摘要
为降低开关功放的成本以利于磁轴承的推广应用,本文分别采用三相四桥臂和五相六桥臂结构作为磁轴承开关功放的主电路,这两种多桥臂开关功放可分别用来驱动磁轴承三个和五个自由度的绕组,所需功率管的总数比传统的全桥功放分别减少1/3和2/5。这不仅减小功放的体积,同时节省了控制器的I/O口资源。本文将两种多桥臂开关功放的电流控制策略作为研究的重点,主要研究电流谐波含量低、动态性能好、负载适应能力强的控制方法,并解决由于多路负载连接于公共桥臂而引起的各相电流间的干扰问题。
研究了一种基于电流PID调节的四桥臂开关功放节点电位控制法,可由各桥臂节点的电位直接获得各开关信号的占空比。该方法计算量小,易于数字实现,并具有三态开关功放电流纹波小且不受母线电压影响的优点。总结出三种典型的电位分配方式,分析了不同的分配方式对输出电流的纹波大小和总开关次数的影响,定性地分析了缓冲电路对死区时间的补偿作用,针对功放的特点又提出了解决四桥臂开关功放输出电流间干扰的过调制处理方法。该控制方法可以推广到具有公共桥臂的任意n桥臂功率变换器的控制当中。
为比较节点电位法与三维空间矢量控制(SVPWM)的性能,本文对后者的实现方法进行简化。从计算机图形学的角度分析了abc和αβ0坐标系下电压矢量分布图之间的异同点,推导出三个基本电压矢量的作用时间与三相电压之间的关系,最后推导出各桥臂开关管的导通时间在24个四面体中的统一计算公式,证明了这两种方法的等效性。简化了现有各种断续脉宽调制(DPWM)的实现方法,并提出了两种三维SVPWM中特有的DPWM方式。为了解决节点电位控制中的输出电流间的干扰问题,需要研究四桥臂功率变换器的过调制控制方法。研究了三维SVPWM中的过调制问题,通过提取电压零轴分量将其转为二维SVPWM过调制问题以简化研究。提出了无需查表的单模式和双模式二维SVPWM过调制的无扇区算法,使得三维SVPWM过调制可由简化的SVPWM算法来实现。
PID控制中输出电流的纹波较小,但是电流的幅值和相位存在误差且随频率升高而逐渐增加,在负载变化后各控制参数需重新调整,其带载能力较弱。本文研究了一种混合电流控制方法以提高四桥臂开关功放的性能。将全桥功放中的采样保持控制引入到各相桥臂的控制当中,并可根据电流误差连续调节公共桥臂的占空比,仿真结果表明该混合控制方法电流失真较小,具有较强的负载适应能力,且输出电流和给定信号之间无幅值和相位误差。
比较和分析了多种控制方法在六桥臂开关功放中的性能,提出一种最大电流误差优先的采样保持控制方法,通过改进公共桥臂的控制策略,使五路电流的误差在每个控制周期都能得到调节。该方法具有与上述混合控制相似的性能,两者输出电流的谐波分布基本相同。
在以DSP和CPLD为核心的两种多桥臂开关功放样机上进行了实验,验证了本文研究的电流控制方法的有效性。本文的工作对电机驱动中多相逆变器的控制研究具有一定的借鉴意义。
In order to popularize the active magnetic bearings (AMB), low costs power amplifier is needed. This paper studied on the four-leg and six-leg switching power amplifiers, which could respectively drive three and five coils of the AMB. The amounts of the switches in two multi-bridge amplifiers were respectively reduced 1/3 and 2/5 comparing with H-bridge power amplifiers. The complexity of the power amplifier is reduced, and the I/O source in the controller is saved. The objective of this paper was to research the current methods with low total harmonic distortion (THD), high stability and strong adaptability to loads, and to resolve the interaction of the output currents for all loads were connected with the neutral leg.
A node potential control method in four-leg power amplifier based on current PID regulating, which has the merits of three-state power amplifiers, was presented. It needs little algebraic operation, so it is easy to be implemented for the duty cycle of each bridge can be obtained directly from each potential. Three typical methods of distribution of the potential were summarized and their influence on current ripple and switch times were compared, the dead-time compensation of the snubber circuit was analyzed. A over-modulation algorithm was proposed and it eliminated the phase interference in the four-leg power amplifier. This method can be extended to control arbitrary n-bridge converter.
