摘要
数字化技术和并联技术是SPWM逆变器研究和应用的两大热点技术。数字控制SPWM逆变器已成为当今逆变器发展的主流，虽然数字控制相比于模拟控制有诸多的优势，但传统PID方案经数字控制后，效果不如模拟控制。
本文从零阶保持和滞后一拍控制这两个方面来研究：SPWM逆变电源的数字控制对系统性能的影响。为使研究工作有效，先对采样周期的研究范围给予了限定，然后从P闭环控制研究入手，进而对PI控制研究，分别将模拟控制逆变器、数字无滞后一拍控制的逆变器和有滞后一拍控制的逆变器对比进行稳定性分析，由此较为清晰地得出数字化过程对逆变器性能影响的相关结论，为分析和设计逆变器提供了指导：根据系统稳定性条件可提供自然频率ω_n的上限值，作为设计逆变器滤波参数的参考的约束条件；经研究可知，在采样周期T_s＞0．25T_d(T_d为阻尼振荡周期)，存在有滞后一拍控制的系统的稳定范围大于无滞后一拍控制系统的稳定范围的反常现象，因此预测控制的引入并不是对任何采样频率都能够有效地提升逆变器的性能，在采样周期T_s＜0．25T_d，预测控制对逆变器的性能有改善；在采样周期T_s＞0．25T_d，预测控制的加入，反而会使逆变器的性能降低；本文首次揭示了按照数字控制理论大于十倍的系统闭环带宽选取采样频率，存在数字控制逆变电源相对模拟控制性能下降的本质原因。
本文通过时域仿真波形验证了SPWM逆变电源的数字化对系统性能影响的稳定性分析所做的结论。在此基础上，对SPWM逆变电源的数字化对系统稳定性的影响做了频域分析和根轨迹分析。采样周期、阻尼比、自然频率、负载的变化以及滞后一拍控制给系统带来的影响都可以归结为它们对系统频域稳定裕度的影响。采样周期的变化，引起控制对象零、极点位置的变化，从而引起根轨迹的变化。通过频域分析和根轨迹分析，对于逆变器数字P控制、数字PI控制在低采样频率处存在的有滞后一拍控制的系统稳定范围大于无滞后一拍控制的系统稳定范围这一反常现象给予解释：通过频域分析可知，它与逆变器在空载情况下是一个具有谐振峰的弱阻尼二阶系统有关；从根轨迹分析可知，滞后一拍的根轨迹受位于原点的开环极点的影响，随着采样频率的降低，根轨迹越来越靠近单位圆内。
数字化控制使得逆变器系统控制的灵活性提高，并使得高性能的逆变器并联系统实现更为容易。逆变器并联不受功率等级局限而且通过组成并联冗余系统可提高可靠性。分散逻辑并联控制方案为一种独立并联控制方式，通过它可实现真正的冗余并联，本文对并联技术的研究是基于分散逻辑并联控制的PID电压瞬时值控制的逆变电源的环流抑制策略。在传统的功率调节的环流抑制策略的基础上，采用一种简化的功率检测的数字均流控制技术，该控制方案简洁、实用，但同时指出基于功率调节的并联系统环流抑制策略受并机阻抗性质的影响，而且在均流的响应快速性等方面均存在缺陷，为此采用基于瞬时平均电流跟踪的环流抑制策略，并从阻抗分析的角度对其抑制环流的原理进行了研究，但该方案又存在着其均流调节器的调节能力有限等不足，故将基于瞬时平均电流跟踪的抑制环流方案与简化检测的功率调节抑制环流方案二者结合以构成新型的均流控制策略，使均流效果进一步提高。
Digital technology and parallel technology are the two hot technologies of research andapplication on SPWM inverter.Digital SPWM inverter has become the mainstream of thedevelopment of inverter.Though digital control possesses many advantages compared withanalog control,the traditional analog control realized by digital method can not acquiregood effect as the analog control.
