摘要
对开关变换器的调制技术进行了系统性的归纳与总结,并给出了5种分类方式,即恒频调制和变频调制、连续调制和离散调制、模拟调制和数字调制、线性调制和非线性调制,以及基本型调制和组合型调制。将脉宽调制(pulse width modulation,PWM)和脉频调制(pulsefrequency modulation,PFM)视为基本型调制,则其余的调制技术均可以认为是基于PWM和/或PFM的组合型调制。根据对偶性与相通性,系统地分析了基本型调制和组合型调制(包括脉冲序列调制、脉冲跨周期调制、正弦脉宽调制、空间矢量脉宽调制等)的原理和特点,揭示了各种调制技术的区别与联系,推断出了脉冲ON调制、正弦脉频调制、空间矢量脉频调制等新颖调制技术。最后,给出了综述结论与研究展望。
Modulation techniques of switching converters are summarized systematically and five kinds of classification methods are given, i.e. constant frequency modulation and variable frequency modulation, continuous modulation and discrete modulation, analog modulation and digital modulation, linear modulation and nonlinear modulation, and basic-type modulation and combination-type modulation. If the pulse width modulation(PWM) and pulse frequency modulation(PFM) are regarded as basic-type modulation, the other modulation techniques can be considered as combination-type modulations based on PWM and/or PFM. According to duality and similarity, the principles and the characteristics of basic-type and combination-type modulations are analyzed systematically, where combination-type modulations include pulse train modulation(PTM), pulse skipping modulation(PSM), sinusoidal PWM(SPWM), and space vector PWM(SVPWM). The differences and relations of various modulation techniques are revealed, and novel modulation techniques, such as pulse ON modulation, sinusoidal PFM(SPFM), and space vector PFM(SVPFM), are deduced. Finally, review conclusions and research prospects are presented.
引文
[1]周国华,许建平.开关变换器调制与控制技术综述[J].中国电机工程学报,2014,34(6):815-831.Zhou Guohua,Xu Jianping.A review of modulation and control techniques for switching converters[J].Proceedings of the CSEE,2014,34(6):815-831(in Chinese).
[2]Yuan Bing,Lai Xinquan,Liu Yuxin.Load current-sensing circuit integrated in high-frequency PWM/PFM hybrid DC-DC buck converter[J].Electronics Letters,2014,50(18):1310-1312.
[3]Luo Ping,Luo Luyang,Li Zhaoji,et al.Skip cycle modulation in switching DC-DC converter[C]//Proceedings of IEEE 2002 International Conference on Communications,Circuits and Systems and West Sino Expositions.Chengdu,China:IEEE,2002:1716-1719.
[4]罗萍,李肇基,熊富贵,等.开关变换器的跨周期调制模式[J].电子与信息学报,2004,26(6):984-988.Luo Ping,Li Zhaoji,Xiong Fugui,et al.Pulse-cycle skip modulation in switching converter[J].Journal of Electronics&Information Technology,2004,26(6):984-988(in Chinese).
[5]牛全民,张波,李肇基.断续导通模式Buck变换器跨周期调制离散解析模型[J].中国电机工程学报,2008,28(12):32-37.Niu Quanmin,Zhang Bo,Li Zhaoji.A discrete-time analytic model of PSM in DCM buck converter[J].Proceedings of the CSEE,2008,28(12):32-37(in Chinese).
[6]Kapat S,Banerjee S,Patra A.Discontinuous map analysis of a DC-DC converter governed by pulse skipping modulation[J].IEEE Transactions on Circuits and Systems I:Regular Papers,2010,57(7):1793-1801.
[7]罗萍,甄少伟,李彦麟,等.不同调制模式下Boost变换器DCM模态的能量模型与稳定性分析[J].中国电机工程学报,2008,28(6):49-54.Luo Ping,Zhen Shaowei,Li Yanlin,et al.Energy models and stability analysis of boost converters in DCM for different modulation modes[J].Proceedings of the CSEE,2008,28(6):49-54(in Chinese).
