多电平直流环节逆变器新型拓扑与调制方法研究
|
摘要
多电平直流环节（Multilevel DC-Link, MLDCL）逆变器由于输出波形质量高、功率器件较少、开关频率低、便于模块化和控制灵活等优点，已成为多电平变换器领域的一个研究热点，越来越被广泛应用于新能源发电和电机驱动。但现有MLDCL逆变器仍存在电路拓扑及控制复杂、直流变换单元难于升压等的不足，影响到系统的性能。
本文主要对MLDCL逆变器电路结构进行研究，分析了MLDCL逆变器电路结构优化、电能变换效率与波形质量控制技术。主要研究成果与创新点有:
探讨了MLDCL逆变器主电路拓扑结构的拓展方法，设计了一类混合型MLDCL逆变电路结构，具有输出波形质量高、器件相对较少的优势。
分析了Newton-Raphson方法求解MLDCL逆变器SHEPWM非线性超越方程组存在计算难度大的根本原因，设计了方程组求解时初始值选取的方法和收敛范围更宽的基于Newton下山法的SHEPWM方程组计算方法。针对Newton下山法存在矩阵奇异或病态的情形，提出了可强迫矩阵正定的改进型Levenberg-Marquardt迭代计算SHEPWM方程组的方法。设计了基于PSO算法的SHEPWM方程组求解方法，克服了数值法求解SHEPWM方程组时矩阵求逆和初值选取困难。
针对MLDCL逆变器各直流变换单元输出功率不相等的不足，设计了基于功率均衡的SHEPWM方法。该方法通过调整各直流变换单元的控制角，得到并求解新的SHEPWM方程组，在二分之一个相电压周期内实现了宽调制度范围的功率均衡。
针对基于功率均衡的SHEPWM方法计算量大、直流变换单元数量受限的缺点，设计了一种基于调制波循环分配策略的MLDCL逆变器SPWM功率均衡控制策略，实现了任意直流变换单元的功率均衡。
为了克服常规MLDCL逆变器直流变换单元不能升压的不足，提出了一种直流变换单元具有升压功能的Z源多电平直流环节逆变器电路拓扑，并设计了最大调制比的SPWM方法，具有高可靠性、高增益、电源电流连续等优点。
Multilevel DC-link inverter has drawn tremendous interest in multilevel converter areas, and moreand more been widely used in new energy power generation and motor drive, mainly due to high outputquality, low switching frequency, easy modularity and flexible control. However, the existing MLDCLinverter has the disadvantages that the topologies and modulation method of MLDCL inverter are toocomplicated, and their DC unit is difficult to boost, which would affect the system performance.
This dissertation focuses on the structure and modulation method of MLDCL inverter topologies.The main contents and innovation of this dissertation are as follows:
The design method of MLDCL inverter circuit topology is discussed. Then, a novel HybridMLDCL inverter is presented, which has the advantages of high quality waveform and less devices.
This dissertation analyzes the causes in solving nonlinear transcendental equations existingSHEPWM by the Newton-Raphson algorithm. Then, the selection methods for initial values and thecalculation method of Newton downhill method with the advantage of wider convergence range forcalculating the SHEPWM equations are designed. And an improved Levenberg-Marquardt iterativealgorithm is presented, which avoiding the disadvantage of singular or pathological in Newton downhillmethod, by forcing matrix positive definite. A novel PSO method is designed for solving SHEPWMequations to overcome the difficulty of matrix inversion and initial selection in numerical method.
For the output power of DC units are unequal with each other in the MLDCL inverter, a method ofSHEPWM based on power balance control is designed. It achieves the result of wide range of powerbalance in half period, by adjusting the control angle of DC unit.
In order to overcome the shortcoming of SHEPWM based on power balance control, a new SPWMmethod based on power balance control is described. The proposed method can self-adjust to achievebalance charge control without a complex circuit or calculation.
To resolve the problems of DC unit unable to boost, an improved MLDCL inverter based Z-sourceis proposed. Additionally, a SPWM method with high reliability, high gain, continuous current isdesigned.
本文主要对MLDCL逆变器电路结构进行研究，分析了MLDCL逆变器电路结构优化、电能变换效率与波形质量控制技术。主要研究成果与创新点有:
探讨了MLDCL逆变器主电路拓扑结构的拓展方法，设计了一类混合型MLDCL逆变电路结构，具有输出波形质量高、器件相对较少的优势。
分析了Newton-Raphson方法求解MLDCL逆变器SHEPWM非线性超越方程组存在计算难度大的根本原因，设计了方程组求解时初始值选取的方法和收敛范围更宽的基于Newton下山法的SHEPWM方程组计算方法。针对Newton下山法存在矩阵奇异或病态的情形，提出了可强迫矩阵正定的改进型Levenberg-Marquardt迭代计算SHEPWM方程组的方法。设计了基于PSO算法的SHEPWM方程组求解方法，克服了数值法求解SHEPWM方程组时矩阵求逆和初值选取困难。
针对MLDCL逆变器各直流变换单元输出功率不相等的不足，设计了基于功率均衡的SHEPWM方法。该方法通过调整各直流变换单元的控制角，得到并求解新的SHEPWM方程组，在二分之一个相电压周期内实现了宽调制度范围的功率均衡。
针对基于功率均衡的SHEPWM方法计算量大、直流变换单元数量受限的缺点，设计了一种基于调制波循环分配策略的MLDCL逆变器SPWM功率均衡控制策略，实现了任意直流变换单元的功率均衡。
为了克服常规MLDCL逆变器直流变换单元不能升压的不足，提出了一种直流变换单元具有升压功能的Z源多电平直流环节逆变器电路拓扑，并设计了最大调制比的SPWM方法，具有高可靠性、高增益、电源电流连续等优点。
Multilevel DC-link inverter has drawn tremendous interest in multilevel converter areas, and moreand more been widely used in new energy power generation and motor drive, mainly due to high outputquality, low switching frequency, easy modularity and flexible control. However, the existing MLDCLinverter has the disadvantages that the topologies and modulation method of MLDCL inverter are toocomplicated, and their DC unit is difficult to boost, which would affect the system performance.
This dissertation focuses on the structure and modulation method of MLDCL inverter topologies.The main contents and innovation of this dissertation are as follows:
The design method of MLDCL inverter circuit topology is discussed. Then, a novel HybridMLDCL inverter is presented, which has the advantages of high quality waveform and less devices.
This dissertation analyzes the causes in solving nonlinear transcendental equations existingSHEPWM by the Newton-Raphson algorithm. Then, the selection methods for initial values and thecalculation method of Newton downhill method with the advantage of wider convergence range forcalculating the SHEPWM equations are designed. And an improved Levenberg-Marquardt iterativealgorithm is presented, which avoiding the disadvantage of singular or pathological in Newton downhillmethod, by forcing matrix positive definite. A novel PSO method is designed for solving SHEPWMequations to overcome the difficulty of matrix inversion and initial selection in numerical method.
For the output power of DC units are unequal with each other in the MLDCL inverter, a method ofSHEPWM based on power balance control is designed. It achieves the result of wide range of powerbalance in half period, by adjusting the control angle of DC unit.
In order to overcome the shortcoming of SHEPWM based on power balance control, a new SPWMmethod based on power balance control is described. The proposed method can self-adjust to achievebalance charge control without a complex circuit or calculation.
To resolve the problems of DC unit unable to boost, an improved MLDCL inverter based Z-sourceis proposed. Additionally, a SPWM method with high reliability, high gain, continuous current isdesigned.
引文
[1] Bose K. Global Warming: Energy, Environmental Pollution, and the Impact of PowerElectronics[J].IEEE Ind. Electron. Magazine,2010,4(3):6–17.
[2] Intemational Energy Ageney. World energy outlook2011[R]. Washington DC: IEA,2011.
[3] Giovanni S., Giovanni P., Samuel V., et al. Renewable Energy Operation and ConversionSchemes： A Summary of Discussions During the Seminar on Renewable EnergySystems[J]. IEEE Ind. Electron. Magazine,2010,4(3):38-51.
[4] Yu X., Starke M. R.,Tolbert L. M., et al. Fuel Cell Power Conditioning for Electric PowerApplications：ASummary[J]. IET Electr. PowerAppl.,2007,1(5):643–656.
[5] Marco L.,Thilo S., John Y. H. Future Energy Systems: Integrating Renewable EnergySources into the Smart Power Grid Through Industrial Electronics[J]. IEEE Ind. Electron.Magazine,2010,4(3):18-37.
[6] Martina C., Agelidis V.G.. Mike M. Multilevel Converters for Single-phase GridConnected Photovoltaic Systems：An Overview[J]. Solar Energy,1999,66(5):325–335.
[7]朱瑛,程明,花为,等.考虑损耗转矩的风力发电系统最大风能跟踪控制[J].中国电机工程学报,2013,33(19):39-46.
[8] Carrasco J. M., Franquelo L.G., Jan T. B.Power-Electronic Systems for the GridIntegration of Renewable Energy Sources: A Survey[J]. IEEE Trans. Ind. Electron.,2006,53(4):1002-1016.
[9] Gu Y.,Li W., Zhao Y.Transformerless Inverter With Virtual DC Bus Concept for Cost-Effective Grid-Connected PV Power Systems[J].IEEE Trans.Power Electron.,2013,28(2):793-805.
[10] Xue Y., Chang L., Kj r S. B. Topologies of Single-phase Inverters for Small DistributedPower Generators:An Overview[J].IEEE Trans. Power Electron.,2004,19(5):1305-1314.
[11]张兴,曹仁贤.太阳能光伏并网发电及其逆变控制[M].北京:机械工业出版社,2011.
[12]刘邦银.建筑集成光伏系统的能量变换与控制技术研究[D].武汉:华中科技大学,2008.
[13] Liao Y.H., Lai C.M. Newly-constructed Single-phase Multistring Multilevel Inverter forFuel-cell Microgrid[C]. IEEE ECCE,2011:1440-1444.
[14]金科.燃料电池供电系统的研究[D].南京:南京航空航天大学,2006.
[15] Patrao I., Emilio F., Fran G,.Transformerless Topologies for Grid-connected Single-phasePhotovoltaic Inverters[J]. Renewable and Sustainable Energy Reviews,2011(15):3423–3431.
[16] Samuel V., Peter Z., Regine M,. Highly Efficient Single-Phase Transformerless Invertersfor Grid-Connected Photovoltaic Systems[J]. IEEE Trans. Ind.Electron.,2010,57(9):3118-3128.
[17] Edris P., Oriol G., Daniel M..Multilevel Converters Control for Renewable EnergyIntegration to the Power Grid [J]. Energy36(2011):950-963.
[18] Zhao Z., Xu M., Chen Q.L,.Derivation, Analysis, and Implementation of a Boost–BuckConverter-Based High-Efficiency PV Inverter[J]. IEEE Trans. Power Electron.,2012,27(3):1304-1313.
[19]肖华锋，谢少军.用于光伏并网的交错型双管Buck-Boost变换器[J].中国电机工程学报,2010,30(21):7-12.
