Control and Drive Techniques for Multiphase Machines: A Review
Liu Zicheng1, 2, Li Yongdong1, Zheng Zedong1
1. Depterment of Electrical Engineering Tsinghua University Beijing 100084 China; 2. School of Electrical Engineering Beijing Jiaotong University Beijing 100044 China
Abstract Multiphase machines are gaining increasing popularity because of their distinct advantages over three-phase alternatives, such as high power at low voltage, high reliability and improved control dimensions. This paper describes the development of multiphase drive techniques at home and abroad, then introduces three control methods including vector control, direct torque control and model predictive control, and compares decoupled fault-tolerant control with optimal fault-tolerant control. Furthermore, the different kinds of multiphase converter topologies are listed, and two kinds of PWM methods are discussed in this paper. Finally, the developing trends of all the above control and drive techniques are summarized.
Liu Zicheng,Li Yongdong,Zheng Zedong. Control and Drive Techniques for Multiphase Machines: A Review[J]. Transactions of China Electrotechnical Society, 2017, 32(24): 17-29.
[1] 李崇坚. 大功率交流电机变频调速技术的研究[J]. 中国工程科学, 2009, 11(5): 31-36. Li Chongjian. Research on the variable speed tech- nology of large power alternating current motor[J]. Engineering Science, 2009, 11(5): 31-36. [2] Ge B, Peng F Z, Li Y. Multilevel converter/inverter topologies and applications[J]. Power Electronics for Renewable Energy Systems, Transportation and Industrial Applications, 2014, 30(5): 422-462. [3] 王琛琛, 李永东. 多电平变换器拓扑关系及新型拓扑[J]. 电工技术学报, 2011, 26(1): 92-99. Wang Chenchen, Li Yongdong. Multilevel converter topologies and two novel topologies[J]. Transactions of China Electrotechnical Society, 2011, 26(1): 92- 99. [4] Ji S, Lu T, Zhao Z, et al. Series-connected HV-IGBTs using active voltage balancing control with status feedback circuit[J]. IEEE Transactions on Power Electronics, 2015, 30(8): 4165-4174. [5] 卢峥, 欧阳红林, 孟超, 等. 多电平双Y移30°永磁同步电机的矢量控制系统[J]. 电工技术学报, 2016, 31(22): 45-56. Lu Zheng, Ouyang Honglin, Meng Chao, et al. Vector control system of multilevel inverter double star winding shifted by 30°permanent magnet synchronous motor[J]. Transactions of China Electrotechnical Society, 2016, 31(22): 45-56. [6] Levi E. Multiphase electric machines for variable- speed applications[J]. IEEE Transactions on Indu- strial Electronics, 2008, 55(5): 1893-1909. [7] Levi E, Bojoi R, Profumo F, et al. Multiphase induction motor drives—a technology status review[J]. IET Electric Power Applications, 2007, 1(4): 489-516. [8] Bojoi R, Cavagnino A, Tenconi A, et al. Multiphase electrical machines and drives in the transportation electrification[C]//IEEE 1st International Forum on Research and Technologies for Society and Industry Leveraging A Better Tomorrow (RTSI), Turin, Italy, 2015: 205-212. [9] 王东, 马伟明, 郭云, 等. 基于非正弦供电方式的多相感应电动机建模[J]. 电工技术学报, 2010, 25(2): 6-14. Wang Dong, Ma Weiming, Guo Yun, et al. Modelling of multiphase induction motor with non-sinusoidal supply[J]. Transactions of China Electrotechnical Society, 2010, 25(2): 6-14. [10] 吴新振, 王祥珩, 罗成. 多相异步电机谐波电流与谐波磁势的对应关系[J]. 