[8]Luo Ping,Li Zhaoji,Zhang Bo.A novel improved PSMmode in DC-DC converter based on energy balance[C]//Proceedings of the 37th IEEE Power Electronics Specialists Conference.Jeju,Korea:IEEE,2006:1-4.
[9]马正华,夏建锋,包伯成,等.断续导电模式Buck变换器双脉冲跨周期调制技术[J].中国电机工程学报,2013,33(12):24-31.Ma Zhenghua,Xia Jianfeng,Bao Bocheng,et al.Dual pulse skipping modulation technique for buck converter operating in discontinuous conduction mode[J].Proceedings of the CSEE,2013,33(12):24-31(in Chinese).
[10]Telefus M,Shteynberg A,Ferdowsi M,et al.Pulse Train,a novel digital control method,applied to a discontinuous conduction mode flyback converter[C]//IEEE Power Electronics Specialist Conference.Acapulco,Mexico:IEEE,2003:1141-1146.
[11]Telefus M,Shteynberg A,Ferdowsi M,et al.Pulse train control technique for flyback converter[J].IEEETransactions on Power Electronics,2004,19(3):757-764.
[12]Wang Jinping,Xu Jianping,Zhou Guohua,et al.Pulsetrain-controlled CCM buck converter with small ESRoutput-capacitor[J].IEEE Transactions on Industrial Electronics,2013,60(12):5875-5881.
[13]Sha Jin,Xu Jianping,Bao Bocheng,et al.Effects of circuit parameters on dynamics of current-modepulse-train-controlled buck converter[J].IEEETransactions on Industrial Electronics,2014,61(3):1562-1573.
[14]Qin Ming,Xu Jianping.Multiduty ratio modulation technique for switching DC-DC converters operating in discontinuous conduction mode[J].IEEE Transactions on Industrial Electronics,2010,57(10):3497-3507.
[15]王金平,许建平,秦明,等.开关DC-DC变换器双频率脉冲序列调制技术[J].中国电机工程学报,2010,30(33):1-8.Wang Jinping,Xu Jianping,Qin Ming,et al.Bi-frequency pulse train modulation technique for switching DC-DCconverters[J].Proceedings of the CSEE,2010,30(33):1-8(in Chinese).
[16]Xu Jianping,Wang Jinping.Bifrequency pulse-train control technique for switching DC-DC converters operating in DCM[J].IEEE Transactions on Industrial Electronics,2011,58(8):3658-3667.
[17]Wang Jinping,Xu Jianping.Peak current mode bifrequency control technique for switching DC-DCconverters in DCM with fast transient response and low EMI[J].IEEE Transactions on Power Electronics,2012,27(4):1876-1884.
[18]Lee P W,Lee Y S,Cheng D K W,et al.Steady-state analysis of an interleaved boost converter with coupled inductors[J].IEEE Transactions on Industrial Electronics,2000,47(4):787-795.
[19]李艳,阮新波,杨东升,等.双输入Buck变换器的交错双沿调制方法[J].电工技术学报,2009,24(4):139-146.Li Yan,Ruan Xinbo,Yang Dongsheng,et al.Interleaved dual-edge modulation scheme for double-input buck converter[J].Transactions of China Electrotechnical Society,2009,24(4):139-146(in Chinese).
[20]阮新波,严仰光.脉宽调制DC/DC全桥变换器的软开关技术[M].北京:科学出版社,1999.Ruan Xinbo,Yan Yangguang.Soft switching technology of DC/DC full bridge converter with pulse width modulation[M].Beijing:Science Press,1999(in Chinese).
[21]赵彪,于庆广,孙伟欣.双重移相控制的双向全桥DC-DC变换器及其功率回流特性分析[J].中国电机工程学报,2012,32(12):43-50.Zhao Biao,Yu Qingguang,Sun Weixin.Bi-directional full-bridge DC-DC converters with dual-phase-shifting control and its backflow power characteristic analysis[J].Proceedings of the CSEE,2012,32(12):43-50(in Chinese).
[22]Wu Kuiyuan,de Silva C W,Dunford W G.Stability analysis of isolated bidirectional dual active full-bridge DC-DC converter with triple phase-shift control[J].IEEETransactions on Power Electronics,2012,27(4):2007-2017.