[20]汪海宁,苏建徽,丁明,等.光伏并网功率调节系统[J].中国电机工程学报,2007,27(2)：75-79．
[21]Agorreta J L,Borrega M,Lopez J，et al．Modeling and Control of N-paralleled Grid-connected Inverters with LCL Filter Coupled due to Grid Impedance in PV Plants[J].IEEETrans. Power Electron.,2011,26(3):770-785.
[22]吴红飞,孙凯,邢岩.新能源发电串联分布式高能效变换系统[J].中国电机工程学报,2012,32(33):1-6.
[23] Li Q., Wolfs P.A Review of the Single Phase Photovoltaic Module Integrated ConverterTopologies with Three Different DC Link Configurations[J]． IEEE Trans． PowerElectron.，2008，23(3):1320-1323．
[24] Kim H., Kim J., Kim H. A High Efficiency Photovoltaic Module Integrated Converterwith theAsymmetrical Half-bridge Flyback[J]. Solar Energy,2010(84):1376–1381.
[25] Erickson, J.R. Integrated Photovoltaic Module[P]. United States Patent: US20120042588,Feb.23,2012.
[26]李艳,阮新波,杨东升.无缓冲单元的多输入直流变换器电路拓扑[J].电工技术学报,2009,24(5):73-79.
[27]李艳,阮新波,杨东升.带缓冲单元的多输入直流变换器电路拓扑[J].电工技术学报.2009,24(6):62-68.
[28] Blaabjerg F., Chen Z., Kjaer B. Power Electronics as Efficient Interface in DispersedPower Generation Systems[J]. IEEE Trans. Power Electron.,2004,19(5):1184-1194.
[29] Kouro S., Malinowski M., Gopakumar K. Recent Advances and Industrial Applicationsof Multilevel Converters[J]. IEEE Trans. Ind. Electron.,2010,57(8):2553-2579.
[30]黄立培,马毅为,孙凯.高效级联式光伏并网逆变器的控制[J].高电压技术,2011.37(3):680-686.
[31] Nicola F., Gianpaolo L., Giovanni P. Distributed Maximum Power Point Tracking ofPhotovoltaic Arrays: Novel Approach and System Analysis[J]. IEEE Trans. Ind.Electron.,2008,55(7):2610-2621.
[32]Villanueva E., Correa P., Rodríguez J. Control of a Single-Phase Cascaded H-BridgeMultilevel Inverter for Grid-Connected Photovoltaic Systems[J]. IEEE Trans. Ind.Electron.,2009,56(11):4399-4406.
[33]马琳,孙凯,Remus T.,等.高效率中点钳位型光伏逆变器拓扑比较[J].电工技术学报,2011,26(2):108-114.
[34]张犁，孙凯，冯兰兰，中点钳位非隔离全桥光伏并网逆变器[J].中国电机工程学报,2012,327(18):16-22.
[35]陆晓楠,孙凯,马毅为,等.适用于光伏发电系统的混合级联式逆变器[J].清华大学学报(自然科学版),2011,51(3):351-355.
[36]Walker G. R., Sernia P. C..Cascaded DC-DC Converter Connection of PhotovoltaicModules[J]. IEEE Trans. Power Electron.,2004,19(4):1130–1139.
[37] Jain S.,Agarwal V. An Integrated Hybrid Power Supply for Distributed GenerationApplications Fed by Nonconventional Energy Sources[J]. IEEE Trans. Energy Convers.2008,23(2):622-631.
[38] Rahim N.A., Selvaraj J. Multistring Five-Level Inverter With Novel PWM ControlScheme for PVApplication[J]. IEEE Trans. Ind. Electron.,2010,57(6):2111-2123.
[39] Barbosal P., Steimer P., Steinke J. et al. Active-neutral-point-clamped (ANPC) MultilevelConverter Technology [C].EPE,2005:11-20.
[40]谭国俊,景巍.有源钳位三电平变频器及其结温平衡控制[J].电工技术学报,2012,27(2):97-102.
[41] Roberto P., Nicola B., Alessandro R.,et al. DC bus Voltage Equalization in Single-phaseSplit-capacitor Three-level Neutral-point-clamped Half-bridge Inverters for PVApplications[C]. IEEE APEC,2011:931-938.
[42] Su G.J.,Adams D. J. Multilevel DC Link Inverter for Bbrushless Permanent MmagnetMotors with very low inductance[C]. IEEE IAS,2001:829–834.
[43] Su G.J. Multilevel DC-link Inverter[J]. IEEE Trans. Ind. Appli,2005,41(3):848-854
[44] Ersoy B., Birol A., Sabri C, A Grid-connected Photovoltaic Power Conversion Systemwith Single-phase Multilevel Inverter[J]. Solar Energy,2010(84):2056–2067.
[45]Nabae A, Takashi I, Akagi H. A New Neutral-point Clamped PWM Inverter[J]. IEEETrans. Ind.Appl.,1981, IA-17:518–523.
[46] Meynard T.A.Foch H. Multi-level Conversion: High Voltage Choppers and Voltage-source Inverters[C]. IEEE PESC1992:397-403
[47]Samir K., Malinowski M., Gopakumar K.,et al. Recent Advances and IndustrialApplications of Multilevel Converters [J]. IEEE Trans. Ind. Electron.,2010,57(8):2553-2580.
[48]Adam G.P., Stephen J. F., Ahmed M. M. Capacitor Balance Issues of the Diode-ClampedMultilevel Inverter Operated in a Quasi Two-State Mode[J]. IEEE Trans. Ind. Electron.,2008,55(8):3088-099.
[49]Carlos M., Juan J. N., Domingo B.Energy-Balance Modeling and Discrete Control forSingle-Phase Grid-Connected PV Central Inverters[J]. IEEE Trans. Ind. Electron.,2008,55(7):2734—2743.
[50]Juan D., Luis M.. High-Level Multistep Inverter Optimization Using a Minimum Numberof Power Transistors[J]. IEEE Trans. Power Electron.2006,21(2):330-337.
[51] Zeng F.P., Tan G.H., Wang J.Z. Novel Single-phase Five-level Voltage-source Inverterfor the Shunt Active Power Filter[J]. IET Power Electron.,2010,3(4):480–489.
[52] Domingo A. R., Reynaldo M. R., Samir A. M., Symmetrical Hybrid Multilevel DC–ACConverters With Reduced Number of Insulated DC Supplies[J]. IEEE Trans. Ind.Electron.,2010,57(7):2307-2314.
[53] Ruan X., Li B., Chen Q.Three-level Converters: A New Approach for High Voltage andHigh Power DC–to–DC Conversion[C].IEEE PESC,2002:663–668.
[54]阮新波.三电平直流变换器及其软开关技术[M].北京:科学出版社,2006.
[55] Babaei E., Farhadi M., Mazgar F. N.Symmetric and Asymmetric Multilevel InverterTopologies with Reduced Switching Devices[J]. Electric Power Systems Research,2012(86):122–130.
[56] Farhadi M.,Babaei E. A Generalized Cascaded Multilevel Inverter Using SeriesConnection of Submultilevel Inverters[J]. IEEE Trans. Power Electron.,2013,28(2):625–636.
[57] Babaei E. A Cascade Multilevel Converter Topology With Reduced Number of Switches[J]. IEEE Trans. Power Electron.,2008,23(6):2657-2664.
[58] Youhei H. Hirotaka K.. A Single-Phase Multilevel Inverter Using SwitchedSeries-Parallel DC Voltage Sources[J]. IEEE Trans. Ind. Electron.,2010,57(8):2643–2650.
[59] Ramkumar S., Kamaraj V.,Thamizharasan S. A New Sseries Parallel Switched MultilevelDc-link Inverter Topology[J]. Electrical Power and Energy Systems,2012,36,pp93–99.
[60] Youhei H., Hirotaka K..A Switched-Capacitor Inverter Using Series-Parallel ConversionWith Inductive Load[J]. IEEE Trans. Ind. Electron.,2012,59(2):878-887.
[61]侯李祥,吕跃刚.新型级联多电平逆变器[J].大功率变流技术,2009,(3):20-23.
[62] Abdalla I., Corda J., Zhang L.Multilevel DC-Link Inverter and Control Algorithm toOvercome the PV Partial Shading[J]. IEEE Trans. Power Electron,2013,28(1):14-18.
[63]刘凤君.环保节能型H桥及SPWM直流电源式逆变器[M].北京:电子工业出版社,2010.
[64] Peng F. Z. Z-source Inverter[C]. IEEE IAS,2002:775–781.
[65]彭方正,房绪鹏,顾斌,等. Z源变换器[J].电工技术学报,2004,19(2):47-51.
[66] Shen, M., Joseph, A., Wang, J., Peng, F.Z., Adams, D.J Comparison of TraditionalInverters and Z-source Inverter for Fuel Cell Vehicles[J]. IEEE Trans. Power Electron.,2007,22(4):1453–1463.
[67] Hanif M., Basu M., Gaughan K..Understanding the Operation of a Z-source Inverter forPhotovoltaic Cpplication with a Design Example[J]. IET Power Electron.,2011,4(3):278–287.
[68]汤雨.Z源逆变器研究[D].南京航空航天大学,2006.
[69]刘鸿鹏.基于Z源网络的光伏并网逆变系统的研究[D].哈尔滨工业大学,2011.
[70] Loh P. C., Flaabjerg B., Feng, S. Y., et al. Pulse-width Modulated Z-sourceNeutral-point-clamped Inverter[C]. IEEE APEC,2006, pp.431–437.
[71] Gao F. Loh,P.C., Blaabjerg F. Five-level Z-source Diode-clamped Inverter[J]. IET PowerElectron.,2010,3(4):500–510.
[72] Zhou Y.,Liu L., Li H., et al. A High Performance Photovoltaic Module-IntegratedConverter (MIC) Based on Cascaded Quasi-Z-Source Inverters (qZSI) using eGaN FETs[J]. IEEE Trans. Power Electron.,2013,28(6):2727-2738.
[73] Banaei M.R., Dehghanzadeh A.R., Salary E.. Z-source-based Multilevel Inverter withReduction of Switches[J]. IET Power Electron.,2012,5(3):385–392.
[74] Nguyen M.K., Lim Y.C., Park S.J. Improved Trans-Z-Source Inverter With ContinuousInput Current and Boost Inversion Capability[J]. IEEE Trans. Power Electron.,2013,28(10):4500-4510.
[75] Banaei M. R., Salary E. Verification of New Family for Cascade Multilevel Inverterswith Reduction of Components[J]. Journal of Electrical Engineering&Technology,2011,6(2):245-254.
[76]曾繁鹏,纪延超,王建赜.新型单相五电平电压源逆变器[J].电机与控制学报,2008,12(3):300-303
[77] Patel H. S., Hoft R. G.. Generalized Techniques of Harmonic Elimination and VoltageControl in Thyristor Inverters，Part I：Harmonic Elimination[J]. IEEE Trans. Ind. Appl.,1973,9(3):310–317..
[78]Li L.，Czarkowski D，Liu Y.，et a1. Multilevel Selective Harmonic Elimination PWMTechnique in Series-connected Voltage Inverter[J]． IEEE Trans. Ind. Appl,2000,36(1):160-170．
[79] Agelidis V. G., Balouktsis A., Dahidah M. S. A. A Five-level Symmetrically DefinedSelective Harmonic Elimination PWM Strategy: Analysis and ExperimentalValidation[J]. IEEE Trans. Power Electron.,2000,23(1):19–26.
