配电系统级联型有源电力滤波器的研究
|
摘要
随着电力系统中非线性负载的日益增多,产生了大量谐波电流,严重的影响了电网电能质量,有源电力滤波技术作为抑制和消除谐波行之有效的手段业已成为研制和开发的重点。本文主要目的是研究适用于配电系统的环境下的高压大容量三相级联多电平有源滤波器(SAPF)。
本文首先分析适用于我国配电系统的逆变器必须具备的三个条件:电压等级高、功率容量大、三相三线制连接。随即按照当前半导体开关器件所能达到的最高电压和容量水平定量给出了三相桥拓扑、三个单相全桥通过组合而成的三相逆变器拓扑和级联多电平逆变器拓扑所能承受的最高电压等级和最大的功率容量,研究发现级联多电平逆变器是最适合在高压大容量环境下应用的逆变器拓扑。
在调制方法的选择上,本文针对所采用的级联多电平逆变器拓扑的特点主要比较了载波移相SPWM的调制方式(CPS-SPWM)和一维空间矢量调制方式(1D-SVPWM)在级联多电平逆变器中的输出特性,对调制波的拟合能力、等效开关频率的提升能力、直流侧均压的影响等因素作了比较,尤其对采用CPS-SPWM调制直流侧不均压时逆变器的输出特性进行了理论计算、仿真推理和实验验证,得出直流侧电压均压与否对采用CPS-SPWM调制的级联多电平逆变器的输出特性影响甚微的结论,加之CPS-SPWM调制具有强力提升级联多电平逆变器等效开关频率的特点使其更适合应用于本文研究的SAPF。
本文在控制上采取分散控制的策略,用简单的PI控制实现电流环、电压环和直流侧均压控制。
最后进行了SAPF的仿真,结果表明这种基于级联多电平拓扑的有源电力滤波器能很好地跟踪补偿电网谐波,具有很快的动态响应速度和较高的检测精度,能快速准确的实现各个变流器单元直流侧电容的均压控制,这对拓展有源电力滤波器在高压领域的应用具有积极意义。
As the nonlinear load of electric power systems increasing, a lot of harmonic current is brought, the power quality is reduced seriously. Active power filter (APF) as the suppression and eliminate harmonic effective method has become the key in research and development of power electronics academic. The purpose of this paper was to study the three-phase cascade multilevel APF with large capacity and high voltage which was suitable for distribution system.
The paper pointed out that the inverter used for the distribution system of our country must possess the three conditions: high voltage grade, large power capacity, for three phases connection. Then gave quantitatively the highest voltage grade and the largest power capacity of Three-phase bridge converter,the inverter topology made of three single-phase full-bridge inverters triangle connected and cascade multilevel inverter in accordance with the highest voltage and power capacity level of the semiconductor switch at present. Through studying, it was found that cascade multilevel inverter was the most suitable inverter for the environment in high voltage and large power capacity.
In order to choose appropriate modulation method,this paper compared two methods: carrier phase shifting sinusoidal pulse width modulation(CPS-SPWM) and 1 dimension space vector pulse width Modulation (1D–SVPWM) who was applied to cascade multilevel inverter in the output characteristic, Comparison results show that:CPS-SPWM is most suitable for this design, for it can not only improve switch frequency but also shows good ability of resisting dc side voltage fluctuation interference. According to the characteristics of cascade multilevel, the distributed control strategy was adopted, simple PI control is widely applied in current loop, voltage ring, Dc side voltage balance control.
At last cascade multilevel inverter topology, the modulation method of CPS-SPWM, the distributed control strategy, simple control method of PI control were selected to be applied to the APF for distribution network developed by this paper.
Simulation result demonstrated that APF based on cascaded multilevel topology could trace and compensate the grid harmonics accurately, and good dynamic response and high detection accuracy are approached. Furthermore, DC capacitors voltage of each link could be balanced fast and accurately. The application of APF in high voltage field is expanded.