[23]侯聂,宋文胜.全桥隔离DC/DC变换器的三重相移控制及其软启动方法[J].中国电机工程学报,2015,35(23):6113-6121.Hou Nie,Song Wensheng.Full-bridge isolated DC/DCconverters with triple-phase-shift control and soft starting control method[J].Proceedings of the CSEE,2015,35(23):6113-6121(in Chinese).
[24]Vorpérian V,?uk S.A complete DC analysis of the series resonant converter[C]//Proceedings of 1982 IEEE Power Electronics Specialists Conference.Cambridge,USA:IEEE,1982:85-100.
[25]Bhat A K S.Fixed-frequency PWM series-parallel resonant converter[J].IEEE Transactions on Industry Applications,1992,28(5):1002-1009.
[26]Burdio J M,Barragan L A,Monterde F,et al.Asymmetrical voltage-cancellation control for full-bridge series resonant inverters[J].IEEE Transactions on Power Electronics,2004,19(2):461-469.
[27]高铁峰,张森,赵剑锋,等.LCC谐振变换器非对称移相控制及效率优化方法[J].电工技术学报,2017,32(8):208-219.Gao Tiefeng,Zhang Sen,Zhao Jianfeng,et al.Asymmetrical phase shift control and efficiency optimization strategy for LCC resonant converter[J].Transactions of China Electrotechnical Society,2017,32(8):208-219(in Chinese).
[28]李菊,阮新波.全桥LLC谐振变换器的混合式控制策略[J].电工技术学报,2013,28(4):72-79.Li Ju,Ruan Xinbo.Hybrid control strategy of full bridge LLC converters[J].Transactions of China Electrotechnical Society,2013,28(4):72-79(in Chinese).
[29]Holtz J.Pulsewidth modulation-a survey[J].IEEETransactions on Industrial Electronics,1992,39(5):410-420.
[30]Zhang Kai,Kang Yong,Xiong Jian,et al.Direct repetitive control of SPWM inverter for UPS purpose[J].IEEETransactions on Power Electronics,2003,18(3):784-792.
[31]张炳义,冯桂宏,王凤翔,等.SPWM电源供电下低速大扭矩永磁同步电动机设计研究[J].电工技术学报,2001,16(6):85-90.Zhang Bingyi,Feng Guihong,Wang Fengxiang,et al.Study on low speed and high torque PMS motor design with SPWM power supply[J].Transactions of China Electrotechnical Society,2001,16(6):85-90(in Chinese).
[32]Van Der Broeck H W,Skudelny H C,Stanke GV.Analysis and realization of a pulsewidth modulator based on voltage space vectors[J].IEEE Transactions on Industry Applications,1988,24(1):142-150.
[33]杨贵杰,孙力,崔乃政,等.空间矢量脉宽调制方法的研究[J].中国电机工程学报,2001,21(5):79-83.Yang Guijie,Sun Li,Cui Naizheng,et al.Study on method of the space vector PWM[J].Proceedings of the CSEE,2001,21(5):79-83(in Chinese).
[34]田亚菲,何继爱,黄智武.电压空间矢量脉宽调制(SVPWM)算法仿真实现及分析[J].电力系统及其自动化学报,2004,16(4):68-71.Tian Yafei,He Jiai,Huang Zhiwu.Simulation and analyzation of space vector PWM[J].Proceedings of the EPSA,2004,16(4):68-71(in Chinese).
[35]郭世明.电力电子技术[M].2版.成都:西南交通大学出版社,2008.Guo Shiming.Power electronics[M].2nd ed.Chengdu:Southwest Jiaotong University Press,2008(in Chinese).
[36]王堃,游小杰,王琛琛,等.低开关频率下SVPWM同步调制策略比较研究[J].中国电机工程学报,2015,35(16):4175-4183.Wang Kun,You Xiaojie,Wang Chenchen,et al.Research on synchronized SVPWM strategies under low switching frequency[J].Proceedings of the CSEE,2015,35(16):4175-4183(in Chinese).
