电动车用矩形波永磁电动机的优化设计研究
|
摘要
本文基于有限元法，对一台矩形波永磁电动机样机的参数、静态转矩特性、稳态运行特性等进行了系统的分析和计算。文中首先阐述了矩形波永磁电动机电磁场数值计算数学模型的建立，在有限元磁场分析的基础上，提出了斜槽式永磁电机磁场的分段计算法；利用分段计算法，对电枢斜槽结构的样机的空载和负载磁场进行了计算，并由此计算了样机的反电动势对应于转子位置角的变化波形和反电动势系数曲线；对直槽和斜槽式结构的气隙磁密分布、反电动势波形和反电动势系数给出了详细的比较和分析。此外，用磁链法和能量法分别计算了样机的自感和互感系数；详细分析了积分路径的选择对电感参数和反电动势计算结果的影响。计算值与实测值的对比表明，本文提出的算法具有较高的计算精度。
文中分别采用麦克斯韦应力法和虚位移法对样机的电磁转矩进行了数值计算。详细分析了有限元网格剖分中，三角单元的形状、求解域内剖分节点的配置以及积分路径选取等对电磁转矩数值计算误差的影响，提出了关于麦克斯韦应力法应用中积分路径所经单元剖分形式的见解；计算和分析了电枢电流相位超前于反电动势时的电磁转矩特性。此外，还对直槽和斜槽式电机的转矩特性作了分析和比较；与直槽结构相比，计算和分析了定子斜槽对纹波转矩的抑制程度以及槽口宽度对纹波转矩的影响。结合实测数据的验证，阐述了两种算法在永磁电机电磁转矩计算中各自所具有的特点。在上述分析基础上，基于场路耦合法，提出了计及电感压降的稳态电路电压方程。与不计电感压降的电路方程比较，采用本文算法计算的稳态转矩／转速特性与实际工况更为接近。
本文把改进的禁忌搜索算法(Tabu Search Algorithm)与电机电磁场逆问题的研究相结合，成功地实施了矩形波永磁电动机的优化设计。文中详细分析了该算法中的目标函数和优化变量的确定原则。对单目标和多目标函数的优化结果进行了深入的分析和比较。在不降低样机电气性能的前提下，优化设计后电动机永磁材料的用量可显著减少，从而使得优化后电机的价格、体积和重量都有相应的减小。
在上述研究工作的基础上，本文完成了以FORTRAN语言编制的轮毂式矩形波永磁电机优化设计软件包。该软件也可用于普通内转子结构的矩形波永磁电机的优化设计，且对正弦波永磁电机的设计和参数计算具有现实的参考与推广价值。
本文还对相应驱动控制电路的特点和原理作了简要叙述。
浙江大学博士论文 摘要
The finite element method is applied to analyze a prototype square wave permanent-magnet motors using in electric vehicles. The parameters, electromagnetic torques and characteristics of the machine are calculated, tested and analyzed systematically. A software package for optimum design of the motor based on an improved Tabu Search Algorithm and inverse problems of electromagnetic field is completed and used to reduce the price and weight of the motor.
At first, the magnetic model of the prototype machine for numerical field calculation is formulated. The magnetic fields, the curves of counter EMF and coefficient of EMF for both straight and skewed slots are calculated. In the case of skewed slots, a subsection method is introduced especially. The self and mutual inductances are obtained by flux linkage method and energy method. The computed results are verified by the tested values.
Then, the electromagnetic torques of the motor with y means of both methods, Maxwell's stress and virtual displacement methods, with straight and skewed slots are determined by Maxwell stress method and virtual displacement method. To reduce the computation error, the technics of mesh division are discussed. Moreover, the electromagnetic torques while the phase of current leads the EMF, and the oriented torques with straight and skewed slots are also calculated and discussed. Compared with test values, it is shown that the numerical results have satisfying accuracy.
Based on the above investigation, the steady state circuit voltage equations established with the inductance voltage included. Compared with conventional formulation, the new one is accurate and useful for engineering practice.
Finally, by using an improved Tabu Search Algorithm combined with inverse problems of electromagnetic field, the prototype machine is optimally designed and a software package is completed. The objective function and optimal variables are discussed. The numerical results show that the consumption of permanent-magnets for the optimized motor is reduced to a great extent compared with the original machine, thus leads to a significant reductions in motor price and weight. The software package is useful for sine wave PM synchronous motor also.
文中分别采用麦克斯韦应力法和虚位移法对样机的电磁转矩进行了数值计算。详细分析了有限元网格剖分中，三角单元的形状、求解域内剖分节点的配置以及积分路径选取等对电磁转矩数值计算误差的影响，提出了关于麦克斯韦应力法应用中积分路径所经单元剖分形式的见解；计算和分析了电枢电流相位超前于反电动势时的电磁转矩特性。此外，还对直槽和斜槽式电机的转矩特性作了分析和比较；与直槽结构相比，计算和分析了定子斜槽对纹波转矩的抑制程度以及槽口宽度对纹波转矩的影响。结合实测数据的验证，阐述了两种算法在永磁电机电磁转矩计算中各自所具有的特点。在上述分析基础上，基于场路耦合法，提出了计及电感压降的稳态电路电压方程。与不计电感压降的电路方程比较，采用本文算法计算的稳态转矩／转速特性与实际工况更为接近。
本文把改进的禁忌搜索算法(Tabu Search Algorithm)与电机电磁场逆问题的研究相结合，成功地实施了矩形波永磁电动机的优化设计。文中详细分析了该算法中的目标函数和优化变量的确定原则。对单目标和多目标函数的优化结果进行了深入的分析和比较。在不降低样机电气性能的前提下，优化设计后电动机永磁材料的用量可显著减少，从而使得优化后电机的价格、体积和重量都有相应的减小。
在上述研究工作的基础上，本文完成了以FORTRAN语言编制的轮毂式矩形波永磁电机优化设计软件包。该软件也可用于普通内转子结构的矩形波永磁电机的优化设计，且对正弦波永磁电机的设计和参数计算具有现实的参考与推广价值。
本文还对相应驱动控制电路的特点和原理作了简要叙述。
浙江大学博士论文 摘要
The finite element method is applied to analyze a prototype square wave permanent-magnet motors using in electric vehicles. The parameters, electromagnetic torques and characteristics of the machine are calculated, tested and analyzed systematically. A software package for optimum design of the motor based on an improved Tabu Search Algorithm and inverse problems of electromagnetic field is completed and used to reduce the price and weight of the motor.