清华大学学报: 自然科学版, 2005, 45(7): 865-868. Wu Xinzhen, Wang Xiangheng, Luo Cheng. Relation- ship between harmonic currents and harmonic magneto-motive forces in multi-phase induction machines[J]. Journal of Tsinghua University: Science and Technology, 2005, 45(7): 865-868. [11] Ward E E, HÃ Rer H. Preliminary investigation of an invertor-fed 5-phase induction motor[J]. Proceedings of the Institution of Electrical Engineers, 1969, 116(6): 980-984. [12] Jahns T M. Improved reliability in solid-state AC drives by means of multiple independent phase drive units[J]. IEEE Transactions on Industry Applications, 1980, IA-16(3): 321-331. [13] Yifan Z, Lipo T A. Space vector PWM control of dual three-phase induction machine using vector space decomposition[J]. IEEE Transactions on Industry Applications, 1995, 31(5): 1100-1109. [14] Zhao Y, Lipo T A. Modeling and control of a multi- phase induction machine with structural unbalance[J]. IEEE Transactions on Energy Conversion, 1996, 11(3): 570-577. [15] Toliyat H A, Lipo T A, White J C. Analysis of a concentrated winding induction machine for adjust- able speed drive applications I. Motor analysis[J]. IEEE Transactions on Energy Conversion, 1991, 6(4): 679-683. [16] Xu H, Toliyat H A, Petersen L J. Resilient current control of five-phase induction motor under asymmetrical fault conditions[C]//Seventeenth Annual IEEE Applied Power Electronics Conference and Exposition, Dallas, 2002: 64-71. [17] Dordevic O, Jones M, Levi E. A comparison of carrier-based and space vector PWM techniques for three-level five-phase voltage source inverters[J]. IEEE Transactions on Industrial Informatics, 2013, 9(2): 609-619. [18] Levi E, Dujic D, Jones M, et al. Analytical determination of DC-Bus utilization limits in multi- phase VSI supplied AC drives[J]. IEEE Transactions on Energy Conversion, 2008, 23(2): 433-443. [19] Bodo N, Jones M, Levi E. A space vector PWM with common-mode voltage elimination for open-end winding five-phase drives with a single DC supply[J]. IEEE Transactions on Industrial Electronics, 2014, 61(5): 2197-2207. [20] Nguyen N K, Meinguet F, Semail E, et al. Fault- tolerant operation of an open-end winding five-phase PMSM drive with short-circuit inverter fault[J]. IEEE Transactions on Industrial Electronics, 2016, 63(1): 595-605. [21] Mohammadpour A, Parsa L. Global fault-tolerant control technique for multiphase permanent-magnet machines[J]. IEEE Transactions on Industry Appli- cations, 2015, 51(1): 178-186. [22] Riveros J A, Barrero F, Levi E, et al. Variable-speed five-phase induction motor drive based on predictive torque control[J]. IEEE Transactions on Industrial Electronics, 2013, 60(8): 2957-2968. [23] Guzman H, Barrero F, Duran M J. IGBT-gating failure effect on a fault-tolerant predictive current- controlled five-phase induction motor drive[J]. IEEE Transactions on Industrial Electronics, 2015, 62(1): 15-20. [24] 孙俊忠, 马伟明, 吴旭升, 等. 3/12相双绕组发电机数学模型研究[J]. 中国电机工程学报, 2003, 23(1): 93-96. Sun Junzhong, Ma Weiming, Wu Xusheng, et al. Study on mathematical model of 3-&12-phase synchronous generators with AC and bridge rectified DC output[J]. Proceedings of the CSEE, 2003, 23(1): 93-96. [25] 王东, 马伟明, 刘德志, 等. 12/3相双绕组感应发电机直流侧突然短路电流分析[J]. 中国电机工程学报, 2005, 25(15): 133-139. Wang Dong, Ma Weiming, Liu Dezhi, et al. Study on currents of sudden DC-side short circuit of a 12/3- phase dual stator-winding induction generator[J]. Proceedings of the CSEE, 2005, 25(15): 133-139. [26] 王东, 吴新振, 程思为, 等. 非正弦供电多相感应电机稳态性能分析[J]. 中国科学: 技术科学, 2015, 45(3): 322-329. Wang Dong, Wu Xinzhen, Cheng Siwei, et al. Steady state performance analysis of multi-phase induction motor with non-sinusoidal supply[J]. Science China: Technical Sciences, 2015, 45(3): 322-329. [27] 郑晓钦, 王东. 十五相感应电机对称缺相运行时的定子漏抗计算[J]. 