[80]费万民，阮新波，张艳莉，居荣.多电平逆变器特定谐波消除脉宽调制方法的初值问题研究[J].中国电机工程学报,2007,27(13):87-92.
[81] Fei W.,. Ruan X., Wu B. A Generalized Formulation of Quarter-wave SymmetrySHE-PWM Problems for Multilevel Inverters[J].IEEE Trans. Power Electron.,2009,24(7):1758–1766.
[82] Franz C., Hans E.. Efficiency Optimal Control for AC Drives with PWM Inverters[J]．IEEE Trans. Ind. Appl,1985,21(4):987-1000.
[83] Holtz J. Pulsewidth Modulation: a Survey[J]. IEEE Trans. Ind. Electron.,1992,39(5):410-420.
[84]张慧,刘开培, M. Braun,等.新型优化脉冲宽度调制方法在大功率逆变器的应用研究[J].电工技术学报,2006,21(6):17-22.
[85] Sun J., Beineke S., Grotstollen H. Optimal PWM based on Real-time Solution ofHarmonic Elimination Equations [J].IEEE Trans on Power Electron.,1996,11(4):612-621.
[86] Enjeti P. N., Ziogas P. D., Lindsay J. F. Programmed PWM techniques to eliminateharmonics:A critical evaluation[J].IEEE Trans.Ind. Applicat.,1990,26(2):302–316.
[87] Agelidis V. G., Balouktsis A., Cossar C.,et al.Five-level Selective Harmonic EliminationPWM Strategies and Multicarrier Phase-shifted Sinusoidal PWM: A Comparison[C].IEEE PESC,2005:1685–1691.
[88] Pontt J., Rodriguez J., Huerta R., et al. Mitigation of Noneliminated Harmonics ofSHEPWM Three-level Multipulse Three-phase Active Front End Converters with lowSwitching Frequency for Meeting Standard IEEE-519-92[C]. IEEE PESC,2003, pp.531–536.
[89]佟为明,陈向阳,程树康,等.变频电源特定消谐技术中非线性方程组解法的研究[J].中国电机工程学报,1998,18(5):357-360.
[90]郭新华,王永兴,赵峰,等.基于SHEPWM的中压大功率牵引永磁同步电机两电平控制[J].电工技术学报,2012,27(11):76-82.
[91]《现代应用数学手册》编委会编.现代应用数学手册:计算与数值分析卷[M].北京:清华大学出版社,2005.
[92] Kelley C.T. Solving Nonlinear Equations with Newton's Method[M]. SIAM,Philadelphia,2003.
[93]黄宇清,谢运祥.逆变器消谐模型求解中矩阵求逆的算法研究[J].华南理工大学学报(自然科学版),2003,3l(1l):1-4.
[94] Huang H., Hu S., Czarkowski D. Solving the I11-conditioned Polynomial for theOptimal PWM[C]. IEEE CHQP,2004:555–558.
[95]黄象鼎,曾钟钢,马亚南.非线性数值分析的理论与方法[M].武汉:武汉大学出版社,2004.
[96]Kujan,P. Numerical Iterative Methods Solving Three-phase Multilevel VoltageConverter[C]. IEEE CACSD,2010:1801–1806.
[97] Enjeti P. N.， Lindsay J. F. Solving Nonlinear Equations of Harmonic Elimination PWMin Power Control[J]. Electron. Lett.,1987,23(12):656–657.
[98]陈新,谢少军.用开关点预置SHEPWM控制方案实现变换器调压[J].电力电子技术,2000,34(4):19-21.
[99]刘文华,宋强,陈远华,等.NPC逆变器SHE-PWM开关角度的计算方法研究[J].中国电机工程学报,2002,22(11):31-34.
[100]Zhang Y.C., Zhao Z.M., Zhu J. A Hybrid PWM Applied to High-Power Three-LevelInverter-Fed Induction-Motor Drives[J].IEEE Trans. Ind. Electron.,2011,58(8):3409-3420.
[101]王榕生,吴汉光.消谐法SHEPWM的谐波影响数值分析[J].电工技术学报,2011,26(9):183-189.
[102] Sun J., Grotstollen H. Solving Nonlinear Equations for Selective Harmonic EliminatedPWM using Predicted Initial Values[C].IEEE IECON,1992, vol.1:259–264.
[103] Chiasson J. N., Tolbert L. M., McKenzie K. J.，et a1．A Complete Solution to theHarmonic Elimination Problem[J].IEEE Trans. Power Electron.,2004,19(2):491-499.
[104] Vassilios G., Anastasios B., Ioannis B., et a1.Multiple Sets of Solutions for HarmonicElimination PWM Bipolar Waveforms: Analysis and Experimental Verification[J]. IEEETrans. Power Electron.,2006,21(2):415-421.
[105] Agelidis V., Balouktsis A., Cossar C.. On Attaining the Multiple Solutions of SelectiveHarmonic Elimination PWM Three-level Waveforms Through Function Minimization[J].IEEE Trans. Ind. Electron.,2008,55(3):996–1004.
[106]张永昌,赵争鸣,张颖超.三电平逆变器SHEPWM多组解特性比较及实验[J].电工技术学报,2007,22(3):60-65.
[107]费万民，张艳莉,王学华,等.多电平逆变器SHEPWM问题解的包含关系[J].中国电机工程学报,2008,28(15):61-66.
[108] Konstantinou G.S. Dahidah,M.S.A., Agelidis V.G.. Solution Trajectories for SelectiveHarmonic Elimination Pulse-width Modulation for Seven-level Waveforms: Analysisand Implementation[J].IET Power Electron.,2012,5(1):22–30.
[109] Suresh A.Y., Panda K. Research on a Cascaded Multilevel Inverter by EmployingThree-phase Transformers[J].IET Power Electron.,2012,5(5):561–570.
[110] Asumadu J. A., Hoft R. G. Microprocessor-based Sinusoidal Waveform Synthesis usingWalsh and Related Orthogonal Functions[J]. IEEE Trans. Power Electron.,1989,4(2):234–241.
[111]单庆晓，潘孟春，唐莺.基于沃尔什变换的多电平谐波消除技术[J].电力电子技术,2004,38(4):32-34.
[112]郑春芳，张波，丘东元.基于沃尔什函数的逆变器选择性谐波消除技术开关角的快速求解[J].中国电机工程学报,2005,25(22):38-44.
[113]秦亮,刘开培,张慧.基于Walsh变换的PWM优化脉冲调制方法[J].电工技术学报,2007,22(4):118-123.
[114]都小利,费万民.多电平逆变器半周期对称SHEPWM方法[J].电工技术学报,2010,25(4):95-102.
[115] Sun J., Grotstollen H. Pulsewidth Modulation Based on Real-time Solution of AlgebraicHarmonic Elimination Equations[C].IEEE IECON,1994., vol.1:79–84.
[116] Kato T..Sequential Homotopy-based Computation of Multiple Solutions for SelectedHarmonic Elimination in PWM Inverters[J].IEEE Trans. Circuits and SystemsI:Fundamental Theory and Applications,1999,46(5):586–593.
[117]李治典,周秦英,李宏,等.实时求解特定消谐方程组的新算法[J].西北工业大学学报,2004,22(1):37-40.
[118]谢运祥.逆变器消谐控制的同伦模型建立及算法分析[J].中国电机工程学报，2002，22(5):27-31.
[119] Chiasson J. N., Tolbert L. M., Kenzie M. K., et al. Elimination of Harmonics in aMultilevel Converter Using the Theory of Symmetric Polynomials and Resultants[J].IEEE Trans. Control Systems Technology,2005,13(2):216-223.
[120]郑春芳，张波.吴方法在电力电子逆变器消谐技术中的应用[J].中国电机工程学报，2005,25(15):40-45.
[121] Bowes S.R., Grewal S., Holliday D.Single-phase Three-level Regular-sampledSelective Harmonic Elimination PWM[J]. IEE Proc. Electr.Power Appl.,2001,148(2):155–161.
[122]周熙炜,刘卫国.空间电压矢量合成的新型选择谐波消去技术[J].中国电机工程学报，2009,29(30):35-41.
[123] Maswood, A.I., Liu, J. Optimal Online Algorithm Derivation for PWM-SHESwitching[J]. Electron. Lett.,1998,34(8):821-823.
[124]刘红兵,刘辉,智泽英.基于曲线拟合技术的最优PWM开关角在线计算[J].电力电子技术,2009,43(11):82-84.
[125]王琛琛,李瑞夫,周明磊.基于TMS320F28335的SHEPWM数字实现[J].北京交通大学学报,2011,35(5):89-93.
[126] Ahmadi D., Zou K., Li C., et al. A Universal Selective Harmonic Elimination Methodfor High-Power Inverters[J]. IEEE Trans. Power Electron.,2011,26(10):2743-2752.
[127]朱思国,陆佳政,欧阳红林,等.基于谐波注入法的级联型逆变器谐波消除研究[J].电工技术学报,2012,27(8):194-202.
[128] Martinez C., Lazaro A., Quesada I.，et a1．THD Minimization for Railway ApplicationsThrough Harmonic Spectrum Optimization. IEEE,2012:609-1614.
[129] Ghazanfari A., Mokhtari H.,. Firouzi M. Simple Voltage Balancing Approach for CHBMultilevel Inverters Considering Low Harmonic Content Based on a Hybrid OptimalModulation Strategy[J]. IEEE Trans. Power Del.,2012,27(4):1937–1946.
[130]汪定伟,王俊伟,王洪峰,等.智能优化方法[M].北京：高等教育出版社,2007.
[131]李士勇.智能优化算法原理与应用[M].哈尔滨:哈尔滨工业大学出版社,2012.
[132] Bonabeau E., Dorigo M., Theraulaz G. Swarm Intelligence: From Natural to ArtificialSystems. Oxford University Press,1999.
[133] Clerc M., Kennedy J.The Particle Swarm: Explosion, Stability and Convergence in aMulti-dimensional Complex Space[J].IEEE Trans. Evol.Comput.,1998,2(3):91–96.
[134] Mohaddes M., Gole A. M., McLaren P.G. A Neural Network Controlled OptimalPulse-width Modulated STATCOM[J]. IEEE Trans. Power Delivery,1999,14(2):481-488.
[135]李春燕,陈新,沈忠亭,等.最优PWM开关角的在线计算[J].南京航空航天大学学报.2005,37(1):40-43．
[136] Shi K L,Hui Li. Optimized PWM Strategy based on Genetic Algorithms[J]. IEEE Trans.Ind. Electron.,2005,52(5):1458-1461.
[137]周尔民.遗传算法应用于多电平最优化阶梯波技术[J].高压电技术,2007,33(5):172-175.
[138]王群京,胡存刚,李国丽.基于遗传算法的三电平逆变器SHEPWM方法的研究[J].中国科学技术大学学报,2009,39(8):848-852.
[139] Sundareswaran K., Jayant K., Shanavas T. N. Inverter Harmonic Elimination Through aColony of Continuously Exploring Ants[J]. IEEE Trans. Ind. Electron.,2007,54(5):2558-2565.
[140]胡存刚，王群京，李国丽,等.一种新的SHEPWM三电平逆变系统的仿真和实验研究[J].系统仿真学报,2008,20(16):4425-4428.