At first, the magnetic model of the prototype machine for numerical field calculation is formulated. The magnetic fields, the curves of counter EMF and coefficient of EMF for both straight and skewed slots are calculated. In the case of skewed slots, a subsection method is introduced especially. The self and mutual inductances are obtained by flux linkage method and energy method. The computed results are verified by the tested values.
Then, the electromagnetic torques of the motor with y means of both methods, Maxwell's stress and virtual displacement methods, with straight and skewed slots are determined by Maxwell stress method and virtual displacement method. To reduce the computation error, the technics of mesh division are discussed. Moreover, the electromagnetic torques while the phase of current leads the EMF, and the oriented torques with straight and skewed slots are also calculated and discussed. Compared with test values, it is shown that the numerical results have satisfying accuracy.
Based on the above investigation, the steady state circuit voltage equations established with the inductance voltage included. Compared with conventional formulation, the new one is accurate and useful for engineering practice.
Finally, by using an improved Tabu Search Algorithm combined with inverse problems of electromagnetic field, the prototype machine is optimally designed and a software package is completed. The objective function and optimal variables are discussed. The numerical results show that the consumption of permanent-magnets for the optimized motor is reduced to a great extent compared with the original machine, thus leads to a significant reductions in motor price and weight. The software package is useful for sine wave PM synchronous motor also.
引文
[1] 叶金虎，徐思海等，“无刷直流电动机”，科学出版社，1991年6月。
[2] 许大中，交流电机调速理论，浙江大学出版社，1991年。
[3] W. Xia, Philips S.M.Chin. "Analysis of different permanent magnet brushless motor drives for electric vehicles", EVS16, China, 1998.
[4] 唐任远等，现代永磁电机—理论与设计，机械工业出版社，1997年。
[5] Liu Tongyan etc., "The drive control system for electric vehicle driven directly by wheel motor", EVS16, China, 1998.
[6] Yue li, Todd A Walls, Jerry D.Lloyd, "A novel two-phase BPM drive system with high power density and low cost, IEEE Trans. on IA., Vol.34, No.5, Sept./Oct. 1998, pp: 1072-1080.
[7] T.J.E.Miller, Alan Huiton, etc., "Design of a synchronous reluctance motor drive" IEEE Trans. on IA., Vol. 27, No.4, July/Aug. 1991. pp:741-749.
[8] T. M. Jahns, "Flux-weakening regime operation of an interior permanent magnet synchronous motor drive," IEEE Trans. on IA., Vol. LA-23, July/Aug. 1987. pp:681-689.
[9] Chan, C.C.; Chau, K.T.; Jiang, J.Z, etc., "Novel permanent magnet motor drives for electric vehicles" , Industrial Electronics, IEEE Trans. on Vol. 43 Issue: 2, April 1996, pp: 331-339.
[10] Shigeo Morimoto, Yoji Taceda, etc. "Expansion of operating limits for permanent magnet motor by current vector control considering inverter capacity", IEEE Trans. on IA, Vol. 26, No. 5, Sept./Octo.,1990. pp:866-871.
[11] Jack, A.G.; Mecrow, B.C.; Weiner, C. "Switched reluctance and permanent magnet motors suitable for vehicle drives-a comparison", Electric Machines and Drives, 1999. International Conference IEMD '99,1999, pp: 505-507.
[12] 倪光正，钱秀英等，《电磁场数值计算》，高等教育出版社，1996年12月。
[13] Ahamad M.Naseser "Comparison of induction, PM, and SR motor technologies in EV traction systems applications". EVS16, China, 1999.
[14] 汤蕴璆，电机内的电磁场(第二版)，科学出版社，1998年1月。
[15] 廖海平，“浙江大学博士学位论文”，1998年12月。
[16] H.R.Bolton etc., "Investigation into a class of Brushless DC Motor with Quasi-square Voltage and Current", IEE Proc. Vol. 133 Pt.B,No.2 pp:103-111.
[17] 胡之光，电机电磁场的分析与计算，机械工业出版社，1982。
[18] B. Sneyers, D. W. Novotny, etc, "Field weakening in buried permanent magnet ac motor drives," IEEE Trans. on IA., vol. IA-21, mar./Apr. 1985. pp:398-407.
[19] T.M. jahns, G.B,. Kliman, etc. "Interior permanent magnet synchronous motor for adjustable speed drives," IEEE Trans. on IA., Vol. LA-22, July/Aug. 1986. pp:738-747.