This paper focused on the research on the digital effect of SPWM inverter systemperformance from two aspects of zero-order-hold and one-step-delay.Firstly,the samplingperiod was limited to make the research effective,then the analog control inverter systemwas analyzed,and discrete system with no-step-delay control was compared with discretesystem with one-step-delay control in the stability from proportion closed-loop control toproportional-integral control.The clear conclusions were obtained on the effect of thedigital process on inverter performance which can provide guidance to the analysis anddesign of the inverter.Under the condition of system stability,the upper limit of the naturalfrequency ofω_n was used as constraints of the design parameters on the inverter filter.Theabnormal phenomenon is found that one-step-delay control has much wider scope thanno-step-delay control when sampling period,T_s＞0.25T_d.So the introduction of predictivecontrol can not improve the performance of inverter in any sampling frequency.Predictivecontrol can upgrade the performance of inverter when T_s＜0.25T_d while predictive controlcan downgrade the performance of inverter when T_s＞0.25T_d on the contrary.It is first timethat the essential reason was revealed why the performance of digital control inverter wasdegraded compared with analog control inverter even if the sample frequency is ten timesgreater than the closed-loop bandwidth according to the digital control system theory.
In this paper,time domain simulation waveforms were done to verify the conclusionsabout the effect of digital control on the stability of the SPWM inverter system.On thisbasis,the analyses of frequency domain and root locus were carried out,too.The change ofsample period,damping ratio,natural frequency,load,one-step-delay effect on theperformance of digital control inverter can be sum up as the change of stable margin in frequency domain.The zero-pole position changes with sample period,and it results in thechange of root locus.By the analysis of frequency domain and root locus,the uniquephenomenon that the stable range of one-step-delay control system is larger than that ofno-step-delay control system in the low sample frequency no matter whether digital Pcontrol or PI control is adopted is explained.It is relative that no-load inverter is thetwo-order weak damp system with resonant peak by the analysis of frequency domain andthe root locus becomes closer to inner unit circle with sample frequency decreasing for theeffect of pole at origin by the analysis of root locus.
Digital control improves the control flexibility of inverter system and realizes high-performance of inverter parallel system more easily.An effective strategy of parallel controlcan break the restriction of the power grade,and compose the parallel redundant system toenhance the reliability.As an independent parallel control method,distributed parallel logiccontrol strategy can realize redundant parallel in deed.This paper studies the circulatingcurrent restraining strategy of PID instantaneous value control based on distributedlogic-control.A new digital current sharing technology is introduced based on simplifiedpower detection and the experiment results are given.The control scheme is simple andpractical.At the same time,the method based on power regulation to restrain the circulatingcurrent is affected by the character of parallel impedance and the disadvantages such as thelow response speed of sharing current were pointed out.So the circulating currentsuppression strategy based on tracing instant average current is adopted in the paper and theprinciple of restraining the circulating current was researched by analysis of impedance.But this strategy has some disadvantages such as the limited ability of current-sharingregulator,etc.The new strategy is combined with tracking instant average currentfeed-forward control and simplified power detection strategy for improve the effect ofsharing current.