[141] Taghizadeh H., Tarafdar H. M. Harmonic Elimination of Cascade Multilevel Inverterswith Nonequal DC Sources Using Particle Swarm Optimization[J]. IEEE Trans. Ind.Electron,2010,57(11):3678-3684.
[142] Ray R. N., Goswami S. K. An Application of PSO Technique for Harmonic Eliminationin a PWM Inverter[J].Applied Soft Computing,2009,9(4):1315-1320
[143]娄慧波,毛承雄,陆继明,等.基于微粒群算法的三电平正弦脉冲宽度调制开关时刻优化[J].中国电机工程学报,2007,27(33):108-112.
[144]王凌,刘波.微粒群优化与调度算法[M].北京：清华大学出版社,2008.
[145]恩格尔伯里特,著,谭营,译.计算群体智能基础[M].北京：清华大学出版社,2009.
[146] Barkati S., Baghli L., Berkoukc E. M.Harmonic Elimination in Diode-clampedMultilevel Inverter using Evolutionary Algorithms[J]. Electric Power Systems Research,2008(78):1736–746.
[147] Debnath S., Ray R.. N. Harmonic Elimination in Multilevel Inverter using GA andPSO:AComparison[C]. IEEE SCEECS.2012:1-5.
[148] Shi Y., Eberhart R. C. A Modified Particle Swarm Optimizer[C]. Proc of the IEEE IntConf on Evolutionary Computation. Piscataway: IEEE Press,1998:69-73.
[149] Ratnaweera A., Halgamuge S. K. Watson H C. Self-organizing Hierarchical ParticleSwarm Optimizer with Time-varying Acceleration Coefficients[J].IEEE Trans. Evol.Comput.,2004,8(3):240–255.
[150]Chatterjee A., Siarry P. Nonlinear Inertia Weight Variation for Dynamic Adaptation inParticle Swarm Optimization[J].Computers and Operations Research,2006,33(3):859-871.
[151]Ko C., Chang Y., Wu C.A PSO Method With Nonlinear Time-Varying Evolution forOptimal Design of Harmonic Filters[J]. IEEE Trans. Power Electron.,2009,24(1):437–444,.
[152]曾华,吴耀华.基于进化停滞周期的局部变异PSO算法及其收敛性分析[J].控制与决策,2010,25(9):1333-1337.
[153]Gandomi A.H.,Yun G.J., Yang X.S.Chaos-Enhanced Accelerated Particle SwarmOptimization J].Commun Nonlinear Sci Numer Simulat,2013(18):327–340.
[154]Ahmad N, Mohammad M E, Reza S. A Novel Particle Swarm Optimization Algorithmwith Ddaptive Inertia Weight[J]. Applied Soft Computing,2011(11):3658–3670.
[155]潘峰,周倩,李位星,高琪.标准粒子群优化算法的马尔科夫链分析[J].自动化学报,2012,38(11):1-9.
[156]高尚,杨靖宇.群智能算法及其应用[M].北京：中国水利水电出版社,2007.
[157] Leon L.M,Peng F.Z.,Cunnyngham T. Charge Balance Control Schemes for CascadeMultilevel Converter in Hybrid Electric Vehicles[J]. IEEE Trans. Indus Electron,2002,49(5):1058-1064.
[158] Casadei D.， Grandi G.， Lega A.，et al．Power Balancing of AMultilevel Converterwith Two Insulated Supplies for Three-Phase Six-Wire Loads[C]．PEA2005，2005:1~10
[159] Oleschuk V., Bojoi R., Griva G.,et al.Dual Inverter-Fed Traction Drive with DC SourcesPower Balancing Based on Synchronized PWM[C].IEMDC,2007:260~265
[160] Lezana P., Rodríguez J., Diego A. Oyarzún.Cascaded Multilevel Inverter WithRegeneration Capability and Reduced Number of Switches[J]. IEEE Trans. Ind.Electron,2008,55(3):1059-1066.
[161] Tolbert L M,Peng F Z, Thomas G. H. Multilevel PWM Methods at Low ModulationIndices[J]. IEEE Trans. Power Electron.,2000,l5(4):719-725.
[162]单庆晓，潘孟春,李圣怡,等.一种新型的级联型逆变器PWM信号随机分配方法研究[J].中国电机工程学报,2004,24(2):156-160
[163] Fukuta Y, Venkataramanan G. DC Bus Ripple Minimization in Cascaded H-bridgeMultilevel Converters under Staircase Modulation[J]. IEEE IAS2002:1988-1993.
[164]孙宜峰,阮新波.级联型多电平逆变器的功率均衡控制策略[J].中国电机工程学报,2006,26(4):126-133.
[165]王学华,阮新波,王蓓蓓,等.阶梯波合成级联型多电平逆变器功率均衡策略[J].中国电机工程学报,2008,28(30):12-19.
[166]IEEE Standard.IEEE Recommended Practices and Requirements for Harmonic Controlin Electrical Power Systems[S]. IEEE Standard519-1992.
[167] Pontt J., Rodríguez J., Huerta R. Mitigation of Noneliminated Harmonics of SHEPWMThree-level Multipulse Three-phase Active Front End Converters with Low SwitchingFrequency for Meeting Sandard IEEE-519-92[J]. IEEE Trans. Power Electron.,2004,19(6):1594-1600.
[168]中国国家标准化管理委员会. GB/T24337-2009电能质量公用电网间谐波[S].北京:北京科文图书业信息技术有限公司,2009.
[169]齐悦,杨耕,窦曰轩,等.PWM控制下多电平混合逆变电路的脉宽调制及拓扑分析[J].电工技术学报,2003,18(4):13-17.
[170]饶建业,李永东.一种混合级联型多电平逆变器拓扑结构[J].电工技术学报,2009,24(3):104-109.
[171]单庆晓,潘孟春,李圣怡.多重逆变器的新型差补PWM技术[J].电力电子技术,2002,36(6):67-69.
[172]王兆安,刘进军.电力电子技术(第5版)[M].北京:机械工业出版社,2009,5.
[173]丁凯，邹云屏,吴智超,等．新型三相混合不对称九电平逆变器研究[J]．中国电机工程学报，2005,25(11):35-41．
[174]Song Q., Liu W., Yuan Z. Multilevel Optimal Modulation and Dynamic ControlStrategies for Statcoms using Cascaded Multilevel Inverters[J].IEEE Trans. Power Del.,2007,22(3):1937–1946.
[175] McGrath B., Holmes D., Meynard T. Reduced PWM Harmonic Distortion forMultilevel Inverters Operating over a Wide Modulation Range[J]. IEEE Trans. PowerElectron.,2006,21(4):941–949.
[176]陈远，张慧，秦亮，刘开培.选择性谐波控制的通用优化多电平PWM方法[J].大功率变频技术,2009(4):10-13.
[177]费万民,张艳莉,阮新波,等.三电平逆变器SHEPWM非线性方程组的求解[J].中国电机工程学报,2008,28(6):62-68.
[178]费万民,阮新波,张艳莉,等.多电平逆变器SHEPWM方法的初值问题研究[J].中国电机工程学报,2007,27(13):87-92．
[179] Jabr R.A. Solution Trajectories of the Harmonic-Elimination Problem[J]. IEEProc.-Electr. PowerAppl.,2006,153(1):97-104.
[180]费万民,张艳莉,都小利.五电平逆变器特定谐波消除脉宽调制方法[J].电工技术学报,2009,24(2):85-93.
[181]薄保中,刘卫国,罗兵,等.三电平逆变器窄脉冲补偿方法研究[J].电力自动化设备,2004,24(8):25-28.
[182]张文义,游文虎,徐会明,等.特定消谐式逆变器中窄脉冲的优化策略[J].电力系统自动化,2006,30(6):53-57.
[183]Victor M. E., V. Fern o P., J. Fernando A. Silva. Narrow Pulse Elimination PWM forMultilevel Digital Audio Power Amplifiers Using Two Cascaded H-Bridges as aNine-Level Converter[J]. IEEE Trans. Power Electron.,2007,22(2):425-434.
[184]袁亚湘,孙文瑜.最优化理论与方法[M].北京：科学出版社,1997.
[185]袁亚湘.非线性优化计算方法[M].北京：科学出版社,2008.
[186]Kennedy J, Eberhart R. Particle Swarm Optimization[C]. in Proc. IEEE Int. Conf.Neural Netw.,1995,4:1942–1948.
[187]Clerc M, Kennedy J. The Particle Swarm: explosion, Stability, and Convergence in aMultidimensional Complex Space[J]. IEEE Trans Evol Comput,2002(6):58–73.
[188]Ray R.N., Chatterjee D., Goswami S.K. Harmonics Elimination in a Multilevel Inverterusing the Particle Swarm Optimisation technique[J]. IET Power Electron.,2009,2(6):646–652.
[189]Lezana P., Rodríguez J., A. Oyarzún D. Cascaded Multilevel Inverter With RegenerationCapability and Reduced Number of Switches[J]. IEEE Trans. Ind. Electron,2008,55(3):1059-1066。
[190]Rodríguez J.,Moran P. J,et al. High-voltage Multilevel Converter with RegenerationCapability[J]. IEEE Trans. Ind. Electron,2002,49(4):839-846.
[191]Ghoreishy H., Varjani A.Y., Farhangi S.Hybrid Cascaded H-bridge Inverter with EvenPower Distribution and Improved Total Harmonic Distortion[J]. IET Power Electron.,2012,5(8):1245–1253.
[192]张云.非对称混合多电平逆变器调制策略及功率均衡控制研究[D].哈尔滨：哈尔滨工业大学,2010.
[193]王学华,阮新波,王蓓蓓,等.阶梯波合成II型混合级联多电平逆变器的功率均衡策略[J].电工技术学报,2009,24(2):78-84.
[194] Pande M., Jin H., Joos G. Modulated Integral Control Technique for CompensatingSwitch Delays and Nonideal DC Buses in Voltage-source Inverters[J]. IEEE Trans. Ind.Electron,1997,44(2):182-190.
[195] Klima J., Chomat M., Schreier L. Analytical Closed-form Investigation of PwmInverter Induction Motor Drive Performance under Dc Bus Voltage Pulsation[J]. IETElectr. Power Appl.,2008,2(6):341–352.
[196]王正,新平.逆变电源母线电容纹波电流与容值优化研究[J].电源学报,2004,(4):86-89.
[197]Samir K., Pablo L., Mauricio A., et al.Multicarrier PWM With DC-Link RippleFeedforward Compensation for Multilevel Inverters [J]. IEEE Trans. Power Electron.,2008,23(1):52-59.
[198]王志冰,于坤山,周孝信.H桥级联多电平变流器的直流母线电压平衡控制策略[J].中国电机工程学报,2012,32(6):56-63.
[199]Hua C.C., Wu C.W., Chuang C.W.A Novel Dc Voltage Charge Balance Control forCascaded Inverters[J]. IET Power Electron.,2009,2(2):147–155
[200]李武华.三绕组耦合电感实现高增益、高效率交错并联软开关Boost变流器[D].杭州：浙江大学,2008.
[201]王成山，李霞林，郭力.基于功率平衡及时滞补偿相结合的双级式变流器协调控制[J].中国电机工程学报,2012,32(25):109-117.