[20] Y. Takeda and T. Hirasa, "Current phase control methods for permanent magnet synchronous motors considering saliency ," in PESC Conf. Rec. Apr. 1988, pp:409-414.
[21] Chalmers, B.J.; Musaba, I, "Performance characteristics of permanent magnet
and reluctance machines to meet EV requirements ", Machines and Drives for Electric and Hybrid Vehicles (Digest No: 1996/152), IEE Colloquium on, 1996,pp: 1-5
[22] Yasuyuki Sugii, Masayuki, Etc. "Applicability of various motors to electric vehicles(EV)", (武汉会议?)
[23] Jack, A.G.; Mecrow, B.C.; Weiner, C. "Switched reluctance and permanent magnet motors suitable for vehicle drives-a comparison ",Electric Machines and Drives, 1999. International Conference IEMD '99,1999,pp: 505-507.
[24] 丁志刚，“无刷直流电动机的研究和开发进展”，微电机，2000年，第33卷，第1期．pp：29-30．
[25] Yuefeng Liao, Liang Feng, etc. "A novel permanent magnet motor with doubly salient structure", IEEE Trans. on IA Vol. 31, No. 5, Sept./Oct. 1995, pp: 1069-1078.
[26] Alexander Kusko, Syed M. Peeran, "Brushless DC motors using unsymmetrical filed magnetization", IEEE Trans. on IA. Vol. LA-23, No.2, Mar/Apr. 1987. pp:319-326.
[27] Gare Bedrosian, "A new method for coupling finite element field solutions with external circuit and kinematics" IEEE Trans. on Mag., Vol. 29, No. 2 Mar., 1993, pp: 1664-1668.
[28] Francis Piriou and Adel Razek "Finite Element Analysis in Electromagnetic Systems Accounting for Electric Circuits" IEEE Trans. on Mag., Vol 29,No. 2 March, 1993, pp 1669-1675
[29] 傅为农，“斜槽异步电机的场路耦合时步法有限元模型及其应用”，上海大学博士学位论文，1997年8月。
[30] Chan T.F, Lie-Tong Yan, etc. "Design of a permanent-magnet brushless DC motor drive for an electric bicycle" Power Electronics and Drive Systems, 1999. PEDS '99. Proceedings of the IEEE 1999 International Conference on Vol. 2, 1999 pp: 714-718.
[31] Wijenayake, A.H.; Bailey, etc. "Design optimization of an axial gap permanent magnet brushless DC motor for electric vehicle applications ", Thirtieth IAS Annual Meeting, Conference Record of the 1995 IEEE, Vol. 1,pp: 685-692.
[32] Fang Lin Luo; Hock Guan Yeo "Advanced PM brushless DC motor control and system for electric vehicles", Industry Applications Conference, 2000. Conference Record of the 2000 IEEE, Vol. 2,2000, pp: 1336-1343.
[33] Alhamadi, M.A.; Demerdash, N.A. "Three dimensional magnetic field computation by a coupled vector-scalar potential method in brushless DC motors with skewed permanent magnet mounts-the no-load and load results", IEEE Trans. on Energy Conversion, Vol. 9 Issue: 1, Mar. 1994,pp: 15-25.
[34] Alhamadi, M.A.; Demerdash, N.A. "Modeling of effects of skewing of rotor mounted permanent magnets on the performance of brushless DC motors ", IEEE Trans. on Energy Conversion,, Vol. 6 Issue: 4, Dec. 1991 pp: 721-729.
[35] Bodin, F.; Siala, S.; Sicot, L. "State space fuzzy controller for a brushless DC motor ", PESC '97 Record., 28th Annual IEEE, Vol. 2,1997, pp: 869-874.
[36] Sozer, Y.; Kaufman, H.; Torrey, D.A. "Direct model reference adaptive control of permanent magnet brushless DC motors ", Control Applications, 1997, Proceedings of the 1997 IEEE International Conference on, 1997, pp: 633-638.
[37] Ghandakly, A.A.; Owed, M.R. "Design of an adaptive speed controller for DC brushless motors ", Thirtieth IAS Annual Meeting, LAS '95., Conference Record of the 1995 IEEE, Vol. 2,1995 pp: 1626-1633
[38] Y. Liao, T.A.Lipo, "A new doubly salient permanent magnet motor for adjustable speed drives", Electric Machines and Power Systems No.2, 1994, pp:259-270.
[39] Alhamadi, M.A.; Demerdash, N.A. "Three dimensional magnetic field computation by a coupled vector-scalar potential method in brushless DC motors with skewed permanent magnet mounts-the formulation and FE grids ", IEEE Trans on Energy Conversion,, Vol.9 Issue: 1, March 1994 pp: 1-14.
[40] Zhu, Z.Q.; Howe, D. "Instantaneous magnetic field distribution in permanent magnet brushless DC motors. Ⅳ. Magnetic field on load ", IEEE Trans. on Mag., Vol. 29 Issue: 1 Part: 2, Jan. 1993 pp: 152-158.
[41] Zhu, Z.Q.; Howe, D. "Instantaneous magnetic field distribution in brushless permanent magnet DC motors. Ⅲ. Effect of stator slotting ", IEEE Trans. on Mag., Vol. 29 Issue: 1 Part: 2, Jan. 1993, pp: 143-151.
[42] Zhu, Z.Q.; Howe, D. "Instantaneous magnetic field distribution in brushless permanent magnet DC motors. Ⅱ. Armature-reaction field ", IEEE Trans. on Mag., Vol. 29 Issue: 1 Part: 2, Jan. 1993, pp: 136-142.