[37]Wang Chenchen,Wang Kun,You Xiaojie.Research on synchronized SVPWM strategies under low switching frequency for six-phase VSI-fed asymmetrical dual stator induction machine[J].IEEE Transactions on Industrial Electronics,2016,63(11):6767-6776.
[38]周国华,许建平.开关变换器数字控制技术[M].北京:科学出版社,2011.Zhou Guohua,Xu Jianping.Digital control techniques of switching converters[M].Beijing:Science Press,2011(in Chinese).
[39]Sable D M,Cho B H,Ridley R B.Use of leading-edge modulation to transform boost and flyback converters into minimum-phase-zero systems[J].IEEE Transactions on Power Electronics,1991,6(4):704-711.
[40]刘啸天,周国华,李振华,等.基于双缘调制的数字电压型控制Buck变换器离散迭代映射建模与动力学分析[J].物理学报,2015,64(22):228401.Liu Xiaotian,Zhou Guohua,Li Zhenhua,et al.Discrete iterative-map modeling and dynamical analysis of digital voltage-mode controlled buck converter with dual-edge modulation[J].Acta Physica Sinica,2015,64(22):228401(in Chinese).
[41]Zhou Guohua,Xu Jianping.Digital peak current control for switching DC-DC converters with asymmetrical dual-edge modulation[J].IEEE Transactions on Circuits and Systems II:Express Briefs,2009,56(11):815-819.
[42]Ridley R B.A new continuous-time model for currentmode control with constant frequency,constant on-time,and constant off-time,in CCM and DCM[C]//Proceedings of the 21st Annual IEEE Conference on Power Electronics Specialists.San Antonio,USA:IEEE,1990:382-389.
[43]Schweitzer B P,Rosenstein A B.Free running-switching mode power regulator:analysis and design[J].IEEETransactions on Aerospace,1964,2(4):1171-1180.
[44]Luo Feng,Ma Dongsheng.An integrated switching DC-DC converter with dual-mode pulse-train/PWMControl[J].IEEE Transactions on Circuits and Systems II:Express Briefs,2009,56(2):152-156.
[45]Zhou Guohua,Xu Jianping,Wang Jinping.Constantfrequency peak-ripple-based control of buck converter in CCM:review,unification,and duality[J].IEEETransactions on Industrial Electronics,2014,61(3):1280-1291.
[46]周国华.基于纹波的开关功率变换器控制技术及其动力学行为研究[D].成都:西南交通大学,2011.Zhou Guohua.Ripple-based control technique and dynamical behavior of switching power converters[D].Chengdu:Southwest Jiaotong University,2011(in Chinese).
[47]Zhou Guohua,Xu Jianping,Zhang Fei.Unified pulse-width modulation scheme for improved digitalpeak-voltage control of switching DC-DC converters[J].International Journal of Circuit Theory and Applications,2014,42(7):671-686.
[48]Zhang Xi,Xu Jianping,Wu Jiahui,et al.Reduced-order mapping and design-oriented instability for constant on-time current-mode controlled buck converters with a PIcompensator[J].Journal of Power Electronics,2017,17(5):1298-1307.
[49]Zhang Xi,Xu Jianping,Bao Bocheng,et al.Asynchronous-switching map-based stability effects of circuit parameters in fixed off-time controlled buck converter[J].IEEE Transactions on Power Electronics,2016,31(9):6686-6697.
[50]Kim B C,Park K B,Moon G W.Asymmetric PWMcontrol scheme during hold-up time for LLC resonant converter[J].IEEE Transactions on Industrial Electronics,2012,59(7):2992-2997.
[51]Chen Yiming,Xu Jianping,Cao Jing,et al.PWM-PFMhybrid controlled LCC resonant converter with wide ZVSrange and narrow switching frequency variation[J].Electronics Letters,2017,53(17):1218-1220.
[52]Redl R,Sun Jian.Ripple-based control of switching regulators-an overview[J].IEEE Transactions on Power Electronics,2009,24(12):2669-2680.
[53]Wang Jinping,Hou Liangkui,Zhang Liang,et al.Analysis of the low-frequency oscillation phenomenon in constanton-time controlled boost converter[C]//Proceedings of2015 IEEE Energy Conversion Congress and Exposition.Montreal,Canada:IEEE,2015:1571-1574.