The three-dimensional (3-D) space vector pulse width modulation (SVPWM) was simplified and its performance was compared with the node potential control method. The relationships, whether in abc orαβ0 coordinates, between three-phase voltages and the following elements: the tetrahedron in which the reference vector resides, three adjacent active switching vectors (or three switching states) and their duration times, were analyzed. Based on the analysis, the calculation of turn-on time of each switch in the actual implementation was simplified, and it was the same with the node potential control method. The implementation of common discontinuous PWM (DPWM) methods in existence were also simplified. In addition, two more DPWM methods peculiar to 3-D SVPWM were presented.
The over-modulation was researched to resolve the phase interference in the four-leg amplifier. Over-modulation of 3-D SVPWM was changed into 2-D problem by separating the zero components from three-phase voltages. Two simple algorithms of single-mode and two-mode over-modulations in 2-D SVPWM were presented, and it is no need to identify the sector in which the voltage vector locates or to lookup tables. That makes the 3-D over-modulation can be implemented by the simplified SVPWM algorithm.
A hybrid control method for four-leg amplifier was studied to overcoming the shortcomings in PID control. In this method, the neutral leg, which duty cycle is continuously adjusted, is controlled separately from other legs according to three current errors and three phase bridges are controlled by sample-hold control used in H-bridge amplifier to enhance dynamic performance and to enlarge the load range.
The performances of various current control methods for six-leg power amplifier were compared. A maximum current error preferred sample-hold control method was proposed. Five currents all can be regulated in one sampling period by modified control method of the neutral leg. This method and the hybrid current control mentioned above were similar in the performance and spectrum of the output currents.
The experiments were carried out with two multi-leg amplifiers using DSP and CPLD as the core controller and the experimental results verified the feasibility and effectiveness of these current control methods. The study of this paper has significance for reference in controlling the multi-leg inverters for multi-phase motors.
引文
[1] G.Schweiter, H. Bleuler, A. Traxler. Active magnetic bearings: basics, properties, and applications of active magnetic bearings. ETH, Switzerland, 1994.
[2]王水泉.五轴主动控制型电磁悬浮轴承的研究,[硕士学位论文].长沙,国防科技大学, 2001.
[3]梅磊.混合型磁悬浮轴承基础研究,[博士学位论文].南京:南京航空航天大学,2008.
[4]李冰.电磁轴承系统集成化技术的研究,[博士学位论文].南京:南京航空航天大学,2003.
[5] F. J. Keith, E. H. Maslen, R. R. Humphris, et al. Switching amplifier design for active magnetic bearings. Proc. 2nd Int. Symposium on Magnetic Bearings, Tokyo Japan, 1990:211~218.
[6] Zhang Jing, Jens Oliver Schulze. Synchronous three-level PWM amplifier for active magnetic bearings. Proc. 4th International Symposium on Magnetic Bearings, Zurich 1994:277~282.
[7] Zhang Jing. Power amplifier for active magnetic bearings, [Doctoral Dissertation]. ETH Zurich, Switzerland, 1995.
[8]臧晓敏,王晓琳,仇志坚等.磁轴承开关功放中电流三态调制技术的研究.中国电机工程学报,2004,24(9):167~172.
[9]刘淑琴,虞烈,谢友柏.电磁轴承驱动级电压与电流对转速和控制精度影响的研究.机械工程学报,1999,35(3):101~104.
[10] A. E. Hartavi, R. N. Tuncay, M. N. Sahinkaya. The effect of current control strategies on power consumption of a magnetically levitated turbomolecular pump. CES/IEEE 5th International Power Electronics and Motion Control Conference 2006 (IPEMC 2006), Shanghai China, 2006:1~5.
[11]张德魁,赵雷,赵鸿宾.电流响应速度及力响应速度对磁轴承系统性能的影响.清华大学学报(自然科学版),2001,6:23~26.
[12]龚伟,周雒维.D类音频功率放大器控制方式综述.重庆大学学报,2003,26(2):117~122.
[13]汪希平,袁崇军,谢友柏.电磁轴承系统的控制策略与功放电路的设计.西安交通大学学报,1995,29(12):68~74.