本文首先分析适用于我国配电系统的逆变器必须具备的三个条件:电压等级高、功率容量大、三相三线制连接。随即按照当前半导体开关器件所能达到的最高电压和容量水平定量给出了三相桥拓扑、三个单相全桥通过组合而成的三相逆变器拓扑和级联多电平逆变器拓扑所能承受的最高电压等级和最大的功率容量,研究发现级联多电平逆变器是最适合在高压大容量环境下应用的逆变器拓扑。
在调制方法的选择上,本文针对所采用的级联多电平逆变器拓扑的特点主要比较了载波移相SPWM的调制方式(CPS-SPWM)和一维空间矢量调制方式(1D-SVPWM)在级联多电平逆变器中的输出特性,对调制波的拟合能力、等效开关频率的提升能力、直流侧均压的影响等因素作了比较,尤其对采用CPS-SPWM调制直流侧不均压时逆变器的输出特性进行了理论计算、仿真推理和实验验证,得出直流侧电压均压与否对采用CPS-SPWM调制的级联多电平逆变器的输出特性影响甚微的结论,加之CPS-SPWM调制具有强力提升级联多电平逆变器等效开关频率的特点使其更适合应用于本文研究的SAPF。
本文在控制上采取分散控制的策略,用简单的PI控制实现电流环、电压环和直流侧均压控制。
最后进行了SAPF的仿真,结果表明这种基于级联多电平拓扑的有源电力滤波器能很好地跟踪补偿电网谐波,具有很快的动态响应速度和较高的检测精度,能快速准确的实现各个变流器单元直流侧电容的均压控制,这对拓展有源电力滤波器在高压领域的应用具有积极意义。
As the nonlinear load of electric power systems increasing, a lot of harmonic current is brought, the power quality is reduced seriously. Active power filter (APF) as the suppression and eliminate harmonic effective method has become the key in research and development of power electronics academic. The purpose of this paper was to study the three-phase cascade multilevel APF with large capacity and high voltage which was suitable for distribution system.
The paper pointed out that the inverter used for the distribution system of our country must possess the three conditions: high voltage grade, large power capacity, for three phases connection. Then gave quantitatively the highest voltage grade and the largest power capacity of Three-phase bridge converter,the inverter topology made of three single-phase full-bridge inverters triangle connected and cascade multilevel inverter in accordance with the highest voltage and power capacity level of the semiconductor switch at present. Through studying, it was found that cascade multilevel inverter was the most suitable inverter for the environment in high voltage and large power capacity.
In order to choose appropriate modulation method,this paper compared two methods: carrier phase shifting sinusoidal pulse width modulation(CPS-SPWM) and 1 dimension space vector pulse width Modulation (1D–SVPWM) who was applied to cascade multilevel inverter in the output characteristic, Comparison results show that:CPS-SPWM is most suitable for this design, for it can not only improve switch frequency but also shows good ability of resisting dc side voltage fluctuation interference. According to the characteristics of cascade multilevel, the distributed control strategy was adopted, simple PI control is widely applied in current loop, voltage ring, Dc side voltage balance control.
At last cascade multilevel inverter topology, the modulation method of CPS-SPWM, the distributed control strategy, simple control method of PI control were selected to be applied to the APF for distribution network developed by this paper.
Simulation result demonstrated that APF based on cascaded multilevel topology could trace and compensate the grid harmonics accurately, and good dynamic response and high detection accuracy are approached. Furthermore, DC capacitors voltage of each link could be balanced fast and accurately. The application of APF in high voltage field is expanded.
引文
[1]何仰赞,温増银等.电力系统分析.武汉,华中科技大学出版社,2002
[2]熊信银,张步涵等.电气工程基础.武汉,华中科技大学出版社,2005
[3] J.Arrilaga,D.A.Bradley,D.S.bodger著.荣键刚等译.电力系统谐波[M].武汉,华科技大学出版社,1994
[4]王兆安,杨君,刘进军,王跃.谐波抑制与无功功率补偿. (第二版).北京,机械工业出版社,2005
[5] Bose B K. Power electronics-a technoiogy review. Proceedings of IEEE, 1992, 80(8): 1303-1334
[6] Kimbark E W. Direct current transmission. Vol.Ⅰ, Ch.8 New York: John Wiley&Sons, 1971
[7] Read J C. The calculation of rectifier and converter performance characteristics. Journal IEE, 1945, 92, pt.Ⅱ:495-590
