuit faults[J]. IEEE Transactions on Industry Applications, 2016, 52(3): 2176-2185. [10] Jeong I, Hyon B J, Nam K.Dynamic modeling and control for SPMSMs with internal turn short fault[J]. IEEE Transactions on Power Electronics, 2013, 28(7): 3495-3508. [11] Hang Jun, Zhang Jianzhong, Cheng Ming, et al.Online interturn fault diagnosis of permanent magnet synchronous machine using zero-sequence com-ponents[J]. IEEE Transactions on Power Electronics, 2015, 30(12): 6731-6741. [12] Jeong H, Moon S, Kim S W.An early stage interturn fault diagnosis of PMSMs by using negative-sequence components[J]. IEEE Transactions on Industrial Electronics, 2017, 64(7): 5701-5708. [13] 张业成, 刘国海, 陈前. 基于电流波动特征的永磁同步电机匝间短路与局部退磁故障分类诊断研究[J]. 电工技术学报, 2022, 37(7): 1634-1643, 1653. Zhang Yecheng, Liu Guohai, Chen Qian.Discrimin-ation of interturn short-circuit and local demag-netization in permanent magnet synchronous motor based on current fluctuation characteristics[J]. Transa-ctions of China Electrotechnical Society, 2022, 37(7): 1634-1643, 1653. [14] 赵洪森, 戈宝军, 陶大军, 等. 定子绕组匝间短路对发电机电磁转矩特性的影响[J]. 电工技术学报, 2016, 31(5): 192-198. Zhao Hongsen, Ge Baojun, Tao Dajun, et al.Influ-ence of stator winding inter-turn short-circuit fault on generator electromagnetic torque characteristics[J]. Transactions of China Electrotechnical Society, 2016, 31(5): 192-198. [15] 牛化敏, 桂林, 孙宇光, 等. 基于多回路理论的交流励磁电机定子绕组内部故障仿真与实验研究[J]. 中国电机工程学报, 2019, 39(12): 3676-3684. Niu Huamin, Gui Lin, Sun Yuguang, et al.Simulation and experimental research on stator winding internal faults of AC excitation machine based on multi-loop theory[J]. Proceedings of the CSEE, 2019, 39(12): 3676-3684. [16] 田代宗, 孙宇光, 王善铭, 等. 多相整流永磁同步发电机绕组内部相间短路的故障分析[J]. 电工技术学报, 2020, 35(6): 1262-1271. Tian Daizong, Sun Yuguang, Wang Shanming, et al.Analysis of stator internal phase-to-phase short-circuit in the multiphase permanent magnet syn-chronous generator with rectifier load system[J]. Transactions of China Electrotechnical Society, 2020, 35(6): 1262-1271. [17] Ben Khader Bouzid M, Champenois G, Maalaoui A, et al. Efficient simplified physical faulty model of a permanent magnet synchronous generator dedicated to the stator fault diagnosis part I: faulty model conception[J]. IEEE Transactions on Industry Appli-cations, 2017, 53(3): 2752-2761. [18] Vaseghi B.Modelling and study of PM machines with inter-turn fault dynamic model-FEM model[J]. Elec-tric Power Systems Research, 2011, 81(8): 1715-1722. [19] Kumar N P, Isha T B.FEM based electromagnetic signature analysis of winding inter-turn short-circuit fault in inverter fed induction motor[J]. CES Transa-ctions on Electrical Machines and Systems, 2019, 3(3): 309-315. [20] 张艳辉, 郑晓钦, 吴新振, 等. 基于有限元场路耦合的十二相整流发电机系统定子匝间短路分析[J]. 电工技术学报, 2019, 34(9): 1842-1849. Zhang Yanhui, Zheng Xiaoqin, Wu Xinzhen, et al.Analysis of stator winding inter-turn short circuit on a 12-phase rectifier generator system based on finite element field-circuit coupling[J]. Transactions of China Electrotechnical Society, 2019, 34(9): 1842-1849. [21] Zhao Jing, Guan Xiaoqing, Li Chenghai, et al.Com-prehensive evaluation of inter-turn short circuit faults in PMSM used for electric vehicles[J]. IEEE Transa-ctions on Intelligent Transportation Systems, 2021, 22(1): 611-621.
2023, Vol. 38 