[14]辛彻.自然采样脉宽调制D类放大器.无线电与电视,2007,7:44~48.
[15] Zheren Lai, M. Keyue. A new extension of one-cycle control and its application to switching power amplifiers. IEEE Transactions on Power Electronics, 1996, 11(1):99~105.
[16]周雒维,龚伟,苏向丰.一种改进的单周控制的开关功率放大器.电工技术学报,2004,19(5):106~110.
[17] K. M. Smediey,Slobodan Cuk.One-cycle control of switching converters.IEEE Transactions on Power Electronics,1995, 10(6):625~633.
[18] Chang Qian, Zhengming Zhao, Yunfeng Liu, et al. Comparisons of PWM and one-cycle control for digital power amplifiers. 3rd International Power Electronic and Motion Control Conference (IPEMC 2000), Beijing China, 2000:1176~1180.
[19] Marian P. Kazmierkowski, Luigi Malesani. Current control techniques for three-phase voltage-source pwm converters: a Survey. IEEE Transactions on Industrial Electronics, 1998, 45(5):691~703.
[20]谢振宇,丘大谋,虞烈.电磁轴承的线圈绕制与功率放大器型式.机械科学与技术,1999,18(4):615~616.
[21] Reto Sch?b, Jürgen Hahn. Five axis active magnetic bearing with only five power switches. Proc. of MAG’97 Industrial Conference and Exhibition on Magnetic Bearings, Alexandria, Virginia, August 1997:334~343.
[22] H. Takano, S. Watanabe, M. Nakaoka. Multiple-bridge PWM current-regulated power amplifier for magnetic resonance imaging system and its feasible digital control implementation. 25th Annual Conference of the IEEE Industrial Electronics Society 1999 (IECON 1999):785~790.
[23]韩思维.双频半桥开关功率放大器的研究,[硕士学位论文].重庆,重庆大学,2006.
[24]李启扬.使用全数位控制多相交错式PWM技术之D类功率放大器实现,[硕士学位论文].台湾新竹:国立交通大学,2006.
[25]白咸林,李瑞来.一种基于三电平电路的新型开关功率放大器.电工技术杂志,2003,3:45~48.
[26]臧晓敏.磁轴承开关型功率放大器的研究,[硕士学位论文].南京:南京航空航天大学,2004.
[27]黄晓蔚,唐钟麟.一种用于有源磁悬浮轴承的基于采样-保持策略的开关型功率放大器.北京工业大学学报,1998,4(1):13~16.
[28]臧晓敏,王晓琳,仇志坚,等.一种改进的基于采样-保持策略磁轴承用电流三态调制开关功放.电工技术学报,2004,19(10):85~90.
[29]李冰,邓智泉,严仰光.磁轴承三态开关功率放大器的电流模式控制.电力电子技术,2003,37(4):52~55.
[30]王军,徐龙祥.软开关技术在磁悬浮轴承功率放大器中的应用.电工技术学报,2009,24(6):85~90.
[31]张亮,房建成.电磁轴承脉宽调制型开关功放的实现及电流纹波分析.电工技术学报,2007,22(3):13~20.
[32]余宇翔,胡业发.磁悬浮主轴数字功率放大器的设计研究.武汉理工大学学报:信息与管理工程版,2005,27(5):230~233.
[33]汪希平,崔卫东.电磁轴承用非接触式位移传感器的研究.上海大学学报,1998,4(1):54~60.
[34]白志峰.磁轴承位移传感器的研究,[硕士学位论文].济南:山东科技大学,2005.
[35]王军.无传感器磁悬浮轴承的研究,[硕士学位论文].南京:南京航空航天大学,2005.
[36]金超武.差动变压器式传感器在磁悬浮轴承中的应用研究,[硕士学位论文].南京:南京航空航天大学,2006.
[37]王秀珍,胡业发,吴华春.磁力轴承中电感位移传感器的研究.机械制造,2009,47(8):28~30.
[38] P. Bühler, R. Siegwart, R. Herzog. Digital control for low cost industrial AMB applications. Proc. 5th International Symposium on Magnetic Bearings, Kanazawa Japan, 1996.