[202]David M., Frede B., O′scar G. Review and Comparison of Step-Up TransformerlessTopologies for Photovoltaic AC-Module Application[J]. IEEE Trans. PowerElectron.,2013,28(6):2649-2663.
[203]张旭辉，温旭辉，赵峰.电机控制器直流侧前置双向Buck/Boost变换器的直接功率控制策略研究[J].中国电机工程学报,2012,32(33):15-22.
[204] Lai J.S., Nelson.D. J. Energy Management Power Converters in Hybrid Electric andFuel Cell Vehicles[C]. Proceedings of the IEEE,2007,95(4):766-777.
[205]Kotsopoulos A., Duarte J.L., Hendrix M.A.M. A Predictive Control Scheme for DCVoltage and AC Current in Grid-connected Photovoltaic Inverters with Minimum DCLink Capacitance[C]. IEEE IECON,2001,1994-1999.
[206]Fang X., Qian Z., Peng F. Z. Single-phase Z-source PWM AC-AC converters[J]. IEEEPower Electron. Lett.,2005,3(4):121-124.
[207]陈元娣,钱亮,朱忠尼,等.带Z源的高频环节AC-AC变换器[J].电工技术学报,2011,26(5):88-943.
[208] Cao D., Peng F. Z. A Family of Z-source and Quasi-Z-source DC-DC Converters[C].IEEE APEC,2009:1097-1101.
[209]齐铂金,杜青,张瑾,等.基于Z网络的升降压DC/DC变换器[J].北京航空航天大学学报,2011,37(6):658-663.
[210]Tang Y., Xie S. J., Zhang C. H. Improved Z-source Inverter with Reduced Z-sourceCapacitor Voltage Stress and Soft-start Capability[J]. IEEE Trans. Power Electron.,2009,24,(2):409–415.
[211]Zhou Y., Liu L., Li H.A High-Performance Photovoltaic Module-Integrated Converter(MIC) Based on Cascaded Quasi-Z-Source Inverters (qZSI) Using eGaN FETs[J]. IEEETrans. Power Electron.,2013,28(6):2727–2738.
[212]Shen M., Wang J., Joseph, A., et al. Constant Boost Control of the Z-Source Inverter toMinimize Current Ripple and Voltage Stress[J]. IEEE Trans. Ind. Appl.,2006,42(3):770-778.
[213]周玉斐,黄文新,赵健伍,等.高增益单级升压逆变器的恒定最大增益控制策略[J].电工技术学报,2013,28(1):179-187.
[214]张超华,汤雨,谢少军.改进Z源逆变器的三次谐波注入控制策略[J].电工技术学报,2009,24(11):114-119.
[215]Markus A. Vogelsberger, Thomas Wiesinger, Hans Ertl. Life-Cycle Monitoring andVoltage-Managing Unit for DC-Link Electrolytic Capacitors in PWM Converters[J].IEEE Trans. Power Electron.,2011,26(2):493-503.
[216] Chavarría J., Biel D., Guinjoan F., et al.Energy-Balance Control of PV CascadedMultilevel Grid-Connected Inverters Under Level-Shifted and Phase-Shifted PWMs[J].IEEE Trans. Ind. Electron,2013,60(1):98-111.
[217] Holmes D.G., Lipo T.A.著，周克亮译.电力电子变换器PWM技术原理与实践[M].北京,人民邮电出版社,2010.
[218] Mozaffari S.A., Danyali S., Sharifian M.B., et al. Brushless DC Motor Drives Suppliedby PV Power System based on Z-source Inverter and FL-IC MPPT controller[J].EnergyConversion and Management2011,(52):3043–3059.
[219] Peng F. Z.,Shen M. S.,Qian Z. M．Maximum Boost Control of the Z-source Inverter[J].EEE Trans. Power Electron.,2005,20(4):833-838．
[2] Intemational Energy Ageney. World energy outlook2011[R]. Washington DC: IEA,2011.
[3] Giovanni S., Giovanni P., Samuel V., et al. Renewable Energy Operation and ConversionSchemes： A Summary of Discussions During the Seminar on Renewable EnergySystems[J]. IEEE Ind. Electron. Magazine,2010,4(3):38-51.
[4] Yu X., Starke M. R.,Tolbert L. M., et al. Fuel Cell Power Conditioning for Electric PowerApplications：ASummary[J]. IET Electr. PowerAppl.,2007,1(5):643–656.
[5] Marco L.,Thilo S., John Y. H. Future Energy Systems: Integrating Renewable EnergySources into the Smart Power Grid Through Industrial Electronics[J]. IEEE Ind. Electron.Magazine,2010,4(3):18-37.
[6] Martina C., Agelidis V.G.. Mike M. Multilevel Converters for Single-phase GridConnected Photovoltaic Systems：An Overview[J]. Solar Energy,1999,66(5):325–335.
[7]朱瑛,程明,花为,等.考虑损耗转矩的风力发电系统最大风能跟踪控制[J].中国电机工程学报,2013,33(19):39-46.
[8] Carrasco J. M., Franquelo L.G., Jan T. B.Power-Electronic Systems for the GridIntegration of Renewable Energy Sources: A Survey[J]. IEEE Trans. Ind. Electron.,2006,53(4):1002-1016.
[9] Gu Y.,Li W., Zhao Y.Transformerless Inverter With Virtual DC Bus Concept for Cost-Effective Grid-Connected PV Power Systems[J].IEEE Trans.Power Electron.,2013,28(2):793-805.
[10] Xue Y., Chang L., Kj r S. B. Topologies of Single-phase Inverters for Small DistributedPower Generators:An Overview[J].IEEE Trans. Power Electron.,2004,19(5):1305-1314.
[11]张兴,曹仁贤.太阳能光伏并网发电及其逆变控制[M].北京:机械工业出版社,2011.
[12]刘邦银.建筑集成光伏系统的能量变换与控制技术研究[D].武汉:华中科技大学,2008.
[13] Liao Y.H., Lai C.M. Newly-constructed Single-phase Multistring Multilevel Inverter forFuel-cell Microgrid[C]. IEEE ECCE,2011:1440-1444.
[14]金科.燃料电池供电系统的研究[D].南京:南京航空航天大学,2006.
[15] Patrao I., Emilio F., Fran G,.Transformerless Topologies for Grid-connected Single-phasePhotovoltaic Inverters[J]. Renewable and Sustainable Energy Reviews,2011(15):3423–3431.
[16] Samuel V., Peter Z., Regine M,. Highly Efficient Single-Phase Transformerless Invertersfor Grid-Connected Photovoltaic Systems[J]. IEEE Trans. Ind.Electron.,2010,57(9):3118-3128.
[17] Edris P., Oriol G., Daniel M..Multilevel Converters Control for Renewable EnergyIntegration to the Power Grid [J]. Energy36(2011):950-963.
[18] Zhao Z., Xu M., Chen Q.L,.Derivation, Analysis, and Implementation of a Boost–BuckConverter-Based High-Efficiency PV Inverter[J]. IEEE Trans. Power Electron.,2012,27(3):1304-1313.
[19]肖华锋，谢少军.用于光伏并网的交错型双管Buck-Boost变换器[J].中国电机工程学报,2010,30(21):7-12.
[20]汪海宁,苏建徽,丁明,等.光伏并网功率调节系统[J].中国电机工程学报,2007,27(2)：75-79．
[21]Agorreta J L,Borrega M,Lopez J，et al．Modeling and Control of N-paralleled Grid-connected Inverters with LCL Filter Coupled due to Grid Impedance in PV Plants[J].IEEETrans. Power Electron.,2011,26(3):770-785.
[22]吴红飞,孙凯,邢岩.新能源发电串联分布式高能效变换系统[J].中国电机工程学报,2012,32(33):1-6.
[23] Li Q., Wolfs P.A Review of the Single Phase Photovoltaic Module Integrated ConverterTopologies with Three Different DC Link Configurations[J]． IEEE Trans． PowerElectron.，2008，23(3):1320-1323．
[24] Kim H., Kim J., Kim H. A High Efficiency Photovoltaic Module Integrated Converterwith theAsymmetrical Half-bridge Flyback[J]. Solar Energy,2010(84):1376–1381.
[25] Erickson, J.R. Integrated Photovoltaic Module[P]. United States Patent: US20120042588,Feb.23,2012.
[26]李艳,阮新波,杨东升.无缓冲单元的多输入直流变换器电路拓扑[J].电工技术学报,2009,24(5):73-79.
[27]李艳,阮新波,杨东升.带缓冲单元的多输入直流变换器电路拓扑[J].电工技术学报.2009,24(6):62-68.
[28] Blaabjerg F., Chen Z., Kjaer B. Power Electronics as Efficient Interface in DispersedPower Generation Systems[J]. IEEE Trans. Power Electron.,2004,19(5):1184-1194.
[29] Kouro S., Malinowski M., Gopakumar K. Recent Advances and Industrial Applicationsof Multilevel Converters[J]. IEEE Trans. Ind. Electron.,2010,57(8):2553-2579.
[30]黄立培,马毅为,孙凯.高效级联式光伏并网逆变器的控制[J].高电压技术,2011.37(3):680-686.
[31] Nicola F., Gianpaolo L., Giovanni P. Distributed Maximum Power Point Tracking ofPhotovoltaic Arrays: Novel Approach and System Analysis[J]. IEEE Trans. Ind.Electron.,2008,55(7):2610-2621.
[32]Villanueva E., Correa P., Rodríguez J. Control of a Single-Phase Cascaded H-BridgeMultilevel Inverter for Grid-Connected Photovoltaic Systems[J]. IEEE Trans. Ind.Electron.,2009,56(11):4399-4406.
[33]马琳,孙凯,Remus T.,等.高效率中点钳位型光伏逆变器拓扑比较[J].电工技术学报,2011,26(2):108-114.
[34]张犁，孙凯，冯兰兰，中点钳位非隔离全桥光伏并网逆变器[J].中国电机工程学报,2012,327(18):16-22.
[35]陆晓楠,孙凯,马毅为,等.适用于光伏发电系统的混合级联式逆变器[J].清华大学学报(自然科学版),2011,51(3):351-355.
[36]Walker G. R., Sernia P. C..Cascaded DC-DC Converter Connection of PhotovoltaicModules[J]. IEEE Trans. Power Electron.,2004,19(4):1130–1139.
[37] Jain S.,Agarwal V. An Integrated Hybrid Power Supply for Distributed GenerationApplications Fed by Nonconventional Energy Sources[J]. IEEE Trans. Energy Convers.2008,23(2):622-631.
[38] Rahim N.A., Selvaraj J. Multistring Five-Level Inverter With Novel PWM ControlScheme for PVApplication[J]. IEEE Trans. Ind. Electron.,2010,57(6):2111-2123.
[39] Barbosal P., Steimer P., Steinke J. et al. Active-neutral-point-clamped (ANPC) MultilevelConverter Technology [C].EPE,2005:11-20.
[40]谭国俊,景巍.有源钳位三电平变频器及其结温平衡控制[J].电工技术学报,2012,27(2):97-102.