[43] Zhu, Z.Q.; Howe, D.; Bolte, E.; Ackermann, B. "Instantaneous magnetic field distribution in brushless permanent magnet DC motors. Ⅰ. Open-circuit field" IEEE Trans. on Mag., Vol. 29 Issue: 1 Part: 2, Jan. 1993, pp: 124-135.
[44] T. A. Lipo, "A d-q model for six-phase induction machines ", in conf. Rec. int. Conf. Electrical Machines, Athens, Greece,, Sept. 15-17, 1980, pp:860-867.
[45] E. E. Ward and H. Harer, "Preliminary investigation of an inverter-fed 5-phase induction motor," Proc. Inst. Elect. Eng., Vol. 116, No. 6, 1969, pp:980-984.
[46] Wijenayake, A.H.; Bailey, J.M.; McCleer, P.J. "Design optimization of an axial gap permanent magnet brushless DC motor for electric vehicle applications" Thirtieth IAS Annual Meeting, IAS '95., Conference Record of the 1995 IEEE, Vol. 1 1995, pp: 685-692.
[47] Patterson, D.; Spee, R. "The design and development of an axial flux permanent magnet brushless DC motor for wheel drive in a solar powered vehicle ", IEEE Trans. on IA, Vol. 31 Issue: 5, Sept./Oct, 1995, pp: 1054-1061.
[48] CC.Chan, J.Z.Jiang, G.H.Chen etc. "A novel high power density permanent magnet variable-speed motor". IEEE Trans. on energy conversion Vol. 8,No. 2,June 1993.pp: 297-303
[49] 沈建新等，“电动自行车轮毂式无刷直流电机结构分析”电工电能新技术，pp．5-7．
[50] Y. Kawase, etc. "3D finite element analysis of motor exited from voltage source taking in to account end-coil efects" IEEE Trans. on Mag. Vol. 33, Mar. 1997. pp: 1686-1689.
[51] A Demenko, "Movement simulation in finite element analysis of electric machine dynamic". IEEE Trans. on Magn. Vol. 32, May. 1996. pp: 1553-1556.
[52] Ju Li, etc, "Analysis of brushless DC motor considering various design schemes by 2D-finite element method", pp PB4-3.
[53] Guo Zhenhong, etc., "Study on noload air-gap flux density waveform of PMSM", Proceedings of CICEM'99, 1999, pp: 199-202.
Proceedings of CICEM'99, 1999,pp: 199-202.
[54] Tomy Sebastian, etc., "Operating limits of inverter-driven permanent magnet motor drives", IEEE Trans. on Industry, Vol. La-23, No. 2, March/April, 1987 pp: 327-333
[55] 马信山，张济世等，“电磁场基础”，清华大学出版社，1995年5月。
[56] C.C.Chan, K.T.Chou, J.Z.Jiang etc., "Novel permanent magnet motor drives for electric vehicles", IEEE Trans. on Industry Electronics Vol. 43, No. 2, April,1996. pp: 331-339
[57] 汤蕴璆；史乃，“电机学”，机械工业出版社，2001年4月。
[58] Jingqiu Qiao, Yunqiu Tand, "Cross-magnetization effect and D, Q axis coupling reactance of turbo-generator", ICEM, Sept, 12-14, 1988. Pisa, Italy. pp:109-112.
[59] 汤蕴璆主编，“电机学—机电能量转换”，机械工业出版社，1986年，6月。
[60] J.L.Coulomb, "The methodology for the determination of global electromechanical quantities from a finite element analysis and its application to the evaluation of magnetic forces, torques and ttiffness", IEEE Trans. on Mag., Vol. 19, No. 6, November 1983, pp: 2514-2519.
[61] K.Reichert, "Problems and trends in force and torque calculations by means of FE-methods", Proceedings of the International conference on Electrical Machines and Applications, ICEMA'96. Harbin China International Academic Publishers, pp: 433-437.
[62] 乔静秋，陈旭东等，“直槽与斜槽式永磁电动机的有限元分析”，电机与控制学报，2001，No．4。
[63] J. Vaananen, "Circuit theoretical approach to couple two-dimensional finite element models with exterrnal circuit equations" IEEE trans. on Mag. Vol. 32, No. 2, Mar. 1996, pp:400-410.
[64] L. Y. Xu and E Ruckstadter, "Direct modeling of switched reluctance machine by coupled filed-circuit Method", IEEE Trans. on EC, No. 3, pp: 237-242.
[65] 盛剑霓，“工程电磁场数值分析”，西安交通大学出版社，1991年11月。
[66] Dai M.; Keyhani A.; Sebastian T., "Torque ripple analysis of a permanent magnet brushless DC motor using finite element method", IEMDC 2001. IEEE International, 2001 pp: 241-245.
[67] Vineeta Gangla, Jaime De La Lee, "Electromechanical forces and torque in brushless permanent magnet machines", IEEE Trans. on Energy Conversion, Vol.6, No. 3, Sept. 1991, pp: 546-552.
[68] S Yang ect., "A novel field-circuit approach for the design and analysis of permanent magnet machines", EVS16, China, 1999.
[69] 毛鼎品，“无刷直流电动机的特性计算公式”，微特电机，1980．No．2，pp：1-8．
[70] Hwang, S.M.; Lieu, D.K., "Reduction of torque ripple in brushless DC motors", IEEE Trans. on Mag., Vol. 31 Issue: 6 Part: 2, Nov. 1995, pp: 3737-3739.