引文
[1]陈坚．电力电子学—电力电子变换和控制技术(第一版)．北京：高等教育出版社，2002
[2]王兆安．黄俊主编电力电子技术 机械工业出版社(第四版)2001．4
[3]沈龙大．电力电子技术及应用的发展状况．基础自动化，1995，2(1)：1～7
[4]钱照明，李崇坚．电力电子——现代科学、工业和国防的重要支撑技术．变流技术与电力牵引：2007，2：1～5，26
[5]Hiromichi Ohashi.Power electronics innovation with next generation advanced power devices.Proceedings of IEEE-INTELEC,2003:9～13
[6]Gourab Majumdar.Future of power semiconductors.Proceedings of IEEE-PESC,2004,1:10～15
[7]钱照明，张军明，吕征宇等．我国电力电子与电力传动面临的挑战与机遇．电工技术学报：2004(19)8：10～22
[8]Chokhawala,R.;Danielsson,B.;Angquist,L.;Power semiconductors in transmission and distribution applications;Power Semiconductor Devices and ICs,2001.ISPSD '01.Proceedings of the 13th International Symposium on;4-7 June 2001:3～10
[9]张凯．基于重复控制原理的CVCF-PWM逆变器波形控制技术研究：[博士学位论文]，华中科技大学，2000．
[10]徐德鸿．21世纪电力电子技术的机遇与挑战．电工技术杂志．2002．10．：1～4
[11]赵贺．电力电子学在电力系统中的应用-灵活交流输电系统．(第一版)．北京：中国电力出版社，2001．38～44．
[12]江哲生．我国电力发展的未来．发电设备：2006(20)1：1～5
[13]Bernet,S.Recent developments of high power converters for industry and traction applications;Power Electronics,IEEE Transactions on;Nov 2000,15 (6):1102～1117
[14]Narain G.Hingorani.High Power Electronics and Flexible AC Transmission System.IEEE Power Engineering Review,1988,3～4
[15]L.Gyugyi.Unified power-flow control concept for flexible AC transmission systems.IEE Proceedings-C,1992,139(4):323～331
[16]L.Gyugyi,T.R.Rietman,and A.Edris et al.The Unified Power Flow Controller:A New Approach to Power Transmission Control.IEEE Trans.Power Delivery,1995,10(2):1085～1097
[17]Kalyan K.Sen,Eric J.Stacy.UPFC—Unified Power Flow Controller:Theory,Modeling,and Applications.IEEE Trans.Power Delivery,1998,13 (4):1453～1460
[18]Hideaki Fujita,Yasuhiro Watanabe,and Hirofumi Akagi.Control and Analysis of a Unified Power Flow Controller.IEEE Trans.Power Electron.,1999,14(6):1021～1027
[19]郑家伟．新能源发电中控制及电力电子技术专题——新能源发电系统中的电力电子变换器．控制理论与应用．2008(25)1：125～132
[20]Bose,B.K.Energy,environment,and advances in power electronics,Power Electronics,IEEE Transactions on,(15)4,July 2000:688 ～ 701
[21]James P Lyons Vlatko Vlatkovic.Power Electronics and Alternative,Energy Generation.In Proceedings of IEEE-PESC2004 (1):16～21.
[22]Lyons,J.P.;Vlatkovic,V.;Power from wind and renewables.Power Electronics and Motion Control Conference,2004.IPEMC 2004.The 4th International,14-16 Aug.2004(1):14～19
[23]徐建中．分布式供电和冷热电联产的前景．节能与环保，2002(3)：10-14
[24]陈静，何湘宁．智能UPS的研究和发展．中国电力，2002，45(3)：77～80
[25]钱照明，张斌，沈宇功．发展可再生能源及变流技术的一些问题， 变流技术与电力牵引，2006，2：13-22
[26]F.A.Huliehel,F.C.Lee,B.H.Cho,et al.A New Design Approach for Distributed Power Systems.Proceeding of the Intersociety Energy Conversion Engineering Conference(IECEC'93):321-323 (1)
[27]P.V.Moll,H.Anderson.Uninterruplible power supplies today.IEEE the 3rd International Conference on Installation Engineering Designing and Maintaining Successful Systems,1988:23～27
[28]D Gali.Control and monitoring of Uninterruplible power system.IEEE the 11th International Telecommunications Energy Conference,INTELEC 89,1989:41～50
[29]洪乃刚．电力电子和电力拖动控制系统的MATLAB仿真．北京：机械工业出版社，2006
[30]Green,M.A.Third generation photovoltaics:comparative evaluation of advanced solar conversion options.Photovoltaic Specialists Conference,2002.Conference Record of the Twenty-Ninth IEEE,19-24 May 2002:1330～1334
[31]Zahedi,A.Solar photovoltaic (PV) energy;latest developments in the building integrated and hybrid PV systems.Renewable Enegry.2006,31:711～718.