[39] Reto Sch?b, Christian Redemann, Thomas Gempp. Radial active magnetic bearing for operation with 3-phase power converter. Proc. 4th International Symposium on Magnetic Suspension Technology, Gifu Japan, 1997:1~13.
[40] Tomas Gempp, Christian Redemann, Reto Sch?b. Active magnetic bearing with large gap for operation with a 3-phase power converter. Internaional Gas Turbine & Aeroengine Congress & Exhibition, Indianapolis Indiana, 1999:1~6.
[41] Hyeong-Joon Ahn. Dynamic performance limitation in driving radial AMB with space vector PWM. Proc. 11th International Symposium on Magnetic Bearings, Nara Japan, 2008.
[42] Chen Shyh-Leh, Hsu Chan-Tang. Optimal design of the 3-pole active magnetic bearing system. IEEE Transactions on Magnetics, 2002, 38(5):3458~3466.
[43] Hsu Chan-Tang, Chen Shyh-Leh. Exact linearization of a voltage-controlled 3-pole active magnetic bearing system. IEEE Transactions on Control Systems Technology, 2002,10(4):618~625.
[44]韩辅君,房建成,刘刚.SVPWM方法在磁轴承开关功放中的设计及应用.电工技术学报,2009,24(5):119~124.
[45] Javier Vadillo, Jose M. Echeverria, Ibon Elosegui, et al. An approach to a 3-pole magnetic bearing system by a matrix converter. Proc. 11th International Symposium on Magnetic Bearings, Nara Japan, 2008.
[46] Thomas M. Jahns, R. W. De Doncker, A.V. Radun, et al. System design considerations for a high-power aerospace resonant link converter. IEEE Transactions on Power Electronics, 1993, 8(4):665~673.
[47]于飞,张晓锋,李槐树,等.五相逆变器的空间矢量PWM控制.中国电机工程学报,2005,25(9):40~46.
[48]刘凤君.三相四桥臂逆变器.电源技术应用,2002,5(1):1~4.
[49]刘凤君.三相四桥臂逆变器的空间相量调制技术.电源技术应用,2002,5(10):1~9.
[50] Ching-Tsai Pan, Ting-Yu Chang. An improved hysteresis current controller for reducing switching frequency. IEEE Transactions on Power Electronics, 1994, 9(1):97~104.
[51] Luigi Malesani, Paolo Mattavelli, Paolo Tomasin. High-performance hysteresis modulation technique for active filters, IEEE Transactions on Power Electronics, 1997, 12(5):876~884.
[52] F. Zare, G. Ledwich. A new hysteresis current control for three-phase inverters based on adjacent voltage vectors and time error. Power Electronics Specialists Conference of IEEE (PESC 2007):431~436.
[53] M. Mohseni, S. Islam. A new vector-based hysteresis current control scheme for three-phase PWM voltage-source inverters. IEEE Transactions on Power Electronics, 2010. (accepted for publication).
[54] E. Aldabas, L. Romeral, J. Llaquet, et al. Current controller for low switching frequency by means of increasing the vectors time application. 28th Annual Conference of the IEEE Industrial Electronics Society 2002 (IECON 2002):166~171.
[55]陈阳.电流型多电平变流器拓扑及PWM控制策略研究,[硕士学位论文].杭州:浙江大学,2006.
[56]刘迎澍,黄田.磁悬浮轴承研究综述.机械工程学报,2000,36(11):5~9.
[57] B. A. Miwa, D. M. Otten, M. F. Schlecht. High efficiency power factor correction using interleaving techniques. IEEE Applied Power Electronics Conf. 1992:557~568.
[58] Albert M. Wu, Jinwen Xiao, Dejan Markovic, et al.Digital PWM control: application in voltage regulation modules. Power Electronics Specialists Conf., 1999, PESC 99:77~83.
[59] Alexandre Schammass, Hannes Bleuler. Experimental results on self-sensing AMB using a threestate PWM amplifier. 8th Int. Symposium on Magnetic Bearings, Mito Japan, 2002:289~292.
[60]李旭,谢运祥.PWM技术实现方法综述.电源技术应用,2005,8(2):51~55.
[61]宋栋梁,吕征宇,汪槱生．一种灵活的可编程三相开关功率放大器．电源技术应用，2003,6(3):84~86.