[54]Liu Xin,Guo Shuxu,Wang Shuai,et al.Analysis and design of a high efficiency boost DC-DC converter based on pulse-frequency modulation[C]//Proceedings of 2007International Symposium on Integrated Circuits.Singapore:IEEE,2007:398-401.
[55]Nashed M,Fayed A A.Current-mode hysteretic buck converter with spur-free control for variable switching noise mitigation[J].IEEE Transactions on Power Electronics,2018,33(1):650-664.
[56]Bao B C,Yang J,Xu J P,et al.Effect of output capacitor ESR on dynamic performance of voltage-mode hysteretic controlled buck converter[J].Electronics Letters,2013,49(20):1293-1294.
[57]Sahu B,Rincon-Mora G A.An accurate,low-voltage,CMOS switching power supply with adaptive on-time pulse-frequency modulation(PFM)control[J].IEEETransactions on Circuits and Systems I:Regular Papers,2007,54(2):312-321.
[58]Chen Xing,Zhou Guohua,Xu Shungang,et al.Quasiconstant-frequency variable off-time control technique for buck-type DC-DC converter[J].Electronics Letters,2015,51(18):1447-1449.
[59]Wu Xiaohui,Wu Xiaobo.Adaptive hysteresis window control(AHWC)technique for hysteretic DC-DC buck converter with constant switching frequency[C]//2010Asia-Pacific Power and Energy Engineering Conference.Chengdu,China:IEEE,2010:1-4.
[60]周国华,陈兴,崔恒丰.双缘COT调制数字电压型控制Buck变换器分析[J].西南交通大学学报,2015,50(1):13-19.Zhou Guohua,Chen Xing,Cui Hengfeng.Analysis of digital voltage-mode controlled buck converter with dual-edge constant on-time modulation[J].Journal of Southwest Jiaotong University,2015,50(1):13-19(in Chinese).
[61]Zhou Guohua,Chen Xin,Cui Hengfeng,et al.High output-regulation accuracy and fast transient response of dual constant on-time controlled switching converter[J].Electronics Letters,2014,50(7):543-545.
[62]Chen Xing,Chen Yiming,Zhou Guohua,et al.Voltagemode controlled switching converter with dual-edge constant off-time modulation[C]//Proceedings of 2014International Power Electronics and Application Conference and Exposition.Shanghai,China:IEEE,2014:226-231.
[63]王金平,许建平,兰燕妮.电流型双频率脉冲序列调制开关变换器[J].电工技术学报,2012,27(7):198-204.Wang Jinping,Xu Jianping,Lan Yanni.Study of current-mode bi-frequency pulse-train modulation for switching converters[J].Transactions of China Electrotechnical Society,2012,27(7):198-204(in Chinese).
[64]王金平,许建平,周国华,等.脉冲序列控制CCM Buck变换器低频波动现象分析[J].物理学报,2011,60(4):747-756.Wang Jinping,Xu Jianping,Zhou Guohua,et al.Analysis of low-frequency oscillation phenomenon in the pulse train controlled buck converter[J].Acta Physica Sinica,2011,60(4):747-756(in Chinese).
[65]Sha Jin,Xu Duo,Chen Yiming,et al.A peak-capacitorcurrent pulse-train-controlled buck converter with fast transient response and a wide load range[J].IEEETransactions on Industrial Electronics,2016,63(3):1528-1538.
[66]王金平.开关DC-DC变换器双频率控制技术研究[D].成都:西南交通大学,2012.Wang Jinping.Investigation of bifrequency control technique for switching DC-DC converters[D].Chengdu:Southwest Jiaotong University,2012(in Chinese).
[67]吴松荣.开关变换器多频率控制技术研究[D].成都:西南交通大学,2013.Wu Songrong.Investigation of multi-frequency control technique for switching converter[D].Chengdu:Southwest Jiaotong University,2013(in Chinese).