电工技术学报, 2016, 31(15): 25-31. Zheng Xiaoqin, Wang Dong. Calculation of stator leakage reactance of fifteen-phase induction motor under symmetrical fault condition[J]. Transactions of China Electrotechnical Society, 2016, 31(15): 25-31. [28] 晏明, 马伟明, 欧阳斌, 等. 双九相储能电机系统性能研究[J]. 中国电机工程学报, 2015, 35(15): 3770-3775. Yan Ming, Ma Weiming, Ouyyang Bin, et al. Study on the characteristics of dual nine-phase energy storage electrical machine[J]. Proceedings of the CSEE, 2015, 35(15): 3770-3775. [29] 庄朝晖. 多相感应电机变频调速系统控制方法研究[D]. 武汉: 华中科技大学, 2001. [30] Wu F, Zheng P, Cheng L, et al. Analysis and experimental evaluation of harmonic leakage inductance for polyphase PM machines having close slot and pole combinations[J]. IEEE Transactions on Magnetics, 2015, 51(11): 1-4. [31] 高宏伟, 杨贵杰, 刘剑. 三次谐波注入式五相永磁同步电机矢量控制策略[J]. 中国电机工程学报, 2014, 34(24): 4101-4108. Gao Hongwei, Yang Guijie, Liu Jian. A vector control strategy for five-phase PMSM with third harmonic injection[J]. Proceedings of the CSEE, 2014, 34(24): 4101-4108. [32] 赵品志, 杨贵杰, 李勇. 基于双同步旋转坐标系的五相永磁同步电动机三次谐波电流抑制方法[J]. 中国电机工程学报, 2011, 31(12): 71-76. Zhao Pinzhi, Yang Guijie, Li Yong. Third harmonic current restraining of five-phase permanent magnet synchronous motor based on dual synchronous rotating coordinates[J]. Proceedings of the CSEE, 2011, 31(12): 71-76. [33] Zhou C, Yang G, Su J. PWM strategy with minimum harmonic distortion for dual three-phase permanent- magnet synchronous motor drives operating in the overmodulation region[J]. IEEE Transactions on Power Electronics, 2016, 31(2): 1367-1380. [34] 刘剑, 苏健勇, 杨贵杰, 等. 六相永磁同步发电机容错控制的谐波补偿研究[J]. 电机与控制学报, 2014, 18(1): 1-10. Liu Jian, Su Jianyong, Yang Guijie, et al. Study of harmonic compensation for six-phase PMSG in fault tolerant control[J]. Electric Machines and Control, 2014, 18(1): 1-10. [35] 王永兴, 温旭辉, 赵峰. 多相永磁同步电机多维优化矢量控制[J]. 中国电机工程学报, 2015, 35(10): 2534-2543. Wang Yongxing, Wen Xuhui, Zhao Feng. Multi- dimensional optimal vector control of multi-phase permanent magnet synchronous motors[J]. Pro- ceedings of the CSEE, 2015, 35(10): 2534-2543. [36] 薛山. 多相永磁同步电机驱动技术研究[D]. 北京: 中国科学院研究生院(电工研究所), 2006. [37] 王永兴, 温旭辉, 赵峰. 六相永磁同步电机缺相容错控制[J]. 电工技术学报, 2015, 30(5): 49-58. Wang Yongxing, Wen Xuhui, Zhao Feng. The fault- tolerant control for six-phase permanent magnet synchronous machines with one phase failure[J]. Transactions of China Electrotechnical Society, 2015, 30(5): 49-58. [38] Kong W, Huang J, Qu R, et al. Nonsinusoidal power supply analysis for concentrated-full-pitch-winding multiphase induction motor[J]. IEEE Transactions on Industrial Electronics, 2016, 63(1): 574-582. [39] 康敏, 黄进, 刘东, 等. 多相异步电机参数的计算与测量[J]. 中国电机工程学报, 2010, 30(24): 81-87. Kang Min, Huang Jin, Liu Dong, et al. Calculation and measurement of parameters of a multiphase induction motor[J]. Proceedings of the CSEE, 2010, 30(24): 81-87. [40] 汤浩. 九相感应电机矢量控制系统的研究[D]. 杭州: 浙江大学, 2013. [41] 白玉茅. 九相感应电机的直接转矩控制研究[D]. 杭州: 浙江大学, 2012. [42] 盛爽, 陆海峰, 瞿文龙, 等. 基于矢量分解和叠加原理的双三相感应电机在全调制比范围内的PWM策略[J]. 中国电机工程学报, 2013, 23(18): 103-110. Sheng Shuang, Lu Haifeng, Qu Wenlong, et al. The PWM strategy in full modulation region for dual three-phase-induction motors based on vector decomposition and superposition principle[J]. Pro- ceedings of the CSEE, 2013, 23(18): 103-110. [43] 盛爽, 陆海峰, 瞿文龙, 等. 双三相感应电机谐波平面电压注入法在线辨识定子电阻和漏感策略[J]. 中国电机工程学报, 2014, 34(6): 872-881. Sheng Shuang, Lu Haifeng, Qu Wenlong, et al. The stator resistance and leakage inductance on-line identification strategy of dual three-phase induction motors by voltage vector injection in harmonic subspace[J]. Proceedings of the CSEE, 2014, 34(6): 872-881. [44] 张杰, 柴建云, 孙旭东, 等. 