[8] Harashima F. Power electronics and motion control-a future perspective. Proceedings of IEEE, 1994, 82(8):1107-1111
[9] Akagi H. New trends in active filters. In: Proceedings of EPE’95, Sevilla, 1995. 17-26
[10] Semlyen A, Medina A. Computation of the periodic steady state in systems with nonlinear components using a hybrid time and frequency domain methodology. IEEE Trans. Power Syst., 1995,10(3):1498-1504
[11] Xia D, Heydt G T. Harmonic power flow studies, PartⅠ:Formulation and Solution. IEEE Trans. Power App. & Syst., 1982, 101(6): 1257-1265
[12] Xia D, Heydt G T. Harmonic power flow studies, PartⅡ:Implementation and pratical application. IEEE Trans. Power App. & Syst., 1982, 101(6): 1266-1270
[13] Arrillaga J,Mcdina A, Lisboa M L Vet al. The harmonic domain: a frame of reference for power system harmonic analysis. IEEE Trans. Power Syst., 1982,101(6):433-440
[14] Akagi H. Trends in active power line conditioners. IEEE Trans. Power Electron., 1994, 9(3): 263-268
[15] Bird B M, Marsh J F,McLellan P R. Harmonic reduction in multiple converters by triple-frequency current injection. Proc. IEE,1969, 116(10):1730-1734
[16] Gyugyi L, Strycula E C. Active ac power filters. In: Proc of IEEE/IAS AnnualMeeting, 1976: 529-535
[17]姜齐荣、赵东元、陈建业,有源电力滤波器.,科学出版社,2005
[18]吴竞昌,孙树勤,宋文南等.电力系统谐波. (第一版).北京,水利电力出版社,1988
[19] J S Lai, F Z Peng. Multilevel converters–A new breed of power converters. IEEE Trans. Ind. Applicat., 1996 ,May/June (32): 509–517
[20] L Tolbert, F Z Peng, T Habetler. Multilevel converters for large electric drives. IEEE Trans Ind. Applicat., 1999, Jan/Feb(35): 36–44
[21] R Teodorescu, F Beaabjerg, J K Pedersen, E Cengelci, S Sulistijo, B Woo, and P Enjeti. Multilevel converters—A survey. Proc European Power Electronics Conf. (EPE’99), Lausanne, Switzerland, 1999
[22] A Nabae, I Takahashi, and H Akagi. A new neutral-point clamped PWM inverter. IEEE Trans. Ind. Applicat., 1981, Sept./Oct (IA-17): 518–523
[23] T A Meynard and H Foch. Multi-level choppers for high voltage applications. Eur. Power Electron. Drives J, 1992, 3( 2-1):41
[24]陈坚.电力电子学—电力电子变换和控制技术.北京:高等教育出版社, 2004.
[25]阮新波,严仰光.四桥臂三相逆变器的控制策略[J].电工技术学报,2005,15(1):61-64.
[26]万山明,吴芳,黄声华.三相四桥臂电压源高频链逆变器[J].中国电机工程学报,2005,25(12):47-51.
[27]乐健,姜齐荣,韩英铎.基于统一数学模型的三相四线并联[J] ,电工技术学报,2007,27(7):109-113.
[28] Jeong G Y, Park T J, Kwon B H. Line-voltage-sensorless active power filter for reactive power compensation. IEE Proc. Electric Power Applicat., 2000, 147(5):385-390
[29] Jeong G Y, Park T J, Kwon B H. Line-voltage-sensorless active power filter for reactive power compensation. IEE Proc. Electric Power Applicat., 2000, 147(5):385-390
[30] Wu R, Dewan S B, Slemon G R. Analysis of an AC-to-DC voltage source converter using PWM with phase and amplitude control. IEEE Trans. Ind. Applicat., 1991, (27):355-364
[31] Fang Zheng Peng, Jih-sheng Lai, John W Mckeever. A muitilevel voltage source inverter with sepatate DC source for static var genenation. IEEE Trans. I.A.,1996,5(32)
[32] C Hochgraf, R Lasseter, D Divan, T A Lipo. Comparison of multilevel inverters for static var compensation. Conf. Rec. IEEE-IAS Annu Meeting, 1994, (10):921–928
[33] P Hammond. A new approach to enhance power quality for medium voltage ac drives. IEEE Trans. Ind. Applicat., 1997, Jan/Feb(33):202–208
[34] E Cengelci, S U Sulistijo, B O Woom, P Enjeti, R Teodorescu, F Blaabjerge. A new medium voltage PWM inverter topology for adjustable speed drives. in Conf. Rec. IEEE-IAS Annu Meeting, St. Louis, MO, Oct. 1998, pp. 1416–1423
[35]王霞、高沁翔.基于检测电源电流控制方式的并联型有源电力滤波器的仿真研究[J].电力电容器,2007,28(5):20-24
[36]王长永,金陶涛,张仲超.基于CPS-SPWM技术的电流源有源滤波器的研究,电力系统白动化[J],2000,24 (13):11-14.
