有源电力滤波器电流检测和控制方法的研究与仿真
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摘要
非线性负载和各种换流设备的应用，对电力系统的谐波“污染”是十分严重的，补偿电力系统谐波，改善供电质量成为迫切需要解决的问题。二十世纪八十年代瞬时无功功率理论的提出，为解决谐波电流实时检测问题提供了有效的解决方法，随着传统LC滤波器固有缺陷的日益突出和电力电子技术的飞速发展，采用有源电力滤波器动态抑制谐波成为重要的发展方向。在我国有源电力滤波器的研究和开发尚处于起始阶段，至今还没有大容量有源电力滤波器的成熟产品问世，因此进行有源电力滤波器的研究和开发工作具有非常重要的意义。
影响有源电力滤波器性能的两个关键环节是谐波电流检测环节和电流跟踪控制环节：本文讨论了基于瞬时无功功率理论的谐波电流检测方法，根据基于i_p、i_q运算方式的谐波电流检测法在三相三线制电路中的应用提出了它在三相四线制电路中的具体应用方案，数学分析证明了该电流检测方法的正确性；本文针对目前广泛采用的两种电流控制方法，提出了改进的三角波脉宽调制电流控制方法和滞环电流矢量控制方法，理论分析和仿真结果证明了改进的电流控制方法的有效性和优越性。
为了验证有源电力滤波器控制方法的正确性，并加深对其控制规律的认识和理解，本文用MATLAB／SIMULINK中的电力系统模块SimPowerSystems Blockset对有源电力滤波器进行了动态仿真研究。仿真结果表明，两种改进的电流控制方法都能有效地滤除负载中的绝大部分谐波，并且与传统的控制方法性相比都有一定的优越性：有利于减小有源电力滤波器的损耗和容量；在相同的控制精度下降低功率器件的开关频率，提高了有源电力滤波器的综合性能。
本文的研究工作对有源电力滤波器实验系统的开发具有一定的指导和参考价值。
For the wide application of the nonlinear loads and all kinds of converter equipments making the power system polluted with a mass of harmonic current, it is urgent to eliminate harmonic and improve power quality. The application of instantaneous reactive power theory provides the effective method of detecting harmonic current; and for the inherent shortcomings of LC filters and the development of power electronic technology, it is being an important way to eliminate harmonic dynamically by active power filters. In china, the studies and exploitations in active power filter is at its beginning stage, and large capacity mature producis have not been coming out yet, so the studies in active power filers have important significance.
The two keys of harmonic current detecting and current tracking controlling have a great impact on the performance of active power filters. Therefore, this paper discusses the harmonic and reactive current detecting method based on the instantaneous reactive power theory and presents the harmonic and reactive
current detecting method based the ip - iq algorithm used in three-phase
three-wire circuits and three-phase four-wire circuits. The mathematics analysis and the simulation results examine the feasibility and validity of the current detecting method. Moreover, this paper puts forward the improved schemes of the two main current controlling methods: the improved triangle-wave linear current controlling method and the hysteresis current vector controlling method. The feasibility and superiority of the two improved current controlling methods is examined by dynamic simulation and theoretical analysis.
To examine the validity of the controlling system of the shunt active power filter and understand the controlling rules furthermore, this paper simulates the shunt active power filter system with SimPowerSystems Blockset in MATLAB/SIMULINK. The simulating results show that the two improved
current controlling methods can filter a majority of the load harmonic current, and they have superiorities to the traditional methods: reducing the capacity and the power loss of the active power filter easily; and decreasing the switching frequency within the controlling precision to improve the performance of the active filter.
The studies in this paper have some guidance on the exploitation of the active power filter experimental system.
影响有源电力滤波器性能的两个关键环节是谐波电流检测环节和电流跟踪控制环节：本文讨论了基于瞬时无功功率理论的谐波电流检测方法，根据基于i_p、i_q运算方式的谐波电流检测法在三相三线制电路中的应用提出了它在三相四线制电路中的具体应用方案，数学分析证明了该电流检测方法的正确性；本文针对目前广泛采用的两种电流控制方法，提出了改进的三角波脉宽调制电流控制方法和滞环电流矢量控制方法，理论分析和仿真结果证明了改进的电流控制方法的有效性和优越性。
为了验证有源电力滤波器控制方法的正确性，并加深对其控制规律的认识和理解，本文用MATLAB／SIMULINK中的电力系统模块SimPowerSystems Blockset对有源电力滤波器进行了动态仿真研究。仿真结果表明，两种改进的电流控制方法都能有效地滤除负载中的绝大部分谐波，并且与传统的控制方法性相比都有一定的优越性：有利于减小有源电力滤波器的损耗和容量；在相同的控制精度下降低功率器件的开关频率，提高了有源电力滤波器的综合性能。
本文的研究工作对有源电力滤波器实验系统的开发具有一定的指导和参考价值。
For the wide application of the nonlinear loads and all kinds of converter equipments making the power system polluted with a mass of harmonic current, it is urgent to eliminate harmonic and improve power quality. The application of instantaneous reactive power theory provides the effective method of detecting harmonic current; and for the inherent shortcomings of LC filters and the development of power electronic technology, it is being an important way to eliminate harmonic dynamically by active power filters. In china, the studies and exploitations in active power filter is at its beginning stage, and large capacity mature producis have not been coming out yet, so the studies in active power filers have important significance.