[71] Ackermann, B. Janssen, etc. "New technique for reducing cogging torque in a class of brushless DC motors", Electric Power Applications, IEEE Proceedings Vol. 139 Issue: 4, July 1992, pp: 315-320
[72] 杨仕友，倪光正等，“电机电磁场逆问题数值计算的改进Tabu算法”，中国电机工程学报，1998年3月，第18卷，第2期，pp：83-86．
[73] 杨仕友，倪光正等，“模拟退火算法的改进及其在电机电磁场逆问题数值计
算中的应用”，电工技术学报，第13卷，第2期，1998年4月，pp：21-23．
[74] Chen Xudong, Qian Jingen, etc., "An improved genetic algorithm for global optimization of electromagnetic problems. IEEE Trans. on Mag. Vol.37, No.5, Sept. 2001, pp:3579-3583.
[75] Chen Xudong, Yang Shiyou, Ni Guangzheng, "An improved Tabu Algorithm applied to global optimizations of inverse problems in electromagnetics", Proceeding of IEEE Trans. on Mag. Vol.38, No.2, March, 2002.
[76] Tang Renyuan, etc, "Optimization of electromagnetic devices by using intelligent simulated annealing algorithm", IEEE Trans. on Mag. Vol. 34, No.5, 1998, pp:2992-2995.
[77] Qiao Jingqiu, Chen Xudong, etc., "The magnetic field analysis of permanent magnet motor using 2D-FEA", Proceeding of The 3rd Asian Symposium on Applied Electromagnetics. pp:275-278.
[78] 张凤阁，王凤祥等，“改进的TABU法在异同步电动机优化中的应用”，电工电能新技术，1998，No．4．pp：36-40．
[79] 王秀和，孙玲玲等，“TABU算法在永磁起动机优化设计中的应用”，电工电能新技术，1997，No．4，pp：24-27．
[80] Yang, Yee-Pien. Chiao, Tze-Chi, "Multiobjective optimal design of a high speed brushless DC motor", Electric machines and power systems.-2000,28(1).pp: 13-30.
[81] Tae Kyung Chung; Suk Ki Kim; Song-Yop Hahn, "Optimal pole shape design for the reduction of cogging torque of brushless DC motor using evolution strategy" IEEE Transactions on Mag., Vol. 33 Issue: 2 Part: 2, Mar. 1997 pp: 1908-1911.
[82] Bianchi, N.; Bolognani, S. "Brushless DC motor design: an optimisation procedure based on genetic algorithms Electrical Machines and Drives", 1997 Eighth International Conference on (Conf. Publ. No. 444), 1997, pp: 16-20.
[83] Ki-Jin Han; Han-Sam Cho; Dong-Hyeok Cho; Hyun-Kyo Jung, "Optimal core shape design for cogging torque reduction of brushless DC motor using genetic algorithm" IEEE Trans. on Mag., Vol. 36 Issue: 4 Part: 1, July 2000, pp: 1927-1931.
[84] 王季秩，“无刷电动机的现在与未来”，微特电机，1999，No．5．
[85] 周涌，“电动车驱动用无刷直流电动机系统的设计”，微特电机，1997．No．3，pp：8-11．
[86] “微特电机设计程序——永磁式直流电动机设计程序”，上海科学技术出版社，1981。
[87] 张琛，“直流无刷电动机原理及应用”，机械工业出版社，1999．7。
[88] 叶云岳，林友仰，“计算机辅助电机优化设计与制造”，浙江大学出版社，1998年。
[89] Fred Glover. "Future paths for integer programming and links to artificial intelligence". Comput. and Ops.Res. 1986, Vol. 13, (5) pp:533-549.
[90] 陈俊峰，“永磁电机”，机械工业出版社，1982年。
[91] 黄海宏，张敬华，“一种多机低速永磁同步电动机”，微特电机，1999年，第4期，pp：6-8．
[2] 许大中，交流电机调速理论，浙江大学出版社，1991年。
[3] W. Xia, Philips S.M.Chin. "Analysis of different permanent magnet brushless motor drives for electric vehicles", EVS16, China, 1998.
[4] 唐任远等，现代永磁电机—理论与设计，机械工业出版社，1997年。
[5] Liu Tongyan etc., "The drive control system for electric vehicle driven directly by wheel motor", EVS16, China, 1998.
[6] Yue li, Todd A Walls, Jerry D.Lloyd, "A novel two-phase BPM drive system with high power density and low cost, IEEE Trans. on IA., Vol.34, No.5, Sept./Oct. 1998, pp: 1072-1080.
[7] T.J.E.Miller, Alan Huiton, etc., "Design of a synchronous reluctance motor drive" IEEE Trans. on IA., Vol. 27, No.4, July/Aug. 1991. pp:741-749.
[8] T. M. Jahns, "Flux-weakening regime operation of an interior permanent magnet synchronous motor drive," IEEE Trans. on IA., Vol. LA-23, July/Aug. 1987. pp:681-689.
[9] Chan, C.C.; Chau, K.T.; Jiang, J.Z, etc., "Novel permanent magnet motor drives for electric vehicles" , Industrial Electronics, IEEE Trans. on Vol. 43 Issue: 2, April 1996, pp: 331-339.
[10] Shigeo Morimoto, Yoji Taceda, etc. "Expansion of operating limits for permanent magnet motor by current vector control considering inverter capacity", IEEE Trans. on IA, Vol. 26, No. 5, Sept./Octo.,1990. pp:866-871.