[37] Zhang Zhongchao,Boon-Teck Ooi. Forced commutated HVDC and SVC based onPhase-shifted multi-converters. IEEE Trans. Power Delivery,1993, 8(2):712-718
[38] Zhang Zhongchao,Boon-Teck Ooi. Multi-modular current source SPWM converter for SMES.IEEE Trans. Power Electron.,1993, 8 (3):250-256
[39] F Z Peng,J S Lai. Multilevel cascade voltage-source inverter with separate DC sources. US Patent 5 642 275, June 24, 1997
[40] P W Hammond. Four-quadrant AC-AC drive and method. US Patent 6 166 513, Dec 2000
[41] M F Aiello, P W Hammond, M Rastogi. Modular multi-level adjustable supply with series connected active inputs. US. Patent 6 236 580, May 2001.
[42] YuXiong,DnajinagChen,XinYang,ChnagshengHu,ZhongehaoZhnag. Analysis and experimentation of anew there-phase multi level current-source inverter. Power Electronics Specialists Conference 2004. PESC04. 2004 IEEE 35th Annual,Volume:l,20-25 June 2004 PP:548-551
[43] YuXiong,DnajiangChen,SongquanDeng,ZhongchaoZhang. A new single-Phase multi level current-source inverter. Applied Power Electronics Conference and Exposition,2004 APEC’04. Nineteenth Annual IEEE,Volume:3,2004. PP: 1682-1685
[44] YuXiong,YinhaiZhang,KunWei,ZhongehaoZhang. Carrier Phase-shifted SPWM based current-source multi-converter. Applied Power Electronics Conference and Exposition,2003.APEC’03. Eighteenth Annual IEEE,Volume:1,9-13Feb.2003.PP:89-93
[45]陈国呈. PWM变频调速及软开关电力变换技术,机械工业出版社,2001.3
[46] S.R. Bowes. New sinusoidal Pulse width modulated inverter. Proc. IEEE Electric Power Applicat.,Volume:122,1975, B(11):1279-1285
[47] Liqiao Wang, Yushui Huang, Zhongchao Zhang. Kai Tang. Cascade multi-level converters With sample-time-staggered space vector modulation. Applied Power Electronics Conference And Exposition,2003.APEC’03-Eighteenth Annual IEEE,Volume:1,9-13Feb.2003,PP:268-273
[48]易龙强,戴瑜兴. SVPWM技术在单相逆变电源中的应用[J] ,电工技术学报,2007,22(9):112-117
[49]高金源等.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
[50]胡寿松.自动控制原理. (第三版).北京:国防工业出版社,1996
[51]魏学良,戴珂,康勇,耿攀.三相三线并联型有源电力滤波器并联控制[J],电力系统自动化2007,31(1):70-73
[52]戴珂,陈晶晶,宫力,陈睿,黄云辉,康勇.采用多DSP的级联型DSTATCOM分散控制策略[J].高电压技术. 2010,36(11):2821-2826
[53]魏学良.三相三线并联型APF电流环数字化控制研究[D],华中科技大学博士学位论文2007
[54]耿俊成,刘文华,袁志昌.链式STATCOM电容电压不平衡现象研究[J].电力系统自动化,2003, 27(16): 53-57
[55]陈峻岭,王平,李耀华,陈永刚. H桥级联型有源电力滤波器直流侧电容电压均衡控制方法.专利号200610113537.8, 2006
[56]陈睿,戴珂,黄云辉,陈晶晶,宫力.级联多电平APF仿真研究[C].中国电工技术学会电力电子学会第十二届学术年会,哈尔滨,2010
[2]熊信银,张步涵等.电气工程基础.武汉,华中科技大学出版社,2005
[3] J.Arrilaga,D.A.Bradley,D.S.bodger著.荣键刚等译.电力系统谐波[M].武汉,华科技大学出版社,1994
[4]王兆安,杨君,刘进军,王跃.谐波抑制与无功功率补偿. (第二版).北京,机械工业出版社,2005
[5] Bose B K. Power electronics-a technoiogy review. Proceedings of IEEE, 1992, 80(8): 1303-1334
[6] Kimbark E W. Direct current transmission. Vol.Ⅰ, Ch.8 New York: John Wiley&Sons, 1971
[7] Read J C. The calculation of rectifier and converter performance characteristics. Journal IEE, 1945, 92, pt.Ⅱ:495-590
[8] Harashima F. Power electronics and motion control-a future perspective. Proceedings of IEEE, 1994, 82(8):1107-1111
[9] Akagi H. New trends in active filters. In: Proceedings of EPE’95, Sevilla, 1995. 17-26
[10] Semlyen A, Medina A. Computation of the periodic steady state in systems with nonlinear components using a hybrid time and frequency domain methodology. IEEE Trans. Power Syst., 1995,10(3):1498-1504