[41] Roberto P., Nicola B., Alessandro R.,et al. DC bus Voltage Equalization in Single-phaseSplit-capacitor Three-level Neutral-point-clamped Half-bridge Inverters for PVApplications[C]. IEEE APEC,2011:931-938.
[42] Su G.J.,Adams D. J. Multilevel DC Link Inverter for Bbrushless Permanent MmagnetMotors with very low inductance[C]. IEEE IAS,2001:829–834.
[43] Su G.J. Multilevel DC-link Inverter[J]. IEEE Trans. Ind. Appli,2005,41(3):848-854
[44] Ersoy B., Birol A., Sabri C, A Grid-connected Photovoltaic Power Conversion Systemwith Single-phase Multilevel Inverter[J]. Solar Energy,2010(84):2056–2067.
[45]Nabae A, Takashi I, Akagi H. A New Neutral-point Clamped PWM Inverter[J]. IEEETrans. Ind.Appl.,1981, IA-17:518–523.
[46] Meynard T.A.Foch H. Multi-level Conversion: High Voltage Choppers and Voltage-source Inverters[C]. IEEE PESC1992:397-403
[47]Samir K., Malinowski M., Gopakumar K.,et al. Recent Advances and IndustrialApplications of Multilevel Converters [J]. IEEE Trans. Ind. Electron.,2010,57(8):2553-2580.
[48]Adam G.P., Stephen J. F., Ahmed M. M. Capacitor Balance Issues of the Diode-ClampedMultilevel Inverter Operated in a Quasi Two-State Mode[J]. IEEE Trans. Ind. Electron.,2008,55(8):3088-099.
[49]Carlos M., Juan J. N., Domingo B.Energy-Balance Modeling and Discrete Control forSingle-Phase Grid-Connected PV Central Inverters[J]. IEEE Trans. Ind. Electron.,2008,55(7):2734—2743.
[50]Juan D., Luis M.. High-Level Multistep Inverter Optimization Using a Minimum Numberof Power Transistors[J]. IEEE Trans. Power Electron.2006,21(2):330-337.
[51] Zeng F.P., Tan G.H., Wang J.Z. Novel Single-phase Five-level Voltage-source Inverterfor the Shunt Active Power Filter[J]. IET Power Electron.,2010,3(4):480–489.
[52] Domingo A. R., Reynaldo M. R., Samir A. M., Symmetrical Hybrid Multilevel DC–ACConverters With Reduced Number of Insulated DC Supplies[J]. IEEE Trans. Ind.Electron.,2010,57(7):2307-2314.
[53] Ruan X., Li B., Chen Q.Three-level Converters: A New Approach for High Voltage andHigh Power DC–to–DC Conversion[C].IEEE PESC,2002:663–668.
[54]阮新波.三电平直流变换器及其软开关技术[M].北京:科学出版社,2006.
[55] Babaei E., Farhadi M., Mazgar F. N.Symmetric and Asymmetric Multilevel InverterTopologies with Reduced Switching Devices[J]. Electric Power Systems Research,2012(86):122–130.
[56] Farhadi M.,Babaei E. A Generalized Cascaded Multilevel Inverter Using SeriesConnection of Submultilevel Inverters[J]. IEEE Trans. Power Electron.,2013,28(2):625–636.
[57] Babaei E. A Cascade Multilevel Converter Topology With Reduced Number of Switches[J]. IEEE Trans. Power Electron.,2008,23(6):2657-2664.
[58] Youhei H. Hirotaka K.. A Single-Phase Multilevel Inverter Using SwitchedSeries-Parallel DC Voltage Sources[J]. IEEE Trans. Ind. Electron.,2010,57(8):2643–2650.
[59] Ramkumar S., Kamaraj V.,Thamizharasan S. A New Sseries Parallel Switched MultilevelDc-link Inverter Topology[J]. Electrical Power and Energy Systems,2012,36,pp93–99.
[60] Youhei H., Hirotaka K..A Switched-Capacitor Inverter Using Series-Parallel ConversionWith Inductive Load[J]. IEEE Trans. Ind. Electron.,2012,59(2):878-887.
[61]侯李祥,吕跃刚.新型级联多电平逆变器[J].大功率变流技术,2009,(3):20-23.
[62] Abdalla I., Corda J., Zhang L.Multilevel DC-Link Inverter and Control Algorithm toOvercome the PV Partial Shading[J]. IEEE Trans. Power Electron,2013,28(1):14-18.
[63]刘凤君.环保节能型H桥及SPWM直流电源式逆变器[M].北京:电子工业出版社,2010.
[64] Peng F. Z. Z-source Inverter[C]. IEEE IAS,2002:775–781.
[65]彭方正,房绪鹏,顾斌,等. Z源变换器[J].电工技术学报,2004,19(2):47-51.
[66] Shen, M., Joseph, A., Wang, J., Peng, F.Z., Adams, D.J Comparison of TraditionalInverters and Z-source Inverter for Fuel Cell Vehicles[J]. IEEE Trans. Power Electron.,2007,22(4):1453–1463.
[67] Hanif M., Basu M., Gaughan K..Understanding the Operation of a Z-source Inverter forPhotovoltaic Cpplication with a Design Example[J]. IET Power Electron.,2011,4(3):278–287.
[68]汤雨.Z源逆变器研究[D].南京航空航天大学,2006.
[69]刘鸿鹏.基于Z源网络的光伏并网逆变系统的研究[D].哈尔滨工业大学,2011.
[70] Loh P. C., Flaabjerg B., Feng, S. Y., et al. Pulse-width Modulated Z-sourceNeutral-point-clamped Inverter[C]. IEEE APEC,2006, pp.431–437.
[71] Gao F. Loh,P.C., Blaabjerg F. Five-level Z-source Diode-clamped Inverter[J]. IET PowerElectron.,2010,3(4):500–510.
[72] Zhou Y.,Liu L., Li H., et al. A High Performance Photovoltaic Module-IntegratedConverter (MIC) Based on Cascaded Quasi-Z-Source Inverters (qZSI) using eGaN FETs[J]. IEEE Trans. Power Electron.,2013,28(6):2727-2738.
[73] Banaei M.R., Dehghanzadeh A.R., Salary E.. Z-source-based Multilevel Inverter withReduction of Switches[J]. IET Power Electron.,2012,5(3):385–392.
[74] Nguyen M.K., Lim Y.C., Park S.J. Improved Trans-Z-Source Inverter With ContinuousInput Current and Boost Inversion Capability[J]. IEEE Trans. Power Electron.,2013,28(10):4500-4510.
[75] Banaei M. R., Salary E. Verification of New Family for Cascade Multilevel Inverterswith Reduction of Components[J]. Journal of Electrical Engineering&Technology,2011,6(2):245-254.
[76]曾繁鹏,纪延超,王建赜.新型单相五电平电压源逆变器[J].电机与控制学报,2008,12(3):300-303
[77] Patel H. S., Hoft R. G.. Generalized Techniques of Harmonic Elimination and VoltageControl in Thyristor Inverters，Part I：Harmonic Elimination[J]. IEEE Trans. Ind. Appl.,1973,9(3):310–317..
[78]Li L.，Czarkowski D，Liu Y.，et a1. Multilevel Selective Harmonic Elimination PWMTechnique in Series-connected Voltage Inverter[J]． IEEE Trans. Ind. Appl,2000,36(1):160-170．
[79] Agelidis V. G., Balouktsis A., Dahidah M. S. A. A Five-level Symmetrically DefinedSelective Harmonic Elimination PWM Strategy: Analysis and ExperimentalValidation[J]. IEEE Trans. Power Electron.,2000,23(1):19–26.
[80]费万民，阮新波，张艳莉，居荣.多电平逆变器特定谐波消除脉宽调制方法的初值问题研究[J].中国电机工程学报,2007,27(13):87-92.
[81] Fei W.,. Ruan X., Wu B. A Generalized Formulation of Quarter-wave SymmetrySHE-PWM Problems for Multilevel Inverters[J].IEEE Trans. Power Electron.,2009,24(7):1758–1766.
[82] Franz C., Hans E.. Efficiency Optimal Control for AC Drives with PWM Inverters[J]．IEEE Trans. Ind. Appl,1985,21(4):987-1000.
[83] Holtz J. Pulsewidth Modulation: a Survey[J]. IEEE Trans. Ind. Electron.,1992,39(5):410-420.
[84]张慧,刘开培, M. Braun,等.新型优化脉冲宽度调制方法在大功率逆变器的应用研究[J].电工技术学报,2006,21(6):17-22.
[85] Sun J., Beineke S., Grotstollen H. Optimal PWM based on Real-time Solution ofHarmonic Elimination Equations [J].IEEE Trans on Power Electron.,1996,11(4):612-621.
[86] Enjeti P. N., Ziogas P. D., Lindsay J. F. Programmed PWM techniques to eliminateharmonics:A critical evaluation[J].IEEE Trans.Ind. Applicat.,1990,26(2):302–316.
[87] Agelidis V. G., Balouktsis A., Cossar C.,et al.Five-level Selective Harmonic EliminationPWM Strategies and Multicarrier Phase-shifted Sinusoidal PWM: A Comparison[C].IEEE PESC,2005:1685–1691.
[88] Pontt J., Rodriguez J., Huerta R., et al. Mitigation of Noneliminated Harmonics ofSHEPWM Three-level Multipulse Three-phase Active Front End Converters with lowSwitching Frequency for Meeting Standard IEEE-519-92[C]. IEEE PESC,2003, pp.531–536.
[89]佟为明,陈向阳,程树康,等.变频电源特定消谐技术中非线性方程组解法的研究[J].中国电机工程学报,1998,18(5):357-360.
[90]郭新华,王永兴,赵峰,等.基于SHEPWM的中压大功率牵引永磁同步电机两电平控制[J].电工技术学报,2012,27(11):76-82.
[91]《现代应用数学手册》编委会编.现代应用数学手册:计算与数值分析卷[M].北京:清华大学出版社,2005.
[92] Kelley C.T. Solving Nonlinear Equations with Newton's Method[M]. SIAM,Philadelphia,2003.
[93]黄宇清,谢运祥.逆变器消谐模型求解中矩阵求逆的算法研究[J].华南理工大学学报(自然科学版),2003,3l(1l):1-4.
[94] Huang H., Hu S., Czarkowski D. Solving the I11-conditioned Polynomial for theOptimal PWM[C]. IEEE CHQP,2004:555–558.
[95]黄象鼎,曾钟钢,马亚南.非线性数值分析的理论与方法[M].武汉:武汉大学出版社,2004.
[96]Kujan,P. Numerical Iterative Methods Solving Three-phase Multilevel VoltageConverter[C]. IEEE CACSD,2010:1801–1806.
[97] Enjeti P. N.， Lindsay J. F. Solving Nonlinear Equations of Harmonic Elimination PWMin Power Control[J]. Electron. Lett.,1987,23(12):656–657.
[98]陈新,谢少军.用开关点预置SHEPWM控制方案实现变换器调压[J].电力电子技术,2000,34(4):19-21.
[99]刘文华,宋强,陈远华,等.NPC逆变器SHE-PWM开关角度的计算方法研究[J].中国电机工程学报,2002,22(11):31-34.