[32]M C Chandorkar,DM Divan,R Adapa.Control of parallel connected inverters in stand-alone AC supply systems [C].IEEE-IAS'91,1991,1003～1009
[33]高军．UPS逆变器数字化控制技术的研究：[博士学位论文]．西安：西安交通大学，2002
[34]Zhongyi He,Mingzhu Li ,Yan Xing .Core techniques of digital control for UPS:Industrial Technology,2005.ICIT 2005.IEEE International Conference on 14-17 Dec.2005:546～ 551
[35]Mihalache L.DSP control method of single-phase inverters for UPS applications.IEEE Applied Power Electronics Conference and Exposition,Dallas,TX,USA,2002
[36]彭力．基于状态空间理论的PWM逆变电源控制技术研究：[博士学位论文]．武汉：华中科技大学图书馆，2004
[37]K.P.Gokhale,A.Kawamura,R.G.Hoft,Deadbeat microprocessor control of PWM inverter for sinusoidal output waveform synthesis,IEEE Transactions on Industry Applications,1988,IA-22 (3):901-910
[38]T.Kawabata,T.Miyashita,Y.Yamamoto,Deadbeat control of three phase PWM inverter,IEEE Transactions on Power Electronics,1990,5(1):21-28
[39]Kawamura A.,Chuarayaratip.R.,Haneyoshi T.,Deadbeat control of PWM inverter with modified pulse patterns for uninterruptible power supply,IEEE Transactions on Industrial Electronics,1988,35,(2):295-300
[40]Hua.C.,Two-level switching pattern deadbeat DSP controlled PWM inverter,IEEE Transactions on Power Electronics,1995.10(3):310-317
[41]Tomoki Yokoyama,Atsuo Kawamura,Disturbance observer based fully digital controlled PWM inverter for CVCF operation,IEEE Transactions on Power Electronics,Sep.1994,9 (5)
[42]Ying-Yu Tzou,Rong-Shyang Ou,Shih-Liang Jung,Meng-Yueh Chang.High-performance programmable AC power source with low harmonic distortion using DSP-based repetitive control technique,IEEE Transactions on Power Electronics,July 1997.12,(4):1201-1210
[43]裴雪军，段善旭，康勇等．基于重复控制与瞬时值反馈控制的逆变电源研究．电力电子技术，2002，(20)：12-14．
[44]B.A.Francis,W.M.Wonham,The internal model principle for linear multivariable regulators.Appl.Math.Opt.,1975.2(2):170-194,
[45]Cosner C.,Anwar G.and Tomizuka M.,Plug in repetitive control for industrial robotic manipulators Proceedings of the 1990 IEEE International Conference on Robotics and Automation,May 13-18 1990:1970-1975
[46]Shinji Hara,Yutaka Yamamoto,Stability of repetitive control systems,Proceedings of 24th Conference on Decision and Control,FL,USA,Dec 1985:326-327
[47]Gene F.Franklin,J.David Powell,Abbas Emami-Naeini,Feedback Control of Dynamic Systems,Addison-Wesley Publishing Company,Inc.,1991
[48]K.D.Yong,V.I.Utkin,et al.A control engineer's guide to sliding mode control.IEEE Trans.Control System Technology,1999,7(3):328-342
[49]Wong L.K.,Leung Frank H.E and Tam Peter K.S.,Control of PWM inverter using a discrete-time sliding mode controller,IEEE-PEDS'99,2:947-950