[11] Xia D, Heydt G T. Harmonic power flow studies, PartⅠ:Formulation and Solution. IEEE Trans. Power App. & Syst., 1982, 101(6): 1257-1265
[12] Xia D, Heydt G T. Harmonic power flow studies, PartⅡ:Implementation and pratical application. IEEE Trans. Power App. & Syst., 1982, 101(6): 1266-1270
[13] Arrillaga J,Mcdina A, Lisboa M L Vet al. The harmonic domain: a frame of reference for power system harmonic analysis. IEEE Trans. Power Syst., 1982,101(6):433-440
[14] Akagi H. Trends in active power line conditioners. IEEE Trans. Power Electron., 1994, 9(3): 263-268
[15] Bird B M, Marsh J F,McLellan P R. Harmonic reduction in multiple converters by triple-frequency current injection. Proc. IEE,1969, 116(10):1730-1734
[16] Gyugyi L, Strycula E C. Active ac power filters. In: Proc of IEEE/IAS AnnualMeeting, 1976: 529-535
[17]姜齐荣、赵东元、陈建业,有源电力滤波器.,科学出版社,2005
[18]吴竞昌,孙树勤,宋文南等.电力系统谐波. (第一版).北京,水利电力出版社,1988
[19] J S Lai, F Z Peng. Multilevel converters–A new breed of power converters. IEEE Trans. Ind. Applicat., 1996 ,May/June (32): 509–517
[20] L Tolbert, F Z Peng, T Habetler. Multilevel converters for large electric drives. IEEE Trans Ind. Applicat., 1999, Jan/Feb(35): 36–44
[21] R Teodorescu, F Beaabjerg, J K Pedersen, E Cengelci, S Sulistijo, B Woo, and P Enjeti. Multilevel converters—A survey. Proc European Power Electronics Conf. (EPE’99), Lausanne, Switzerland, 1999
[22] A Nabae, I Takahashi, and H Akagi. A new neutral-point clamped PWM inverter. IEEE Trans. Ind. Applicat., 1981, Sept./Oct (IA-17): 518–523
[23] T A Meynard and H Foch. Multi-level choppers for high voltage applications. Eur. Power Electron. Drives J, 1992, 3( 2-1):41
[24]陈坚.电力电子学—电力电子变换和控制技术.北京:高等教育出版社, 2004.
[25]阮新波,严仰光.四桥臂三相逆变器的控制策略[J].电工技术学报,2005,15(1):61-64.
[26]万山明,吴芳,黄声华.三相四桥臂电压源高频链逆变器[J].中国电机工程学报,2005,25(12):47-51.
[27]乐健,姜齐荣,韩英铎.基于统一数学模型的三相四线并联[J] ,电工技术学报,2007,27(7):109-113.
[28] Jeong G Y, Park T J, Kwon B H. Line-voltage-sensorless active power filter for reactive power compensation. IEE Proc. Electric Power Applicat., 2000, 147(5):385-390
[29] Jeong G Y, Park T J, Kwon B H. Line-voltage-sensorless active power filter for reactive power compensation. IEE Proc. Electric Power Applicat., 2000, 147(5):385-390
[30] Wu R, Dewan S B, Slemon G R. Analysis of an AC-to-DC voltage source converter using PWM with phase and amplitude control. IEEE Trans. Ind. Applicat., 1991, (27):355-364
[31] Fang Zheng Peng, Jih-sheng Lai, John W Mckeever. A muitilevel voltage source inverter with sepatate DC source for static var genenation. IEEE Trans. I.A.,1996,5(32)
[32] C Hochgraf, R Lasseter, D Divan, T A Lipo. Comparison of multilevel inverters for static var compensation. Conf. Rec. IEEE-IAS Annu Meeting, 1994, (10):921–928
[33] P Hammond. A new approach to enhance power quality for medium voltage ac drives. IEEE Trans. Ind. Applicat., 1997, Jan/Feb(33):202–208
[34] E Cengelci, S U Sulistijo, B O Woom, P Enjeti, R Teodorescu, F Blaabjerge. A new medium voltage PWM inverter topology for adjustable speed drives. in Conf. Rec. IEEE-IAS Annu Meeting, St. Louis, MO, Oct. 1998, pp. 1416–1423
[35]王霞、高沁翔.基于检测电源电流控制方式的并联型有源电力滤波器的仿真研究[J].电力电容器,2007,28(5):20-24
[36]王长永,金陶涛,张仲超.基于CPS-SPWM技术的电流源有源滤波器的研究,电力系统白动化[J],2000,24 (13):11-14.