[68]吴松荣,许建平,龚华彬,等.双频率控制开关变换器低频波动现象抑制方法[J].电力自动化设备,2014,34(1):61-66.Wu Songrong,Xu Jianping,Gong Huabin,et al.Low-frequency oscillation suppression of bi-frequency controlled switching converter[J].Electric Power Automation Equipment,2014,34(1):61-66(in Chinese).
[69]刘姝晗,许建平,沙金.谷值电流型脉冲序列控制反激变换器分析[J].电工技术学报,2014,29(8):119-127.Liu Shuhan,Xu Jianping,Sha Jin.Valley current mode pulse train control for flyback converters[J].Transactions of China Electrotechnical Society,2014,29(8):119-127(in Chinese).
[70]黎宁昊,许建平,沙金.滞环电容电流脉冲序列控制开关DC/DC变换器[J].电力电子技术,2017,51(7):26-29.Li Ninghao,Xu Jianping,Sha Jin.Hysteretic capacitor current pulse train control for switching DC/DCconverter[J].Power Electronics,2017,51(7):26-29(in Chinese).
[71]牟清波,许建平,王金平,等.脉冲序列调制-脉冲跳周期调制Buck变换器研究[J].电力电子技术,2010,44(10):59-61.Mou Qingbo,Xu Jianping,Wang Jinping,et al.Study of pulse train modulation pulse skipping modulation buck converter[J].Power Electronics,2010,44(10):59-61(in Chinese).
[72]钟曙,沙金,许建平,等.脉冲跨周期调制连续导电模式Buck变换器低频波动现象研究[J].物理学报,2014,63(19):198401.Zhong Shu,Sha Jin,Xu Jianping,et al.Low-frequency oscillation of continuous conduction mode buck converter with pulse skipped modulation[J].Acta Physica Sinica,2014,63(19):198401(in Chinese).
[73]包伯成,冯霏,潘赛虎.脉冲跨周期调制连续导电模式Buck变换器低频波动现象及其抑制技术[J].电工技术学报,2014,29(4):38-44,62.Bao Bocheng,Feng Fei,Pan Saihu.Low-frequency oscillation phenomenon and its suppression technique in pulse skipping modulation CCM buck converter[J].Transactions of China Electrotechnical Society,2014,29(4):38-44,62(in Chinese).
[74]Zhong Shu,Xu Jianping,Liu Shuhan,et al.Pulse on/off modulation technique for switching converter[C]//Proceedings of 2013 International Conference on Communications,Circuits and Systems.Chengdu,China:IEEE,2013:382-385.
[75]Dahidah M S A,Konstantinou G,Agelidis V G.A review of multilevel selective harmonic elimination PWM:formulations,solving algorithms,implementation and applications[J].IEEE Transactions on Power Electronics,2015,30(8):4091-4106.
[76]王堃,游小杰,王琛琛,等.低开关频率下SHEPWM和SVPWM同步调制策略比较研究[J].电工技术学报,2015,30(14):333-341.Wang Kun,You Xiaojie,Wang Chenchen,et al.Research on the comparison of synchronized modulation of SHEPWM and SVPWM under low switching frequency[J].Transactions of China Electrotechnical Society,2015,30(14):333-341(in Chinese).
[77]Lamb J,Mirafzal B.An adaptive SPWM technique for cascaded multilevel converters with time-variant DCsources[J].IEEE Transactions on Industry Applications,2016,52(5):4146-4155.
[78]Li Hong,Yang Zhichang,Wang Boyu,et al.On thermal impact of chaotic frequency modulation SPWMtechniques[J].IEEE Transactions on Industrial Electronics,2017,64(3):2032-2043.
[79]吴安顺,黄运加,罗中明,等.梯形脉宽调制型逆变器的单片机控制[J].哈尔滨电工学院学报,1994,17(3):220-223.Wu Anshun,Huang Yunjia,Luo Zhongming,et al.Trapezoidal pulsewidth modulating inverter controlled by single-chip microcomputer[J].HIET Journal,1994,17(3):220-223(in Chinese).
[80]王志良,郝玉东,胡汉金.滞环控制的电流跟踪型SPWM逆变器[J].西北工业大学学报,1996,14(3):472-475.Wang Zhiliang,Hao Yudong,Hu Hanjin.A currentfollowing SPWM inverter with delay-loop control[J].Journal of Northwestern Polytechnical University,1996,14(3):472-475(in Chinese).