双三相异步电机电流预测控制算法[J]. 电工技术学报, 2015, 30(9): 12-21. Zhang Jie, Chai Jianyun, Sun Xudong, et al. Predictive current control methods for dual three phase induction machine[J]. Transactions of China Electrotechnical Society, 2015, 30(9): 12-21. [45] 刘自程, 郑泽东, 彭凌, 等. 船舶电力推进中十五相感应电机同轴运行及容错控制策略[J]. 电工技术学报, 2014, 29(3): 65-74. Liu Zicheng, Zheng Zedong, Peng Ling, et al. Fixed joint double fifteen-phase induction motor control and fault-tolerant control in ship propulsion system[J]. Transactions of China Electrotechnical Society, 2014, 29(3): 65-74. [46] 喻超, 刘建设, 沈枫. 一种15相电机分通道控制系统及控制方法: 中国, 104518724[P]. 2015-04-15. [47] 国内最大功率船用电力推进系统进入“中国时代”[EB/OL]. 2015-07-13. http://www.csic712.com/newsview. asp?News_ID=274. [48] Huangsheng X, Toliyat H A, Petersen L J. Rotor field oriented control of five-phase induction motor with the combined fundamental and third harmonic currents[C]//Sixteenth Annual IEEE Applied Power Electronics Conference and Exposition, Anaheim, CA, 2001: 392-398. [49] 王东, 吴新振, 郭云珺, 等. 非正弦供电十五相感应电机谐波电压确定[J]. 中国电机工程学报, 2012, 32(24): 126-133. Wang Dong, Wu Xinzhen, Guo Yunjun, et al. Determination of harmonic voltages for fifteen-phase induction motors with non-sinusoidal supply[J]. Pro- ceedings of the CSEE, 2012, 32(24): 126-133. [50] 袁飞雄, 黄声华, 龙文枫. 六相永磁同步电机谐波电流抑制技术[J]. 电工技术学报, 2011, 26(9): 31-36. Yuan Feixiong, Huang Shenghua, Long Wenfeng. Techniques to restrain harmonics of six-phase per- manent magnet synchronous motors[J]. Transactions of China Electrotechnical Society, 2011, 26(9): 31-36. [51] Liu Z, Zheng Z, Xu L, et al. Current balance control for symmetrical multiphase inverters[J]. IEEE Transa- ctions on Power Electronics, 2016, 31(6): 4005-4012. [52] Toliyat H A, Xu H. A novel direct torque control (DTC) method for five-phase induction machines[C]// Fifteenth Annual IEEE Applied Power Electronics Conference and Exposition, New Orleans, USA, 2000: 162-168. [53] Parsa L, Toliyat H A. Sensorless direct torque control of five-phase interior permanent-magnet motor drives[J]. IEEE Transactions on Industry Applications, 2007, 43(4): 952-959. [54] Guzman H, Duran M J, Barrero F, et al. Speed control of five-phase induction motors with integrated open- phase fault operation using model-based predictive current control techniques[J]. IEEE Transactions on Industrial Electronics, 2014, 61(9): 4474-4484. [55] De Lillo L, Empringham L, Wheeler P W, et al. Multiphase power converter drive for fault-tolerant machine development in aerospace applications[J]. IEEE Transactions on Industrial Electronics, 2010, 57(2): 575-583. [56] McCoy T J. Trends in ship electric propulsion[C]// IEEE Power Engineering Society Summer Meeting, Chicago, IL, USA, 2002: 343-346. [57] Wenping C, Mecrow B C, Atkinson G J, et al. Overview of electric motor technologies used for more electric aircraft (MEA)[J]. IEEE Transactions on Industrial Electronics, 2012, 59(9): 3523-3531. [58] Ryu H M, Kim J W, Sul S K. Synchronous-frame current control of multiphase synchronous motor under asymmetric fault condition due to open phases[J]. IEEE Transactions on Industry Appli- cations, 2006, 42(4): 1062-1070. [59] 朱鹏, 张晓锋, 乔鸣忠, 等. 五相集中整距绕组感应电机缺相容错控制[J]. 