[100]Zhang Y.C., Zhao Z.M., Zhu J. A Hybrid PWM Applied to High-Power Three-LevelInverter-Fed Induction-Motor Drives[J].IEEE Trans. Ind. Electron.,2011,58(8):3409-3420.
[101]王榕生,吴汉光.消谐法SHEPWM的谐波影响数值分析[J].电工技术学报,2011,26(9):183-189.
[102] Sun J., Grotstollen H. Solving Nonlinear Equations for Selective Harmonic EliminatedPWM using Predicted Initial Values[C].IEEE IECON,1992, vol.1:259–264.
[103] Chiasson J. N., Tolbert L. M., McKenzie K. J.，et a1．A Complete Solution to theHarmonic Elimination Problem[J].IEEE Trans. Power Electron.,2004,19(2):491-499.
[104] Vassilios G., Anastasios B., Ioannis B., et a1.Multiple Sets of Solutions for HarmonicElimination PWM Bipolar Waveforms: Analysis and Experimental Verification[J]. IEEETrans. Power Electron.,2006,21(2):415-421.
[105] Agelidis V., Balouktsis A., Cossar C.. On Attaining the Multiple Solutions of SelectiveHarmonic Elimination PWM Three-level Waveforms Through Function Minimization[J].IEEE Trans. Ind. Electron.,2008,55(3):996–1004.
[106]张永昌,赵争鸣,张颖超.三电平逆变器SHEPWM多组解特性比较及实验[J].电工技术学报,2007,22(3):60-65.
[107]费万民，张艳莉,王学华,等.多电平逆变器SHEPWM问题解的包含关系[J].中国电机工程学报,2008,28(15):61-66.
[108] Konstantinou G.S. Dahidah,M.S.A., Agelidis V.G.. Solution Trajectories for SelectiveHarmonic Elimination Pulse-width Modulation for Seven-level Waveforms: Analysisand Implementation[J].IET Power Electron.,2012,5(1):22–30.
[109] Suresh A.Y., Panda K. Research on a Cascaded Multilevel Inverter by EmployingThree-phase Transformers[J].IET Power Electron.,2012,5(5):561–570.
[110] Asumadu J. A., Hoft R. G. Microprocessor-based Sinusoidal Waveform Synthesis usingWalsh and Related Orthogonal Functions[J]. IEEE Trans. Power Electron.,1989,4(2):234–241.
[111]单庆晓，潘孟春，唐莺.基于沃尔什变换的多电平谐波消除技术[J].电力电子技术,2004,38(4):32-34.
[112]郑春芳，张波，丘东元.基于沃尔什函数的逆变器选择性谐波消除技术开关角的快速求解[J].中国电机工程学报,2005,25(22):38-44.
[113]秦亮,刘开培,张慧.基于Walsh变换的PWM优化脉冲调制方法[J].电工技术学报,2007,22(4):118-123.
[114]都小利,费万民.多电平逆变器半周期对称SHEPWM方法[J].电工技术学报,2010,25(4):95-102.
[115] Sun J., Grotstollen H. Pulsewidth Modulation Based on Real-time Solution of AlgebraicHarmonic Elimination Equations[C].IEEE IECON,1994., vol.1:79–84.
[116] Kato T..Sequential Homotopy-based Computation of Multiple Solutions for SelectedHarmonic Elimination in PWM Inverters[J].IEEE Trans. Circuits and SystemsI:Fundamental Theory and Applications,1999,46(5):586–593.
[117]李治典,周秦英,李宏,等.实时求解特定消谐方程组的新算法[J].西北工业大学学报,2004,22(1):37-40.
[118]谢运祥.逆变器消谐控制的同伦模型建立及算法分析[J].中国电机工程学报，2002，22(5):27-31.
[119] Chiasson J. N., Tolbert L. M., Kenzie M. K., et al. Elimination of Harmonics in aMultilevel Converter Using the Theory of Symmetric Polynomials and Resultants[J].IEEE Trans. Control Systems Technology,2005,13(2):216-223.
[120]郑春芳，张波.吴方法在电力电子逆变器消谐技术中的应用[J].中国电机工程学报，2005,25(15):40-45.
[121] Bowes S.R., Grewal S., Holliday D.Single-phase Three-level Regular-sampledSelective Harmonic Elimination PWM[J]. IEE Proc. Electr.Power Appl.,2001,148(2):155–161.
[122]周熙炜,刘卫国.空间电压矢量合成的新型选择谐波消去技术[J].中国电机工程学报，2009,29(30):35-41.
[123] Maswood, A.I., Liu, J. Optimal Online Algorithm Derivation for PWM-SHESwitching[J]. Electron. Lett.,1998,34(8):821-823.
[124]刘红兵,刘辉,智泽英.基于曲线拟合技术的最优PWM开关角在线计算[J].电力电子技术,2009,43(11):82-84.
[125]王琛琛,李瑞夫,周明磊.基于TMS320F28335的SHEPWM数字实现[J].北京交通大学学报,2011,35(5):89-93.
[126] Ahmadi D., Zou K., Li C., et al. A Universal Selective Harmonic Elimination Methodfor High-Power Inverters[J]. IEEE Trans. Power Electron.,2011,26(10):2743-2752.
[127]朱思国,陆佳政,欧阳红林,等.基于谐波注入法的级联型逆变器谐波消除研究[J].电工技术学报,2012,27(8):194-202.
[128] Martinez C., Lazaro A., Quesada I.，et a1．THD Minimization for Railway ApplicationsThrough Harmonic Spectrum Optimization. IEEE,2012:609-1614.
[129] Ghazanfari A., Mokhtari H.,. Firouzi M. Simple Voltage Balancing Approach for CHBMultilevel Inverters Considering Low Harmonic Content Based on a Hybrid OptimalModulation Strategy[J]. IEEE Trans. Power Del.,2012,27(4):1937–1946.
[130]汪定伟,王俊伟,王洪峰,等.智能优化方法[M].北京：高等教育出版社,2007.
[131]李士勇.智能优化算法原理与应用[M].哈尔滨:哈尔滨工业大学出版社,2012.
[132] Bonabeau E., Dorigo M., Theraulaz G. Swarm Intelligence: From Natural to ArtificialSystems. Oxford University Press,1999.
[133] Clerc M., Kennedy J.The Particle Swarm: Explosion, Stability and Convergence in aMulti-dimensional Complex Space[J].IEEE Trans. Evol.Comput.,1998,2(3):91–96.
[134] Mohaddes M., Gole A. M., McLaren P.G. A Neural Network Controlled OptimalPulse-width Modulated STATCOM[J]. IEEE Trans. Power Delivery,1999,14(2):481-488.
[135]李春燕,陈新,沈忠亭,等.最优PWM开关角的在线计算[J].南京航空航天大学学报.2005,37(1):40-43．
[136] Shi K L,Hui Li. Optimized PWM Strategy based on Genetic Algorithms[J]. IEEE Trans.Ind. Electron.,2005,52(5):1458-1461.
[137]周尔民.遗传算法应用于多电平最优化阶梯波技术[J].高压电技术,2007,33(5):172-175.
[138]王群京,胡存刚,李国丽.基于遗传算法的三电平逆变器SHEPWM方法的研究[J].中国科学技术大学学报,2009,39(8):848-852.
[139] Sundareswaran K., Jayant K., Shanavas T. N. Inverter Harmonic Elimination Through aColony of Continuously Exploring Ants[J]. IEEE Trans. Ind. Electron.,2007,54(5):2558-2565.
[140]胡存刚，王群京，李国丽,等.一种新的SHEPWM三电平逆变系统的仿真和实验研究[J].系统仿真学报,2008,20(16):4425-4428.
[141] Taghizadeh H., Tarafdar H. M. Harmonic Elimination of Cascade Multilevel Inverterswith Nonequal DC Sources Using Particle Swarm Optimization[J]. IEEE Trans. Ind.Electron,2010,57(11):3678-3684.
[142] Ray R. N., Goswami S. K. An Application of PSO Technique for Harmonic Eliminationin a PWM Inverter[J].Applied Soft Computing,2009,9(4):1315-1320
[143]娄慧波,毛承雄,陆继明,等.基于微粒群算法的三电平正弦脉冲宽度调制开关时刻优化[J].中国电机工程学报,2007,27(33):108-112.
[144]王凌,刘波.微粒群优化与调度算法[M].北京：清华大学出版社,2008.
[145]恩格尔伯里特,著,谭营,译.计算群体智能基础[M].北京：清华大学出版社,2009.
[146] Barkati S., Baghli L., Berkoukc E. M.Harmonic Elimination in Diode-clampedMultilevel Inverter using Evolutionary Algorithms[J]. Electric Power Systems Research,2008(78):1736–746.
[147] Debnath S., Ray R.. N. Harmonic Elimination in Multilevel Inverter using GA andPSO:AComparison[C]. IEEE SCEECS.2012:1-5.
[148] Shi Y., Eberhart R. C. A Modified Particle Swarm Optimizer[C]. Proc of the IEEE IntConf on Evolutionary Computation. Piscataway: IEEE Press,1998:69-73.
[149] Ratnaweera A., Halgamuge S. K. Watson H C. Self-organizing Hierarchical ParticleSwarm Optimizer with Time-varying Acceleration Coefficients[J].IEEE Trans. Evol.Comput.,2004,8(3):240–255.
[150]Chatterjee A., Siarry P. Nonlinear Inertia Weight Variation for Dynamic Adaptation inParticle Swarm Optimization[J].Computers and Operations Research,2006,33(3):859-871.
[151]Ko C., Chang Y., Wu C.A PSO Method With Nonlinear Time-Varying Evolution forOptimal Design of Harmonic Filters[J]. IEEE Trans. Power Electron.,2009,24(1):437–444,.
[152]曾华,吴耀华.基于进化停滞周期的局部变异PSO算法及其收敛性分析[J].控制与决策,2010,25(9):1333-1337.
[153]Gandomi A.H.,Yun G.J., Yang X.S.Chaos-Enhanced Accelerated Particle SwarmOptimization J].Commun Nonlinear Sci Numer Simulat,2013(18):327–340.
[154]Ahmad N, Mohammad M E, Reza S. A Novel Particle Swarm Optimization Algorithmwith Ddaptive Inertia Weight[J]. Applied Soft Computing,2011(11):3658–3670.
[155]潘峰,周倩,李位星,高琪.标准粒子群优化算法的马尔科夫链分析[J].自动化学报,2012,38(11):1-9.
[156]高尚,杨靖宇.群智能算法及其应用[M].北京：中国水利水电出版社,2007.
[157] Leon L.M,Peng F.Z.,Cunnyngham T. Charge Balance Control Schemes for CascadeMultilevel Converter in Hybrid Electric Vehicles[J]. IEEE Trans. Indus Electron,2002,49(5):1058-1064.
[158] Casadei D.， Grandi G.， Lega A.，et al．Power Balancing of AMultilevel Converterwith Two Insulated Supplies for Three-Phase Six-Wire Loads[C]．PEA2005，2005:1~10
[159] Oleschuk V., Bojoi R., Griva G.,et al.Dual Inverter-Fed Traction Drive with DC SourcesPower Balancing Based on Synchronized PWM[C].IEMDC,2007:260~265
[160] Lezana P., Rodríguez J., Diego A. Oyarzún.Cascaded Multilevel Inverter WithRegeneration Capability and Reduced Number of Switches[J]. IEEE Trans. Ind.Electron,2008,55(3):1059-1066.