[50]Carpita M.,Farina P.And Tenconi S.,Single phase,sliding mode controlled inverter with three levels output voltage for UPS or power conditioning applications,Proceedings of the 5th European Conference on Power Electronics and Applications,Sep 13-16 1993,4:272-277
[51]Jung Shih-Liang,Tzou Ying-Yu,Discrete sliding-mode control of a PWM inverter for sinusoidal output waveform synthesis with optimal sliding curve ,IEEE Transactions on Power Electronics,Jul 1996,11 (4):567-577
[52]Jezernik K.,Zadravec D.,Sliding mode controller for a single phase inverter ,IEEE-APEC' 90:185-190
[53]Ito,Y.Furuhashi,T.Okuma,S.Uchikawa,Y.:A digital current controller for a PWM inverter using a neural network and its stability,Power Electronics Specialists Conference,1990.PESC '90 Record.,21st Annual IEEE:11-14 June 1990:219-224
[54]B.R.Lin,Neural and fuzzy applications for converter control,ANNIE'95,5:549-555
[55]Tzou Ying-Yu,Ho Lien-Hsun and Ou Rong-Shyang,Fuzzy control of a closed-loop regulated PWM inverter under large load variations,IEEE-IECON'93,1:267-272
[56]B.R.Lin,Hua Chihchiang,Uninterruptible power supply with fuzzy logic approach,IEEE-IECON'93,2:1123-1128
[57]B.R.Lin,Power converter control based on neural and fuzzy methods,Electric Power Systems Research,Dec 1995,35(3):193-206
[58]B.R.Lin,R.G.Hoft,Real-time digital control of PWM inverter with fuzzy logic compensator for nonlinear loads,IEEE-IAS'93,Part 2 (of 3):862-869
[59]PWM inverters with constant modulation frequency [J].IEEETrans.OnInd.Applicat.1990,26(1):88-92.
[60]陈息坤，林新春，康勇等．大功率UPS的并联控制技术．电力电子技术，2002，36(4)：34～36
[61]Ito Y.;Kanno,Y.;Iino,M.;Iyama,O.Digitally controlled parallel redundant UPS.Sanken Technical Report,1996,28(1):22-30
[62]Jiann-Fuh Chen,Ching-Lung Chu.Combination voltage-controlled and current-controlled PWM inverters for UPS parallel operation.IEEE Transactions on Power Electronics.1995,(10):547-558.
[63]JM Guerrero,L G deVicuna,JMatas,et al.A high-performance DSP-controller for parallel operation of online UPS systems.APEC' 2004,2004,463～469
[64]汪东，邓焰，何湘宁．UPS电源系统的并联技术与电池管理．电气应用，2007．23(5)： 6-13
[65]Jiann-FuhChen,Ching-Lung Chu.Combination Voltage-Controlled and Current-Controlled PWM Inverters for Parallel Operation of UPS.Industrial Electronics,Control and Instrumentation,Proceedings of the IECON '93,1993,2(4):1111～1116
[66]Ueda F.,Matsui K.,Asao M.et al.Parallel-Connections of Pulse Width Modulated Inverters Using Current Sharing Reactors.IEEE Trans.Power Electron.,1995,10(6):673～679
[67]Chen Y.-K.,Wu T.-F.,Wu Y.-E.et al.A Current-Sharing Control Strategy for Paralleled Multi-Inverter Systems using Microprocessor-Based Robust Control.IEEE International Conference on Electrical and Electronic Technology,1991:647～653