[62]李冰,邓智泉,严仰光.一种新颖的永磁偏置三自由度电磁轴承.南京航空航天大学学报2003,35(1):81~85.
[63]刘帘曦,杨银堂,朱樟明.一种无滤波器的高效立体声D类音频功率放大器.西安电子科技大学学报(自然科学版),2009,36(2):308~313.
[64]孙驰,毕增军,魏光辉.一种新颖的三相四桥臂逆变器解耦控制的建模与仿真.中国电机工程学报,2004,24(1):124~130.
[65]陈宏志,刘秀翀.四桥臂三相逆变器的解耦控制.中国电机工程学报,2007,27(19):74~79.
[66]乐健,姜齐荣,韩英铎.一种新型的四桥臂三电平并联有源电力滤波器的空间矢量控制策略.中国电机工程学报,2006,26(14):59~64.
[67]刘海春,谢少军,王国凤.一种新颖的应用于三相四线有源电力滤波器的混合电流控制方法.山东大学学报(工学版),2007,37(6):10~14.
[68]阮新波,严仰光.四桥臂三相逆变器的控制策略.电工技术学报,2000,15(1):61~64.
[69]杨宏.四桥臂三相逆变器的控制和实现,[博士学位论文].南京:南京航空航天大学,2004.
[70]吴睿,谢少军.基于abc坐标系空间矢量控制的电压源型逆变器研究.电工技术学报,2005,20(12):47~52.
[71] Jang-Hwan Kim, Seung-Ki Sul.A carrier-based PWM method for three-phase four-leg voltage source converters. IEEE Transactions on Power Electronics, 2004, 19(1):66~75.
[72]孙进,侯振义,苏彦民.三相四臂对逆变电源控制方法的研究.电工技术学报,2004,19(4):61~65.
[73]孙驰,鲁军勇,马伟明.一种新的三相四桥臂逆变器控制方法.电工技术学报,2007,22(2):57~73.
[74]刘秀翀,张化光,陈宏志.四桥臂逆变器中第四桥臂的控制策略.中国电机工程学报,2007,27(33):87~92.
[75]官二勇,宋平岗,叶满园.基于三次谐波注入法的三相四桥臂逆变电源.电工技术学报,2005,20(12):43~52.
[76]王少杰,罗安.谐波域死区效应分析及补偿方法的研究.电工技术学报,2009,24(8):111~118.
[77]刘军锋,李叶松.死区对电压型逆变器输出误差的影响及其补偿.电工技术学报,2007,22(5):117~122.
[78] Richard Zhang, V. Himamshu Prasad, Dushan Boroyevich, et al. Three-dimensional space vector modulation for four-leg voltage-source converters. IEEE Transactions on Power Electronics, 2002, 17(3):314~326.
[79] Manuel A. Perales, M. M. Prats, Ramón Portillo, et al. Three-dimensional space vector modulation in abc coordinates for four-leg voltage source converters. Power Electronics Letters IEEE, 2003, 1(4):104~109.
[80]龚春英,熊宇,郦鸣,等.四桥臂三相逆变电源的三维空间矢量控制技术研究.电工技术学报,2004,19(12):29~36.
[81] H. W. Van Der Broeck, H. Skudelny, G. V. Stanke. Analysis and realization of a pulse width modulator based on voltage space vectors. IEEE Transactions on Industry Applications, 1988, 24(1):142~150.
[82] A. K. Gupta, A. M. Khambadkone. A space vector PWM scheme for multilevel inverters based on two-level space vector PWM. IEEE Trans. Ind. Electron., 2006, 53(5):1631~1639.
[83] A.R. Beig, G. Narayanan, V. T. Ranganathan. Modified SVPWM algorithm for three-level VSI with synchronized and symmetrical waveforms. IEEE Trans. Ind. Electron., 2007, 54(1):486~494.
[84] M. A. S.Aneesh, A. Gopinath, M. R. Baiju. A simple space vector PWM generation scheme for any general n-level inverter. IEEE Trans. Ind. Electron., 2009, 56(5):1649~1656.
[85] Thomas M. Jahns, R. W. De Doncker, A.V. Radun, et al. System design considerations for a high-power aerospace resonant link converter. IEEE Trans. Power Electron., 8(4):665~673.