[161] Tolbert L M,Peng F Z, Thomas G. H. Multilevel PWM Methods at Low ModulationIndices[J]. IEEE Trans. Power Electron.,2000,l5(4):719-725.
[162]单庆晓，潘孟春,李圣怡,等.一种新型的级联型逆变器PWM信号随机分配方法研究[J].中国电机工程学报,2004,24(2):156-160
[163] Fukuta Y, Venkataramanan G. DC Bus Ripple Minimization in Cascaded H-bridgeMultilevel Converters under Staircase Modulation[J]. IEEE IAS2002:1988-1993.
[164]孙宜峰,阮新波.级联型多电平逆变器的功率均衡控制策略[J].中国电机工程学报,2006,26(4):126-133.
[165]王学华,阮新波,王蓓蓓,等.阶梯波合成级联型多电平逆变器功率均衡策略[J].中国电机工程学报,2008,28(30):12-19.
[166]IEEE Standard.IEEE Recommended Practices and Requirements for Harmonic Controlin Electrical Power Systems[S]. IEEE Standard519-1992.
[167] Pontt J., Rodríguez J., Huerta R. Mitigation of Noneliminated Harmonics of SHEPWMThree-level Multipulse Three-phase Active Front End Converters with Low SwitchingFrequency for Meeting Sandard IEEE-519-92[J]. IEEE Trans. Power Electron.,2004,19(6):1594-1600.
[168]中国国家标准化管理委员会. GB/T24337-2009电能质量公用电网间谐波[S].北京:北京科文图书业信息技术有限公司,2009.
[169]齐悦,杨耕,窦曰轩,等.PWM控制下多电平混合逆变电路的脉宽调制及拓扑分析[J].电工技术学报,2003,18(4):13-17.
[170]饶建业,李永东.一种混合级联型多电平逆变器拓扑结构[J].电工技术学报,2009,24(3):104-109.
[171]单庆晓,潘孟春,李圣怡.多重逆变器的新型差补PWM技术[J].电力电子技术,2002,36(6):67-69.
[172]王兆安,刘进军.电力电子技术(第5版)[M].北京:机械工业出版社,2009,5.
[173]丁凯，邹云屏,吴智超,等．新型三相混合不对称九电平逆变器研究[J]．中国电机工程学报，2005,25(11):35-41．
[174]Song Q., Liu W., Yuan Z. Multilevel Optimal Modulation and Dynamic ControlStrategies for Statcoms using Cascaded Multilevel Inverters[J].IEEE Trans. Power Del.,2007,22(3):1937–1946.
[175] McGrath B., Holmes D., Meynard T. Reduced PWM Harmonic Distortion forMultilevel Inverters Operating over a Wide Modulation Range[J]. IEEE Trans. PowerElectron.,2006,21(4):941–949.
[176]陈远，张慧，秦亮，刘开培.选择性谐波控制的通用优化多电平PWM方法[J].大功率变频技术,2009(4):10-13.
[177]费万民,张艳莉,阮新波,等.三电平逆变器SHEPWM非线性方程组的求解[J].中国电机工程学报,2008,28(6):62-68.
[178]费万民,阮新波,张艳莉,等.多电平逆变器SHEPWM方法的初值问题研究[J].中国电机工程学报,2007,27(13):87-92．
[179] Jabr R.A. Solution Trajectories of the Harmonic-Elimination Problem[J]. IEEProc.-Electr. PowerAppl.,2006,153(1):97-104.
[180]费万民,张艳莉,都小利.五电平逆变器特定谐波消除脉宽调制方法[J].电工技术学报,2009,24(2):85-93.
[181]薄保中,刘卫国,罗兵,等.三电平逆变器窄脉冲补偿方法研究[J].电力自动化设备,2004,24(8):25-28.
[182]张文义,游文虎,徐会明,等.特定消谐式逆变器中窄脉冲的优化策略[J].电力系统自动化,2006,30(6):53-57.
[183]Victor M. E., V. Fern o P., J. Fernando A. Silva. Narrow Pulse Elimination PWM forMultilevel Digital Audio Power Amplifiers Using Two Cascaded H-Bridges as aNine-Level Converter[J]. IEEE Trans. Power Electron.,2007,22(2):425-434.
[184]袁亚湘,孙文瑜.最优化理论与方法[M].北京：科学出版社,1997.
[185]袁亚湘.非线性优化计算方法[M].北京：科学出版社,2008.
[186]Kennedy J, Eberhart R. Particle Swarm Optimization[C]. in Proc. IEEE Int. Conf.Neural Netw.,1995,4:1942–1948.
[187]Clerc M, Kennedy J. The Particle Swarm: explosion, Stability, and Convergence in aMultidimensional Complex Space[J]. IEEE Trans Evol Comput,2002(6):58–73.
[188]Ray R.N., Chatterjee D., Goswami S.K. Harmonics Elimination in a Multilevel Inverterusing the Particle Swarm Optimisation technique[J]. IET Power Electron.,2009,2(6):646–652.
[189]Lezana P., Rodríguez J., A. Oyarzún D. Cascaded Multilevel Inverter With RegenerationCapability and Reduced Number of Switches[J]. IEEE Trans. Ind. Electron,2008,55(3):1059-1066。
[190]Rodríguez J.,Moran P. J,et al. High-voltage Multilevel Converter with RegenerationCapability[J]. IEEE Trans. Ind. Electron,2002,49(4):839-846.
[191]Ghoreishy H., Varjani A.Y., Farhangi S.Hybrid Cascaded H-bridge Inverter with EvenPower Distribution and Improved Total Harmonic Distortion[J]. IET Power Electron.,2012,5(8):1245–1253.
[192]张云.非对称混合多电平逆变器调制策略及功率均衡控制研究[D].哈尔滨：哈尔滨工业大学,2010.
[193]王学华,阮新波,王蓓蓓,等.阶梯波合成II型混合级联多电平逆变器的功率均衡策略[J].电工技术学报,2009,24(2):78-84.
[194] Pande M., Jin H., Joos G. Modulated Integral Control Technique for CompensatingSwitch Delays and Nonideal DC Buses in Voltage-source Inverters[J]. IEEE Trans. Ind.Electron,1997,44(2):182-190.
[195] Klima J., Chomat M., Schreier L. Analytical Closed-form Investigation of PwmInverter Induction Motor Drive Performance under Dc Bus Voltage Pulsation[J]. IETElectr. Power Appl.,2008,2(6):341–352.
[196]王正,新平.逆变电源母线电容纹波电流与容值优化研究[J].电源学报,2004,(4):86-89.
[197]Samir K., Pablo L., Mauricio A., et al.Multicarrier PWM With DC-Link RippleFeedforward Compensation for Multilevel Inverters [J]. IEEE Trans. Power Electron.,2008,23(1):52-59.
[198]王志冰,于坤山,周孝信.H桥级联多电平变流器的直流母线电压平衡控制策略[J].中国电机工程学报,2012,32(6):56-63.
[199]Hua C.C., Wu C.W., Chuang C.W.A Novel Dc Voltage Charge Balance Control forCascaded Inverters[J]. IET Power Electron.,2009,2(2):147–155
[200]李武华.三绕组耦合电感实现高增益、高效率交错并联软开关Boost变流器[D].杭州：浙江大学,2008.
[201]王成山，李霞林，郭力.基于功率平衡及时滞补偿相结合的双级式变流器协调控制[J].中国电机工程学报,2012,32(25):109-117.
[202]David M., Frede B., O′scar G. Review and Comparison of Step-Up TransformerlessTopologies for Photovoltaic AC-Module Application[J]. IEEE Trans. PowerElectron.,2013,28(6):2649-2663.
[203]张旭辉，温旭辉，赵峰.电机控制器直流侧前置双向Buck/Boost变换器的直接功率控制策略研究[J].中国电机工程学报,2012,32(33):15-22.
[204] Lai J.S., Nelson.D. J. Energy Management Power Converters in Hybrid Electric andFuel Cell Vehicles[C]. Proceedings of the IEEE,2007,95(4):766-777.
[205]Kotsopoulos A., Duarte J.L., Hendrix M.A.M. A Predictive Control Scheme for DCVoltage and AC Current in Grid-connected Photovoltaic Inverters with Minimum DCLink Capacitance[C]. IEEE IECON,2001,1994-1999.
[206]Fang X., Qian Z., Peng F. Z. Single-phase Z-source PWM AC-AC converters[J]. IEEEPower Electron. Lett.,2005,3(4):121-124.
[207]陈元娣,钱亮,朱忠尼,等.带Z源的高频环节AC-AC变换器[J].电工技术学报,2011,26(5):88-943.
[208] Cao D., Peng F. Z. A Family of Z-source and Quasi-Z-source DC-DC Converters[C].IEEE APEC,2009:1097-1101.
[209]齐铂金,杜青,张瑾,等.基于Z网络的升降压DC/DC变换器[J].北京航空航天大学学报,2011,37(6):658-663.
[210]Tang Y., Xie S. J., Zhang C. H. Improved Z-source Inverter with Reduced Z-sourceCapacitor Voltage Stress and Soft-start Capability[J]. IEEE Trans. Power Electron.,2009,24,(2):409–415.
[211]Zhou Y., Liu L., Li H.A High-Performance Photovoltaic Module-Integrated Converter(MIC) Based on Cascaded Quasi-Z-Source Inverters (qZSI) Using eGaN FETs[J]. IEEETrans. Power Electron.,2013,28(6):2727–2738.
[212]Shen M., Wang J., Joseph, A., et al. Constant Boost Control of the Z-Source Inverter toMinimize Current Ripple and Voltage Stress[J]. IEEE Trans. Ind. Appl.,2006,42(3):770-778.
[213]周玉斐,黄文新,赵健伍,等.高增益单级升压逆变器的恒定最大增益控制策略[J].电工技术学报,2013,28(1):179-187.
[214]张超华,汤雨,谢少军.改进Z源逆变器的三次谐波注入控制策略[J].电工技术学报,2009,24(11):114-119.
[215]Markus A. Vogelsberger, Thomas Wiesinger, Hans Ertl. Life-Cycle Monitoring andVoltage-Managing Unit for DC-Link Electrolytic Capacitors in PWM Converters[J].IEEE Trans. Power Electron.,2011,26(2):493-503.
[216] Chavarría J., Biel D., Guinjoan F., et al.Energy-Balance Control of PV CascadedMultilevel Grid-Connected Inverters Under Level-Shifted and Phase-Shifted PWMs[J].IEEE Trans. Ind. Electron,2013,60(1):98-111.
[217] Holmes D.G., Lipo T.A.著，周克亮译.电力电子变换器PWM技术原理与实践[M].北京,人民邮电出版社,2010.
[218] Mozaffari S.A., Danyali S., Sharifian M.B., et al. Brushless DC Motor Drives Suppliedby PV Power System based on Z-source Inverter and FL-IC MPPT controller[J].EnergyConversion and Management2011,(52):3043–3059.
[219] Peng F. Z.,Shen M. S.,Qian Z. M．Maximum Boost Control of the Z-source Inverter[J].EEE Trans. Power Electron.,2005,20(4):833-838．