[81]陈增禄,毛惠丰,周炳根,等.SPWM数字化自然采样法的理论及应用研究[J].中国电机工程学报,2005,25(1):32-37.Chen Zenglu,Mao Huifeng,Zhou Binggen,et al.A study on theory and application of digital natural sampling based SPWM[J].Proceedings of the CSEE,2005,25(1):32-37(in Chinese).
[82]李扶中,熊蕊.一种新型的不对称规则SPWM采样法[J].电力电子技术,2007,41(4):93-95.Li Fuzhong,Xiong Rui.A novel sampling method of SPWM with nonsymmetrical rules[J].Power Electronics,2007,41(4):93-95(in Chinese).
[83]Wu Bin.High-power converters and AC drives[M].New York:Wiley-IEEE Press,2006.
[84]Espinoza J R,Joos G.Current-source converter on-line pattern generator switching frequency minimization[J].IEEE Transactions on Industrial Electronics,1997,44(2):198-206.
[85]高春侠,张磊,张加胜.新型磁通分量跟踪型SVPWM控制技术仿真[J].大功率变流技术,2009(1):14-16.Gao Chunxia,Zhang Lei,Zhang Jiasheng.Simulation of a novel SVPWM control with flux tracking[J].High Power Converter Technology,2009(1):14-16(in Chinese).
[86]周卫平,吴正国,唐劲松,等.SVPWM的等效算法及SVPWM与SPWM的本质联系[J].中国电机工程学报,2006,26(2):133-137.Zhou Weiping,Wu Zhengguo,Tang Jinsong,et al.A novel algorithm of SVPWM and the study on the essential relationship between SVPWM and SPWM[J].Proceedings of the CSEE,2006,26(2):133-137(in Chinese).
[87]姜卫东,王伟,王金平,等.基于混合脉宽调制的并联并网变换器控制方法[J].电力系统自动化,2017,41(22):124-132.Jiang Weidong,Wang Wei,Wang Jinping,et al.Control method for parallel grid-connected converters based on hybrid pulse width modulation[J].Automation of Electric Power Systems,2017,41(22):124-132(in Chinese).
[88]Chen Min,Sun Dan.A unified space vector pulse width modulation for dual two-level inverter system[J].IEEETransactions on Power Electronics,2017,32(2):889-893.
[89]Tan Longcheng,Wu Bin,Narimani M,et al.A space virtual-vector modulation with voltage balance control for nested neutral-point clamped converter under low output frequency conditions[J].IEEE Transactions on Power Electronics,2017,32(5):3458-3466.
[90]Li Junjie,Jiang Jianguo,Qiao Shutong.A space vector pulse width modulation for five-level nested neutral point piloted converter[J].IEEE Transactions on Power Electronics,2017,32(8):5991-6004.
[91]Sakthisudhursun B,Pandit J K,Aware M V.Simplified three-level five-phase SVPWM[J].IEEE Transactions on Power Electronics,2016,31(3):2429-2436.
[92]王琛琛,王堃,游小杰,等.低开关频率下双定子感应电机SVPWM同步调制策略研究[J].中国电机工程学报,2017,37(13):3883-3891.Wang Chenchen,Wang Kun,You Xiaojie,et al.Research on the synchronized SVPWM strategies under low switching frequency for dual stator induction machines[J].Proceedings of the CSEE,2017,37(13):3883-3891(in Chinese).
[93]卢锋,田铭兴,朱强化.有源电力滤波器不定频滞环SVPWM电流控制方法[J].电力电子技术,2014,48(1):48-51.Lu Feng,Tian Mingxing,Zhu Qianghua.Indeterminate frequency hysteresis SVPWM current control method for active power filter[J].Power Electronics,2014,48(1):48-51(in Chinese).
[94]Ba?kys A,Bleizgys V,Gobis V.The impact of output voltage modulation strategies on power losses in inverter[J].Electronics and Electrical Engineering,2009,94(6):47-50.