[68]J F Chen,C L Chu.Combination voltage-controlled and current-controlled PWM inverters for UPS parallel operation.IEEE Trans.Power Electron,1995,10(5):547～558
[69]邢岩，严仰光．一种新的并联运行逆变器系统的研究．电力电子技术，1999，33(6)：11～12
[70]陈息坤．高频模块化UPS及其并联控制技术研究：[博士学位论文]．武汉：华中科技大学,2005．
[71]Liviu Mihalache,Paralleling Control Technique with No Intercommunication Signals for Resonant Controller-Based Inverters,Industry Applications Conference,2003.38th IAS Annual Meeting.Oct.2003:1882 - 1889
[72]林新春．UPS无互联线并联控制技术研究：[博士学位论文]华中科技大学,2003
[73]邢岩，严仰光．一种实现瞬时均流的UPS冗余并联新方法清华大学学报(自然科学版)2003(43)3：333-336
[74]刑岩，严仰光．电流型逆变器的冗余并联控制方法．中国电机工程学报，2004，24(11)：199-202．
[75]T.G.Koo,Y.B.Byun,K.Y.Joe,et al.A Wireless Parallel Operation Control of a two-module UPS system for Equivalent Load Sharing.IEEE IECON 2000,2000: 2291～2296
[76]Yi Sun,Wenlong Qu,Bin Liang An Advanced Synchronization and Current-sharing Method for Paralleled DC/AC Inverters without Interconnection,Electrical Machines and Systems,27-29 Sept.2005.ICEMS 2005.proceedings of the Eighth International Conference on,2005(2):1013-1016
[77]Perreault D.J.,Selders R.L.Jr.,Kassakian J.G.Frequency-Based Current-Sharing Techniques for Paralleled Power Converters.IEEE Trans.Power Electron.,1998,13(4):626-634
[78]肖岚，胡文斌，蒋渭忠等．基于主从控制的逆变器并联系统研究．东南大学学报，2002,32(1)：133～137
[79]段善旭，孟宇，陈坚．电压型逆变电源并联控制技术研究．中国国际电源新技术研讨会．1999．23-25
[80]K Takao,H Shigenor.Parallel operation of voltage source inverters [J].IEEE Trans.Ind.App.1,1988,24 (2):281～287
[81]TKawabata,N Sashida,Y Yamamoto.Parallel processing inverter system [J].IEEE Trans.PowerElectronics,1991,6(3):442～450
[82]J.L.;Bobis,J.P.;A model for designing digital PID controllersTong,Industrial Electronics,Control,Instrumentation,and Automation,1992.'Power Electronics and Motion Control'.,Proceedings of the 1992 International Conference on,9-13 Nov.1992:1157- 1162(3)
[83]余蜜；张宇；康勇；单鸿涛；段善旭．基于改变环流阻抗的并联解耦控制策略电工技术学报，2008．10(23)10：58-63+68
[84]喻娅娅，王印松，许鹏春．数字控制中的保持器与系统稳定性的关系．自动化技术与应用，2004，23(11)：17-19．
[85]高金源．计算机控制系统·计算机控制系统：理论、设计与实现．北京：北京航空航天大学出版社．2001．
[86]孔雪娟．数字控制PWM逆变电源关键技术研究：[博士学位论文]．武汉：华中科技大学图书馆，2005
[87]K.-D.Wu,J.-C.Wu,H.-L.Jou,C.-Y.Chen and C.-Y.Lin Simplified control method for parallel-connected DC/AC inverters,Industrial Electronics,2000.ISIE 2000.Proceedings of the 2000 IEEE International Symposium on,Dec.2000:271～276
[88]duan shanxu,meng yu,kang yong et al.Parallel operation control technique of voltage source inverters in UPS.IEEE international conference on power electronics and drive systems.1999:883～887.
[89]张松涛．高频链结构不间断电源及其并联均流控制方式的研究[硕士学位论文]．哈尔滨工业大学，2003