中国电机工程学报, 2011, 31(33): 131-137. Zhu Peng, Zhang Xiaofeng, Qiao Zhongming, et al. Tolerant control strategy for five-phase concentrated full-pitch windings induction motor under open phases fault[J]. Proceedings of the CSEE, 2011, 31(33): 131-137. [60] Toliyat H A. Analysis and simulation of five-phase variable-speed induction motor drives under asymmetrical connections[J]. IEEE Transactions on Power Electronics, 1998, 13(4): 748-756. [61] 周长攀, 杨贵杰, 苏健勇, 等. 基于正常解耦变换的双三相永磁同步电机缺相容错控制策略[J]. 电工技术学报, 2017, 32(3): 86-96. Zhou Changpan, Yang Guijie, Su Jianyong, et al. The control strategy for dual three-phase PMSM based on normal decoupling transformation under fault condition due to open phases[J]. Transactions of China Elec- trotechnical Society, 2017, 32(3): 86-96. [62] Tani A, Mengoni M, Zarri L, et al. Control of multiphase induction motors with an odd number of phases under open-circuit phase faults[J]. IEEE Transactions on Power Electronics, 2012, 27(2): 565-577. [63] Che H S, Duran M J, Levi E,et al. Post fault operation of an asymmetrical six-phase induction machine with single and two isolated neutral points[J]. IEEE Transactions on Power Electronics, 2014, 29(10): 5406-5416. [64] Huangsheng X, Toliyat H A, Petersen L J. Resilient current control of five-phase induction motor under asymmetrical fault conditions[C]//Applied Power Electronics Conference and Exposition, Dallas, 2002: 64-71. [65] Morsy A S, Abdelkhalik A S, Abbas A, et al. Open loop V/f control of multiphase induction machine under open-circuit phase faults[C]//IEEE Applied Power Electronics Conference and Exposition, Long Beach, CA, 2013: 1170-1176. [66] Iqbal A, Abu-Rub H, Rodriguez J, et al. Simple carrier-based PWM technique for a three-to- nine-phase direct AC-AC converter[J]. IEEE Transa- ctions on Industrial Electronics, 2011, 58(11): 5014- 5023. [67] Chai M, Xiao D, Dutta R, et al. Space vector PWM techniques for three-to-five-phase indirect matrix converter in the overmodulation region[J]. IEEE Transactions on Industrial Electronics, 2016, 63(1): 550-561. [68] Stemmler H, Guggenbach P. Configurations of high- power voltage source inverter drives[C]//Fifth European Conference on Power Electronics and Applications, Brighton, UK, 1993: 7-14. [69] Sun C, Ai S, Hu L, et al. The development of a 20MW PWM driver for advanced fifteen-phase propulsion induction motors[J]. Journal of Power Electronics, 2015, 15(1): 146-159. [70] Liu Z, Zheng Z, Li Y,et al. A carrier-based PWM method with zero-sequence current elimination for multiphase double-end winding drives[C]//18th Inter- national Conference on Electrical Machines and Systems (ICEMS), Pattaya, Thailand, 2015: 1519- 1523. [71] Edpuganti A, Rathore A K. New optimal pulse width modulation for single DC-link dual-inverter fed open- end stator winding induction motor drive[J]. IEEE Transactions on Power Electronics, 2015, 30(8): 4386-4393. [72] Somani A, Gupta R K, Mohapatra K K, et al. On the causes of circulating currents in PWM drives with open-end winding AC machines[J]. IEEE Transa- ctions on Industrial Electronics, 2013, 60(9): 3670- 3678. [73] Darijevic M, Jones M, Levi E. An open-end winding four-level five-phase drive[J]. IEEE Transactions on Industrial Electronics, 2016, 63(1): 538-549. [74] Ren Y, Zhu Z Q. Enhancement of steady-state performance in direct-torque-controlled dual three- phase permanent-magnet synchronous machine drives with modified switching table[J]. IEEE Transactions on Industrial Electronics, 2015, 62(6): 3338-3350. [75] Chen S, Lipo T A, Fitzgerald D. Source of induction motor bearing currents caused by PWM inverters[J]. IEEE