[37] Zhang Zhongchao,Boon-Teck Ooi. Forced commutated HVDC and SVC based onPhase-shifted multi-converters. IEEE Trans. Power Delivery,1993, 8(2):712-718
[38] Zhang Zhongchao,Boon-Teck Ooi. Multi-modular current source SPWM converter for SMES.IEEE Trans. Power Electron.,1993, 8 (3):250-256
[39] F Z Peng,J S Lai. Multilevel cascade voltage-source inverter with separate DC sources. US Patent 5 642 275, June 24, 1997
[40] P W Hammond. Four-quadrant AC-AC drive and method. US Patent 6 166 513, Dec 2000
[41] M F Aiello, P W Hammond, M Rastogi. Modular multi-level adjustable supply with series connected active inputs. US. Patent 6 236 580, May 2001.
[42] YuXiong,DnajinagChen,XinYang,ChnagshengHu,ZhongehaoZhnag. Analysis and experimentation of anew there-phase multi level current-source inverter. Power Electronics Specialists Conference 2004. PESC04. 2004 IEEE 35th Annual,Volume:l,20-25 June 2004 PP:548-551
[43] YuXiong,DnajiangChen,SongquanDeng,ZhongchaoZhang. A new single-Phase multi level current-source inverter. Applied Power Electronics Conference and Exposition,2004 APEC’04. Nineteenth Annual IEEE,Volume:3,2004. PP: 1682-1685
[44] YuXiong,YinhaiZhang,KunWei,ZhongehaoZhang. Carrier Phase-shifted SPWM based current-source multi-converter. Applied Power Electronics Conference and Exposition,2003.APEC’03. Eighteenth Annual IEEE,Volume:1,9-13Feb.2003.PP:89-93
[45]陈国呈. PWM变频调速及软开关电力变换技术,机械工业出版社,2001.3
[46] S.R. Bowes. New sinusoidal Pulse width modulated inverter. Proc. IEEE Electric Power Applicat.,Volume:122,1975, B(11):1279-1285
[47] Liqiao Wang, Yushui Huang, Zhongchao Zhang. Kai Tang. Cascade multi-level converters With sample-time-staggered space vector modulation. Applied Power Electronics Conference And Exposition,2003.APEC’03-Eighteenth Annual IEEE,Volume:1,9-13Feb.2003,PP:268-273
[48]易龙强,戴瑜兴. SVPWM技术在单相逆变电源中的应用[J] ,电工技术学报,2007,22(9):112-117
[49]高金源等.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
[50]胡寿松.自动控制原理. (第三版).北京:国防工业出版社,1996
[51]魏学良,戴珂,康勇,耿攀.三相三线并联型有源电力滤波器并联控制[J],电力系统自动化2007,31(1):70-73
[52]戴珂,陈晶晶,宫力,陈睿,黄云辉,康勇.采用多DSP的级联型DSTATCOM分散控制策略[J].高电压技术. 2010,36(11):2821-2826
[53]魏学良.三相三线并联型APF电流环数字化控制研究[D],华中科技大学博士学位论文2007
[54]耿俊成,刘文华,袁志昌.链式STATCOM电容电压不平衡现象研究[J].电力系统自动化,2003, 27(16): 53-57
[55]陈峻岭,王平,李耀华,陈永刚. H桥级联型有源电力滤波器直流侧电容电压均衡控制方法.专利号200610113537.8, 2006
[56]陈睿,戴珂,黄云辉,陈晶晶,宫力.级联多电平APF仿真研究[C].中国电工技术学会电力电子学会第十二届学术年会,哈尔滨,2010