[90]胡寿松．自动控制原理．第三版．北京：国防工业出版社，1996
[91]邹云屏，李潇．信号变换与处理．第一版．武汉：华中理工大学出版社，1994．234～244．
[92]魏克新，王云亮，陈云敏等编著．MATLAB语言与自动控制系统设计．机械工业出版社．2004．8第2版
[93]薛定宇．控制系统计算机辅助设计：MATLAB语言及应用．清华大学出版社1996．6第1版
[94]魏学良．三相三线并联型APF电流环数字化控制研究，[博士学位论文]．武汉：华中科技大学图书馆，2007
[95]刘树棠，黄建国译．离散时间信号处理．西安：西安交通大学出版，2001
[96]绪方胜彦．离散时间控制系统．西安：西安交通大学出版社，1990
[97]Gene F．Franklin等．动态系统的数字控制(第三版)清华大学出版社．2001．9第1版
[98]陈宏，胡育文．逆变电源并联技术．电工技术学报，2002，1 7(5)：55～59．
[99]D J Perreault,R L Selders,JG Kassakian.Frequency-based current-sharing techniques for paralleled power converters [J].IEEE Trans.of PE,1998,13(4):626～634
[100]Malesani L,Tenti P A novel hysteresis control method for current controlled VSI.Industry Applications,IEEE Trans.Part 1,Jan-Feb 1990,26(1):88-92
[101]Zhao Qinglin,Chen Zhongying and Wu Weiyang.Improved Control for Parallel Inverter withCurrent-Sharing Control Scheme,Power Electronics and Motion Control Conference,2006.IPEMC '06.CES/IEEE 5th International,2006:1 - 5
[102]Yan Xing,Lipei Huang,Sun,S.et al.Novel Control for Redundant Parallel UPSs with Instantaneous Current Sharing.IEEE PCC Conf Rec.,2002:959～963
[103]刘小四，熊 蕊．逆变器并联运行时环流的产生及抑制研究．电力电子技术．1999(33)3：16～18
[104]周伟成；周永忠；张海军；马皓；最大电流均流技术及应用．电力电子技术，2008年42(1)：45-47
[105]杨淑英，张兴，张崇巍．基于下垂特性的逆变器并联技术研究．电工电能新技术．2006(25)2：7-10,80
[106]曾建友．单相双变换在线式UPS及其并联运行研究[硕士学位论文]武汉：华中科技大学，2003
[107]刘永桥．三电平逆变器的控制及并联技术研究[硕士学位论文]。武汉：华中科技大学图书馆，2007
[108]张昌盛．高频UPS双环控制及并联运行关键技术研究：[硕士学位论文]。武汉：华中科技大学图书馆，2005．
[109]殷民．基于环流阻抗的UPS逆变器并联技术研究：[硕士学位论文]。武汉：华中科技大学图书馆，2007．
[110]Yu Zhang,Shanxu Duan,Yong Kang,and Jian Chen,The Restrain of Harmonic Circulating Currents between Parallel Inverters,IPEMC '06.CES/IEEE 5th International ,Aug.2006:1-5
[111]Xiao Sun,Yim-Shu,Dehong Xu.Modeling,Analysis,and Implementation of Parallel Multi-Inverter Systems With Instantaneous Average-Current-Sharing Scheme.IEEE Transactions on Power Electronics,May,2003 (18)3:844-856
[112]Lee C S,Kim S,Kim C B,et al.Parallel UPS with a instantaneous current sharing control[J].Industrial Electronics Society,1998.IECON'98.Proceedings of the 24th Annual Conference of the IEEE,1998,(1):568-573.
[113]余蜜；康勇；张宇；单鸿涛；段善旭基于环流阻抗的逆变器并联控制策略．中国电机工程学报，2008(28)1 8：42-46
[114]张宇．三相逆变器动态特性及其并联系统环流抑制的研究：[博士学位论文]．华中科技大学．2005．
[115]张宇，段善旭，康勇，陈坚．逆变器并联系统中谐波环流抑制的研究．中国电机工程学报，2006,26(12)：67～72
[116]陈良亮，肖岚，胡文斌等．双闭环控制电压源逆变器并联系统环流特性研究．电工技术学报．2004．5．(19)5：21-24．
[117]姚玮，高明智，陈敏，可调阻抗无互联线并联逆变器的控制方法．电力电子技术．2007．9．(41)9：21-23
[118]单鸿涛，康勇段善旭张宇余蜜刘永桥陈国英．模块化UPS并联的新型数字均流控制技术．高电压技术．2008，34(2)：289-292
[119]徐慧 电压控制型三相逆变器的并联与并网技术研究：[硕士学位论文]。武汉：华中科技大学图书馆，2007．
[120]单鸿涛，康勇，段善旭，余蜜，刘永桥，陈国英．新型模块化UPS并联数字均流控制技术研究 电气传动 2008，38(1)：39-42
[121]单鸿涛，彭力，孔雪娟，欧阳晖，刘钊，王淑惠．数字化过程对PWM逆变电源性能的影响机理．中国电机工程学报2009．29(6)：29-35