Transactions on Energy Conversion, 1996, 11(1): 25-32. [76] Zhang R, Wu X, Wang T. Analysis of common mode EMI for three-phase voltage source converters[C]// IEEE 34th Annual Power Electronics Specialist Conference, Acapulco, Mexico, 2003: 1510-1515. [77] Parsa L, Toliyat H A. Fault-tolerant interior- permanent-magnet machines for hybrid electric vehicle applications[J]. IEEE Transactions on Vehicular Technology, 2007, 56(4): 1546-1552. [78] Sadeghi S, Parsa L, Toliyat H A. Extending speed range of five-phase PM machines by changing the stator windings connections[C]//IEEE International Electric Machines & Drives Conference, Niagara Falls, 2011: 1540-1545. [79] Iqbal A, Levi E. Space vector PWM techniques for sinusoidal output voltage generation with a five- phase voltage source inverter[J]. Electric Power Components and Systems, 2006, 34(2): 119-140. [80] Huangsheng X, Toliyat H A, Petersen L J. Five-phase induction motor drives with DSP-based control system[J]. IEEE Transactions on Power Electronics, 2002, 17(4): 524-533. [81] 王又珑. 十五相感应电机磁场分析及驱动技术研究[D]. 北京: 中国科学院电工研究所, 2009. [82] 薛山, 温旭辉. 一种新颖的多相SVPWM[J]. 电工技术学报, 2006, 21(2): 68-72. Xue Shan, Wen Xuhui. Novel multiphase SVPWM[J]. Transactions of China Electrotechnical Society, 2006, 21(2): 68-72. [83] 高宏伟, 杨贵杰, 刘剑. 基于调制函数的五相电压源逆变器SVPWM算法[J]. 电机与控制学报, 2014, 18(2): 56-61. Gao Hongwei, Yang Guijie, Liu Jian. SVPWM algorithm for five-phase voltage source inverter based on modulation functions[J]. Electric Machines and Control, 2014, 18(2): 56-61. [84] Dordevic O, Levi E, Jones M. A vector space decomposition based space vector PWM algorithm for a three-level seven-phase voltage source inver- ter[J]. IEEE Transactions on Power Electronics, 2013, 28(2): 637-649. [85] Ryu H, Kim J, Sul S. Analysis of multiphase space vector pulse-width modulation based on multiple dq spaces concept[J]. IEEE Transactions on Power Electronics, 2005, 20(6): 1364-1371. [86] 刘东, 黄进, 于文娟, 等. 空间矢量PWM多相变频调速系统非正弦供电技术[J]. 电机与控制学报, 2010, 14(9): 41-47. Liu Dong, Huang Jin, Yu Wenjuan, et al. Non- sinusoidal output voltage for multiphase variable speed drives with space vector PWM[J]. Electric Machines and Control, 2010, 14(9): 41-47. [87] Iqbal A, Moinuddin S. Comprehensive relationship between carrier-based PWM and space vector PWM in a five-phase VSI[J]. IEEE Transactions on Power Electronics, 2009, 24(10): 2379-2390. [88] 于飞, 张晓锋, 乔鸣忠. 基于零序信号注入的载波型多相PWM控制技术[J]. 电工技术学报, 2009, 24(2): 127-131. Yu Fei, Zhang Xiaofeng, Qiao Mingzhong. Multi- phase carrier PWM control technology based on zero-sequence signal injection[J]. Transactions of China Electrotechnical Society, 2009, 24(2): 127-131. [89] Karugaba S, Ojo O. A carrier-based PWM modu- lation technique for balanced and unbalanced reference voltages in multiphase voltage-source inverters[J]. IEEE Transactions on Industry Appli- cations, 2012, 48(6): 2102-2109. [90] Bodo N, Levi E, Jones M, et al. Investigation of carrier-based PWM Techniques for a five-phase open-end winding drive topology[J]. IEEE Transa- ctions on Industrial Electronics, 2013, 60(5): 2054- 2065. [91] Glose D, Kennel R. Carrier-based pulse width modulation for symmetrical six-phase drives[J]. IEEE Transactions on Power Electronics, 2015, 30(12): 6873-6882. [92] Liu Z, Zheng Z, Sudhoff S D, et al. Reduction of common-mode voltage in multiphase two-level inverters using SPWM with phase-shifted carriers[J]. IEEE Transactions on Power Electronics, 2016, 31(9): 6631-6645.
2017, Vol. 32 