[11] Jack, A.G.; Mecrow, B.C.; Weiner, C. "Switched reluctance and permanent magnet motors suitable for vehicle drives-a comparison", Electric Machines and Drives, 1999. International Conference IEMD '99,1999, pp: 505-507.
[12] 倪光正，钱秀英等，《电磁场数值计算》，高等教育出版社，1996年12月。
[13] Ahamad M.Naseser "Comparison of induction, PM, and SR motor technologies in EV traction systems applications". EVS16, China, 1999.
[14] 汤蕴璆，电机内的电磁场(第二版)，科学出版社，1998年1月。
[15] 廖海平，“浙江大学博士学位论文”，1998年12月。
[16] H.R.Bolton etc., "Investigation into a class of Brushless DC Motor with Quasi-square Voltage and Current", IEE Proc. Vol. 133 Pt.B,No.2 pp:103-111.
[17] 胡之光，电机电磁场的分析与计算，机械工业出版社，1982。
[18] B. Sneyers, D. W. Novotny, etc, "Field weakening in buried permanent magnet ac motor drives," IEEE Trans. on IA., vol. IA-21, mar./Apr. 1985. pp:398-407.
[19] T.M. jahns, G.B,. Kliman, etc. "Interior permanent magnet synchronous motor for adjustable speed drives," IEEE Trans. on IA., Vol. LA-22, July/Aug. 1986. pp:738-747.
[20] Y. Takeda and T. Hirasa, "Current phase control methods for permanent magnet synchronous motors considering saliency ," in PESC Conf. Rec. Apr. 1988, pp:409-414.
[21] Chalmers, B.J.; Musaba, I, "Performance characteristics of permanent magnet
and reluctance machines to meet EV requirements ", Machines and Drives for Electric and Hybrid Vehicles (Digest No: 1996/152), IEE Colloquium on, 1996,pp: 1-5
[22] Yasuyuki Sugii, Masayuki, Etc. "Applicability of various motors to electric vehicles(EV)", (武汉会议?)
[23] Jack, A.G.; Mecrow, B.C.; Weiner, C. "Switched reluctance and permanent magnet motors suitable for vehicle drives-a comparison ",Electric Machines and Drives, 1999. International Conference IEMD '99,1999,pp: 505-507.
[24] 丁志刚，“无刷直流电动机的研究和开发进展”，微电机，2000年，第33卷，第1期．pp：29-30．
[25] Yuefeng Liao, Liang Feng, etc. "A novel permanent magnet motor with doubly salient structure", IEEE Trans. on IA Vol. 31, No. 5, Sept./Oct. 1995, pp: 1069-1078.
[26] Alexander Kusko, Syed M. Peeran, "Brushless DC motors using unsymmetrical filed magnetization", IEEE Trans. on IA. Vol. LA-23, No.2, Mar/Apr. 1987. pp:319-326.
[27] Gare Bedrosian, "A new method for coupling finite element field solutions with external circuit and kinematics" IEEE Trans. on Mag., Vol. 29, No. 2 Mar., 1993, pp: 1664-1668.
[28] Francis Piriou and Adel Razek "Finite Element Analysis in Electromagnetic Systems Accounting for Electric Circuits" IEEE Trans. on Mag., Vol 29,No. 2 March, 1993, pp 1669-1675
[29] 傅为农，“斜槽异步电机的场路耦合时步法有限元模型及其应用”，上海大学博士学位论文，1997年8月。
[30] Chan T.F, Lie-Tong Yan, etc. "Design of a permanent-magnet brushless DC motor drive for an electric bicycle" Power Electronics and Drive Systems, 1999. PEDS '99. Proceedings of the IEEE 1999 International Conference on Vol. 2, 1999 pp: 714-718.
[31] Wijenayake, A.H.; Bailey, etc. "Design optimization of an axial gap permanent magnet brushless DC motor for electric vehicle applications ", Thirtieth IAS Annual Meeting, Conference Record of the 1995 IEEE, Vol. 1,pp: 685-692.
[32] Fang Lin Luo; Hock Guan Yeo "Advanced PM brushless DC motor control and system for electric vehicles", Industry Applications Conference, 2000. Conference Record of the 2000 IEEE, Vol. 2,2000, pp: 1336-1343.
[33] Alhamadi, M.A.; Demerdash, N.A. "Three dimensional magnetic field computation by a coupled vector-scalar potential method in brushless DC motors with skewed permanent magnet mounts-the no-load and load results", IEEE Trans. on Energy Conversion, Vol. 9 Issue: 1, Mar. 1994,pp: 15-25.
[34] Alhamadi, M.A.; Demerdash, N.A. "Modeling of effects of skewing of rotor mounted permanent magnets on the performance of brushless DC motors ", IEEE Trans. on Energy Conversion,, Vol. 6 Issue: 4, Dec. 1991 pp: 721-729.
[35] Bodin, F.; Siala, S.; Sicot, L. "State space fuzzy controller for a brushless DC motor ", PESC '97 Record., 28th Annual IEEE, Vol. 2,1997, pp: 869-874.
[36] Sozer, Y.; Kaufman, H.; Torrey, D.A. "Direct model reference adaptive control of permanent magnet brushless DC motors ", Control Applications, 1997, Proceedings of the 1997 IEEE International Conference on, 1997, pp: 633-638.