[86] R. Zhang, D. Boroyevich, H. Prasad, et al. A three-phase inverter with a neutral leg with space vector modulation. in Proc. IEEE APEC’97 Conf., 1997:857~863.
[87] J. I. Leon, S. Vazquez, R. Portillo, et al. Three-dimensional feedforward space vector modulation applied to multilevel diode-clamped converters. IEEE Trans. Ind. Electron., 2009, 56(1):101~109.
[88] L. de Lillo, L. Empringham, P. W. Wheeler, et al. Multiphase power converter drive for fault-tolerant machine development in aerospace applications. IEEE Trans. Ind. Electron., 2010, 57(2):575~583.
[89] P. Verdelho, G. D. Marques. A current control system based inαβ0 variables for a four-leg PWM voltage converter. in Proc. IEEE IECON’98 Conf., 1998:1847~1852.
[90] S. M. Ali, M. P. Kazmierkowski. Current regulation of four-leg PWM-VSI. in Proc. IEEE IECON’98 Conf., 1998:1853~1858.
[91] M. A. Perales, M. M. Prats, R. C. Portillo, et al. Three-dimensional space vector modulation in abc coordinates for four-leg voltage source converters. IEEE Trans. Power Electron. Letters, 2003:104~109.
[92] L. G. Franquelo, M. M. Prats, R. C. Portillo, et al. Three-dimensional space-vector modulation algorithm for four-leg multilevel converters using abc coordinates. IEEE Trans. Ind. Electron., 2006, 53(2):458~466.
[93] O. Lopez, J. Alvarez, J. Doval-Gandoy, et al. Comparison of the FPGA implementation of two multilevel space vector PWM algorithms. IEEE Trans. Ind. Electron., 2008 55(4):1537~1547.
[94] R. Baghernejad, A. Bakhshai, D. Yazdani. A real-time neuro-computing three-dimensional space vector algorithm for three -phase four-leg converters. in Proc. IEEE IECON’2005 Conf., 2005:1066~1070.
[95] Jang-Hwan Kim, Seung-Ki Sul. A carrier-based PWM method for three-phase four-leg voltage source converters. IEEE Trans. Power Electron., 2004, 19(1):66~75.
[96] Ning Yi Dai, Man Chung Wong; Fan Ng; et al. A FPGA-based generalized pulse width modulator for three-leg center-split and four-leg voltage source inverters. IEEE Trans. Power Electron., 2008, 23(3):1472~1484.
[97] Keliang Zhou, Danwei Wang. Relationship between space-vector modulation and three-phase carrier-based PWM: a comprehensive analysis. IEEE Trans. Ind. Electron., 2002, 49(1):186~196.
[98] D. G. Holmes. The significance of zero space vector placement for carrier-based PWM schemes. IEEE Trans. Ind. Applicat., 1996, 32(5):1122~1129.
[99] Vladimir Blasko. Analysis of a hybrid PWM based on modified space-vector and triangle-comparison methods. IEEE Trans. Ind. Applicat., 1997, 33(3):756~764.
[100] A. M. Hava, R. J. Kerkman, T. A. Lipo. Simple analytical and graphical methods for carrier-based PWM-VSI drives. IEEE Trans. Power Electron., 1999, 14(1):49~61.
[101] S. R. Bowes, Yen-Shin Lai. The relationship between space-vector modulation and regular-sampled PWM. IEEE Trans. Ind. Electron., 1997, 44(5):670~679.
[102] Jian Sun, H. Grotstollen. Optimized space vector modulation and regular-sampled PWM: a reexamination. in Proc. IEEE IAS 1996:956~963.
[103] R. Burgos, Rixin Lai, Yunqing Pei, et al. Space vector modulator for vienna-type rectifiers based on the equivalence between two- and three-level converters: a carrier-based implementation. IEEE Trans. Power Electron., 2008, 23(4):1888~1898.
[104] A. M. Hava, R. J. Kerkman, T. A. Lipo. A high-performance generalized discontinuous PWM algorithm. IEEE Trans. Ind. Applicat., 1998, 34(5):1059~1070.
[105]周克亮译.电力电子变换器PWM技术原理与实践.北京:人民邮电出版社,2010.
[106] G. Narayanan, V. T. Ranganathan, D. Zhao, et al. Space vector based hybrid PWM techniques for reduced current ripple. IEEE Trans. Ind. Electron., 2008, 55(4):1614~1627.
[107] J. W. Kollar, H. Ertl, F. C. Zach. Influence of the modulation method on the conduction and switching losses of a PWM converter system. IEEE Trans. Ind. Applicat., 1991, 27(6): 1063~1075.
[108] Andrzej M. Trzynadlowski, Lynn Kirlin, et al. Space vector PWM technique with minimum switching loss and a variable pulse rate. IEEE Trans. Ind. Electron., 1997, 44(2):173~181.
[109] Dae-Woong Chung, Joohn-Sheok Kim, Seung-Ki Sul. Unified voltage modulation technique for real-time three-phase power conversion. IEEE Trans. Ind. Applicat., 1998, 34(2):374~380.
[110] Olorunfemi Ojo. The generalized discontinuous PWM scheme for three-phase voltage source inverters. IEEE Trans. Ind. Electron., 2004, 51(6):1280~1289.
[111] R. P. Burgos, G. Chen, F. Wang, D. Boroyevich. Minimum-loss minimum-distortion space vector sequence generator for high-reliability three-phase power converters for Aircraft Applications. in Proc. IEEE IPEMC 2004:1356~1361.
[112] Lucian Asiminoaei, Pedro Rodríguez, Frede Blaabjerg. Application of discontinuous PWM modulation in active power filters. IEEE Trans. Power Electron., 2008,23(4):1692~1706.
[113] P. Rodríguez, J. Pou, A. Luna, et al. Three-dimensional SVM for modular power electronics systems. in Proc. IEEE IECON’2005 Conf., 2005:497~502.
[114] O. Ojo, P. M. Kshirsagar. Concise modulation strategies for four-leg voltage source inverters. IEEE Trans. Power Electron., 2004, 19(1):46~53.
[115] Gan Dong, O. Ojo. Current regulation in four-leg voltage-source converters. IEEE Trans. Ind. Electron., 2007, 54(4):2095~2015.
[116] R. Zhang, V. H. Prasad, D. Boroyevich, et al. Three dimensional space vector modulation for four-leg voltage-source converters. IEEE Trans. Power Electron. 2002, 17(3):314~326.
[117] V. Himamshu Prasad, Dushan Boroyevich, Richard Zhang. Analysis and comparison of space vector modulation schemes for a four-leg voltage source inverter. in Proc. IEEE APEC’97, 1997:864~871.
[118] Changrong Liu, Jason Lai, Fred C. Lee, et al. Common-mode components comparison for different SVM schemes in three-phase four-legged converterin. in Proc. IEEE IPEMC 2000:633~638.
[119] D. O. Neacsu, E. Wagner, B. S. Borowy. A simulation benchmark for selection of the PWM algorithms for three-phase interleaved converters. IEEE Trans. Ind. Electron., 2008, 55(4):1628~1636.
[120] Yun Wei Li, Bin Wu, D. Xu, et al. Space vector sequence investigation and synchronization methods for active front-end rectifiers in high-power current-source drives. IEEE Trans. Ind. Electron., 2008, 55(3):1022~1034.
[121] A. Gopinath, A. S. A. Mohamed, M. R. Baiju. Fractal based space vector PWM for multilevel inverters—a novel approach. IEEE Trans. Ind. Electron., 2009, 56(4):1230~1237.
[122] H. J. Park, M. J. Youn. A new time-domain discontinuous space vector PWM technique in overmodulation region. IEEE Trans. Ind. Electron., 2003, 50(2):349~355.
[123] D. Dujic, M. Jones, S. N. Vukosavic, et al. A general PWM method for a (2n+1)-leg inverter supplying n three-phase machines. IEEE Trans. Ind. Electron., 2009, 56(10):4107~4118.
[124] Changrong Liu, Dengming Peng; J. Lai, et al. Four-legged converter 3-D SVM scheme over-modulation study. in Proc. IEEE APEC’2000:562~568.
[125] Jang-Hwan Kim, Seung-Ki Sul. Overmodulation strategy for a three-phase four-leg voltage source converter. in Proc. IEEE IAS 2003:656~663.