[37] Ghandakly, A.A.; Owed, M.R. "Design of an adaptive speed controller for DC brushless motors ", Thirtieth IAS Annual Meeting, LAS '95., Conference Record of the 1995 IEEE, Vol. 2,1995 pp: 1626-1633
[38] Y. Liao, T.A.Lipo, "A new doubly salient permanent magnet motor for adjustable speed drives", Electric Machines and Power Systems No.2, 1994, pp:259-270.
[39] Alhamadi, M.A.; Demerdash, N.A. "Three dimensional magnetic field computation by a coupled vector-scalar potential method in brushless DC motors with skewed permanent magnet mounts-the formulation and FE grids ", IEEE Trans on Energy Conversion,, Vol.9 Issue: 1, March 1994 pp: 1-14.
[40] Zhu, Z.Q.; Howe, D. "Instantaneous magnetic field distribution in permanent magnet brushless DC motors. Ⅳ. Magnetic field on load ", IEEE Trans. on Mag., Vol. 29 Issue: 1 Part: 2, Jan. 1993 pp: 152-158.
[41] Zhu, Z.Q.; Howe, D. "Instantaneous magnetic field distribution in brushless permanent magnet DC motors. Ⅲ. Effect of stator slotting ", IEEE Trans. on Mag., Vol. 29 Issue: 1 Part: 2, Jan. 1993, pp: 143-151.
[42] Zhu, Z.Q.; Howe, D. "Instantaneous magnetic field distribution in brushless permanent magnet DC motors. Ⅱ. Armature-reaction field ", IEEE Trans. on Mag., Vol. 29 Issue: 1 Part: 2, Jan. 1993, pp: 136-142.
[43] Zhu, Z.Q.; Howe, D.; Bolte, E.; Ackermann, B. "Instantaneous magnetic field distribution in brushless permanent magnet DC motors. Ⅰ. Open-circuit field" IEEE Trans. on Mag., Vol. 29 Issue: 1 Part: 2, Jan. 1993, pp: 124-135.
[44] T. A. Lipo, "A d-q model for six-phase induction machines ", in conf. Rec. int. Conf. Electrical Machines, Athens, Greece,, Sept. 15-17, 1980, pp:860-867.
[45] E. E. Ward and H. Harer, "Preliminary investigation of an inverter-fed 5-phase induction motor," Proc. Inst. Elect. Eng., Vol. 116, No. 6, 1969, pp:980-984.
[46] Wijenayake, A.H.; Bailey, J.M.; McCleer, P.J. "Design optimization of an axial gap permanent magnet brushless DC motor for electric vehicle applications" Thirtieth IAS Annual Meeting, IAS '95., Conference Record of the 1995 IEEE, Vol. 1 1995, pp: 685-692.
[47] Patterson, D.; Spee, R. "The design and development of an axial flux permanent magnet brushless DC motor for wheel drive in a solar powered vehicle ", IEEE Trans. on IA, Vol. 31 Issue: 5, Sept./Oct, 1995, pp: 1054-1061.
[48] CC.Chan, J.Z.Jiang, G.H.Chen etc. "A novel high power density permanent magnet variable-speed motor". IEEE Trans. on energy conversion Vol. 8,No. 2,June 1993.pp: 297-303
[49] 沈建新等，“电动自行车轮毂式无刷直流电机结构分析”电工电能新技术，pp．5-7．
[50] Y. Kawase, etc. "3D finite element analysis of motor exited from voltage source taking in to account end-coil efects" IEEE Trans. on Mag. Vol. 33, Mar. 1997. pp: 1686-1689.
[51] A Demenko, "Movement simulation in finite element analysis of electric machine dynamic". IEEE Trans. on Magn. Vol. 32, May. 1996. pp: 1553-1556.
[52] Ju Li, etc, "Analysis of brushless DC motor considering various design schemes by 2D-finite element method", pp PB4-3.
[53] Guo Zhenhong, etc., "Study on noload air-gap flux density waveform of PMSM", Proceedings of CICEM'99, 1999, pp: 199-202.
Proceedings of CICEM'99, 1999,pp: 199-202.
[54] Tomy Sebastian, etc., "Operating limits of inverter-driven permanent magnet motor drives", IEEE Trans. on Industry, Vol. La-23, No. 2, March/April, 1987 pp: 327-333
[55] 马信山，张济世等，“电磁场基础”，清华大学出版社，1995年5月。
[56] C.C.Chan, K.T.Chou, J.Z.Jiang etc., "Novel permanent magnet motor drives for electric vehicles", IEEE Trans. on Industry Electronics Vol. 43, No. 2, April,1996. pp: 331-339
[57] 汤蕴璆；史乃，“电机学”，机械工业出版社，2001年4月。
[58] Jingqiu Qiao, Yunqiu Tand, "Cross-magnetization effect and D, Q axis coupling reactance of turbo-generator", ICEM, Sept, 12-14, 1988. Pisa, Italy. pp:109-112.
[59] 汤蕴璆主编，“电机学—机电能量转换”，机械工业出版社，1986年，6月。
[60] J.L.Coulomb, "The methodology for the determination of global electromechanical quantities from a finite element analysis and its application to the evaluation of magnetic forces, torques and ttiffness", IEEE Trans. on Mag., Vol. 19, No. 6, November 1983, pp: 2514-2519.
[61] K.Reichert, "Problems and trends in force and torque calculations by means of FE-methods", Proceedings of the International conference on Electrical Machines and Applications, ICEMA'96. Harbin China International Academic Publishers, pp: 433-437.