[126] S. Bolognani,M. Zigliotto.Novel digital continuous control of SVM inverters in theovermodulation range.IEEE Trans. on Ind. Applicat., 1997, 33(2):525~530.
[127] J. Holtz,W. Lotzkat,A. M. Khambadkone.On continuous control of pwm inverters in the overmodulation range including the six-step mode.IEEE Trans. on Power Electron., 1993, 8(4):546~553.
[128]金舜,钟彦儒,程为彬.新颖的SVPWM过调制策略及其在三电平逆变器中的应用.中国电机工程学报,2006,26(20):84~90.
[129]吴芳,万山明,黄声华.一种过调制算法及其在永磁同步电动机弱磁控制中的应用.电工技术学报,2010,25(1):58-63.
[130]马志文,郑琼林,林飞.具有全调制范围的空间矢量脉宽调制算法研究.北京交通大学学报,2007,31(2):89~102.
[131]陆海峰,瞿文龙,张磊,等.基于调制函数的SVPWM算法.电工技术学报,2008,23(2):37~43.
[132]杨文强,蔡旭,姜建国.空间电压矢量PWM的过调制策略.上海交通大学学报,2005,39:53~56.
[133] Ahmet M. Hava, Russel J. Kerkman,Thomas A. Lipo.Carrier-based PWM-VSI overmodulation strategies: Analysis, Comparison, and Design.IEEE Trans. on Power Electron., 1998, 13(4):674~689.
[134]张立伟,刘钧,温旭辉,等.基于基波电压幅值线性输出控制的SVPWM过调制新算法.电机工程学报,2005,25(19):12~18.
[135]李和明,李亚斌,彭咏龙.基于FPGA的三相电流型PWM整流器过调制策略的研究.中国电机工程学报,2007,27(22):94~100.
[136]谈龙成,李耀华,王平,等.适用于电流型变流器的空间矢量过调制策略.中国电机工程学报,2008,5(25):39~43.
[137]金舜,钟彦儒,程为彬.应用单双模式过调制技术的三电平SVPWM.西安理工大学学报,2006,22(1):5~9.
[138]陈鑫兵,何礼高.三电平逆变器空间矢量过调制控制策略的研究.电气应用,2006,25(5):22~25.
[139]李明,马小平,陈爱丽.一种改进的三电平逆变器空间电压矢量PWM控制技术.东南大学学报(自然科学版),2003,33:179~182.
[140]粟梅,李丹云,孙尧,等.双级矩阵变换器的过调制策略.中国电机工程学报,2008,28(3):47~52.
[141]朱建林,张建华,郭有贵,等.过调制矩阵变换器的电压传输特性及谐波分析.中国电机工程学报,2007,27(10):110~113.
[142]梅杨,黄立培,李正熙.矩阵式变换器驱动异步电机调速系统抑制输入电压扰动的研究.电工技术学报,2009,24(10):47~52.
[143]谌海霞,蔡灏,李小颖.双级矩阵变换器的过调制策略研究及实现.电力电子技术,2008,42(8):79~81.
[144]洪佩孙.不对称运行与对称分量法.江苏电机工程,2002,21(5):47~50.
[145] Liu Haichun, Ding Zhihui, Xie Shaojun. A novel hybrid current control strategy applied in three-phase four-leg APF. Power Electronics and Motion Control Conference 2009 (IPEMC 2009):2365~2370.
[146]杨宏,阮新波,严仰光.四桥臂三相逆变器的PWM控制.南京航空航天大学学报,2002,34(6):575~579.
[147]张德魁,赵雷,赵鸿宾.电流响应速度及力响应速度对磁轴承系统性能的影响.清华大学学报(自然科学版),2001,41(6):23~26.
[148] ZhaoYifan, T. A. Lipo. Modeling and control of a multi-phase induction machine with structural unbalance. IEEE Transactions on Energy Conversion, 1996, 11(3):570~577.
[149]欧阳红林,周马山,童调生.多相永磁同步电动机不对称运行的矢量控制.中国电机工程学报,2004,24(7):145~150.
[150]薛山,温旭辉.一种新颖的多相SVPWM.电工技术学报,2006,21(2):68~72.