[62] 乔静秋，陈旭东等，“直槽与斜槽式永磁电动机的有限元分析”，电机与控制学报，2001，No．4。
[63] J. Vaananen, "Circuit theoretical approach to couple two-dimensional finite element models with exterrnal circuit equations" IEEE trans. on Mag. Vol. 32, No. 2, Mar. 1996, pp:400-410.
[64] L. Y. Xu and E Ruckstadter, "Direct modeling of switched reluctance machine by coupled filed-circuit Method", IEEE Trans. on EC, No. 3, pp: 237-242.
[65] 盛剑霓，“工程电磁场数值分析”，西安交通大学出版社，1991年11月。
[66] Dai M.; Keyhani A.; Sebastian T., "Torque ripple analysis of a permanent magnet brushless DC motor using finite element method", IEMDC 2001. IEEE International, 2001 pp: 241-245.
[67] Vineeta Gangla, Jaime De La Lee, "Electromechanical forces and torque in brushless permanent magnet machines", IEEE Trans. on Energy Conversion, Vol.6, No. 3, Sept. 1991, pp: 546-552.
[68] S Yang ect., "A novel field-circuit approach for the design and analysis of permanent magnet machines", EVS16, China, 1999.
[69] 毛鼎品，“无刷直流电动机的特性计算公式”，微特电机，1980．No．2，pp：1-8．
[70] Hwang, S.M.; Lieu, D.K., "Reduction of torque ripple in brushless DC motors", IEEE Trans. on Mag., Vol. 31 Issue: 6 Part: 2, Nov. 1995, pp: 3737-3739.
[71] Ackermann, B. Janssen, etc. "New technique for reducing cogging torque in a class of brushless DC motors", Electric Power Applications, IEEE Proceedings Vol. 139 Issue: 4, July 1992, pp: 315-320
[72] 杨仕友，倪光正等，“电机电磁场逆问题数值计算的改进Tabu算法”，中国电机工程学报，1998年3月，第18卷，第2期，pp：83-86．
[73] 杨仕友，倪光正等，“模拟退火算法的改进及其在电机电磁场逆问题数值计
算中的应用”，电工技术学报，第13卷，第2期，1998年4月，pp：21-23．
[74] Chen Xudong, Qian Jingen, etc., "An improved genetic algorithm for global optimization of electromagnetic problems. IEEE Trans. on Mag. Vol.37, No.5, Sept. 2001, pp:3579-3583.
[75] Chen Xudong, Yang Shiyou, Ni Guangzheng, "An improved Tabu Algorithm applied to global optimizations of inverse problems in electromagnetics", Proceeding of IEEE Trans. on Mag. Vol.38, No.2, March, 2002.
[76] Tang Renyuan, etc, "Optimization of electromagnetic devices by using intelligent simulated annealing algorithm", IEEE Trans. on Mag. Vol. 34, No.5, 1998, pp:2992-2995.
[77] Qiao Jingqiu, Chen Xudong, etc., "The magnetic field analysis of permanent magnet motor using 2D-FEA", Proceeding of The 3rd Asian Symposium on Applied Electromagnetics. pp:275-278.
[78] 张凤阁，王凤祥等，“改进的TABU法在异同步电动机优化中的应用”，电工电能新技术，1998，No．4．pp：36-40．
[79] 王秀和，孙玲玲等，“TABU算法在永磁起动机优化设计中的应用”，电工电能新技术，1997，No．4，pp：24-27．
[80] Yang, Yee-Pien. Chiao, Tze-Chi, "Multiobjective optimal design of a high speed brushless DC motor", Electric machines and power systems.-2000,28(1).pp: 13-30.
[81] Tae Kyung Chung; Suk Ki Kim; Song-Yop Hahn, "Optimal pole shape design for the reduction of cogging torque of brushless DC motor using evolution strategy" IEEE Transactions on Mag., Vol. 33 Issue: 2 Part: 2, Mar. 1997 pp: 1908-1911.
[82] Bianchi, N.; Bolognani, S. "Brushless DC motor design: an optimisation procedure based on genetic algorithms Electrical Machines and Drives", 1997 Eighth International Conference on (Conf. Publ. No. 444), 1997, pp: 16-20.
[83] Ki-Jin Han; Han-Sam Cho; Dong-Hyeok Cho; Hyun-Kyo Jung, "Optimal core shape design for cogging torque reduction of brushless DC motor using genetic algorithm" IEEE Trans. on Mag., Vol. 36 Issue: 4 Part: 1, July 2000, pp: 1927-1931.
[84] 王季秩，“无刷电动机的现在与未来”，微特电机，1999，No．5．
[85] 周涌，“电动车驱动用无刷直流电动机系统的设计”，微特电机，1997．No．3，pp：8-11．
[86] “微特电机设计程序——永磁式直流电动机设计程序”，上海科学技术出版社，1981。
[87] 张琛，“直流无刷电动机原理及应用”，机械工业出版社，1999．7。
[88] 叶云岳，林友仰，“计算机辅助电机优化设计与制造”，浙江大学出版社，1998年。
[89] Fred Glover. "Future paths for integer programming and links to artificial intelligence". Comput. and Ops.Res. 1986, Vol. 13, (5) pp:533-549.
[90] 陈俊峰，“永磁电机”，机械工业出版社，1982年。
[91] 黄海宏，张敬华，“一种多机低速永磁同步电动机”，微特电机，1999年，第4期，pp：6-8．