The two keys of harmonic current detecting and current tracking controlling have a great impact on the performance of active power filters. Therefore, this paper discusses the harmonic and reactive current detecting method based on the instantaneous reactive power theory and presents the harmonic and reactive
current detecting method based the ip - iq algorithm used in three-phase
three-wire circuits and three-phase four-wire circuits. The mathematics analysis and the simulation results examine the feasibility and validity of the current detecting method. Moreover, this paper puts forward the improved schemes of the two main current controlling methods: the improved triangle-wave linear current controlling method and the hysteresis current vector controlling method. The feasibility and superiority of the two improved current controlling methods is examined by dynamic simulation and theoretical analysis.
To examine the validity of the controlling system of the shunt active power filter and understand the controlling rules furthermore, this paper simulates the shunt active power filter system with SimPowerSystems Blockset in MATLAB/SIMULINK. The simulating results show that the two improved
current controlling methods can filter a majority of the load harmonic current, and they have superiorities to the traditional methods: reducing the capacity and the power loss of the active power filter easily; and decreasing the switching frequency within the controlling precision to improve the performance of the active filter.
The studies in this paper have some guidance on the exploitation of the active power filter experimental system.
引文
[1] 王兆安，杨君，刘进军．谐波抑制和无功功率补偿[M]．北京：机械工业出版社，1998．
[2] Shiguo Luo, Zhencheng Hou. An Adaptive Detecting Method for Harmonic and Reactive Currents[J]. IEEE Trans On Ind Electron, 1995, 42(1):85-89.
[3] 王群，吴宁等．有源电力滤波器谐波电流检测的一种新方法[J]．电工技术学报，1997，12(1)：1—5．
[4] 陈建业．有源滤波器——结构、原理和应用[D]．2003．
[5] Akagi H. Trends in Active Power Line Conditioners[J]. IEEE Trans Power Election, 1994, 9(3): 263—268.
[6] 查晓明，王瑾，伍晓风等．基于PWM控制的并联型有源电力滤波器的MATLAB仿真研究[J] ．电力系统及其自动化学报，2001，13(3)：30—33．
[7] 谢运祥，唐中琦．电力有源滤波器及其应用技术的发展[J] ．电工技术杂志，2000，19(4)：1—3．
[8] 曾江，刁勤华，倪以信等．基于最优电压矢量的有源滤波器电流控制新方法[J]．电力系统自动化，2000，24(6)：25—31．
[9] Bhim Singh, Kamal Al-Haddad, Ambrish Chandra. A new control approach to three-phase active filter for harmonics and reactive power compensation[J]. IEEE Transactions on Power Systems, 1998, 13(1): 133-138.
[10] Akagi H, Kanazawa Y, Nabae A. Generalized theory of the instantaneous reactive power in three-phase circuits[J]. IEEE & JIEE, 1983:1375—1386.
[11] 王兆安，李民，卓放．三相电路瞬时无功功率理论的研究[J] ．电工技术学报，1992，7(3)：55—59．
[12] 杨君，王兆安．三相电路谐波电流两种检测方法的对比研究[J] ．电工技术学报，1995，10(2)：43—48．
[13] 李圣青，罗飞，张昌凡．基于i_p及i_q运算方式的改进型谐波电流检测方法[J] ．电气传动，2003，23(2)：48—50．
[14] 李群湛著．电气化铁道并联综合补偿及其应用[M] ．北京：中国铁道出版社，1993．
[15] 刘进军，刘波，王兆安．基于瞬时无功功率理论的串联混合型单相电力有源滤波器[J] ．中国电机工程学报，1997，17(1)：37—41．
[16] 高明振，任震，唐卓尧，李群湛．无源—有源混合滤波器容量优化设计[J] ．铁道学报，1999，21(5)：43—46．
[17] 蒋平，王宝安，赵剑峰等．配电网串并联复合有源电力滤波器的仿真研究[J] ．电力系统自动化，2002，26(19)：36-40．
[18] 贾时平，李圣怡．并联有源滤波器的最优电压滞环电流控制[J] ．电力自动化设备，2002，22(4)：14—17．
[19] 曾国宏，郝荣泰．有源滤波器滞环电流控制的矢量方法[J]．电力系统自动化，2003，27(5)：31—35．
[20] 秦梅、周林，叶一麟．三相平衡和补平衡系统中有害电流的检测技术[J]．电工技术杂志，2000，19(6)：4—6．
[21] 史伟伟，蒋全，胡敏强等．串联型有源电力滤波器功率电路设计[J] ．电力自动化设备，2002，22(4)：5—9．
[22] Malesani L, Mattavalli P, Tomasin P. High-performance hysteresis modulation technique for active filers[J]. IEEE Trans on PE, 1997, 12(5):876—884.
[23] Habrouk M E, Darwish M K, Mehta P. Active Power Filets: A Review[J]. IEE Proc—Electr Power Appl, 2000, 147(5): 403—413.
[24] 曾国宏，郝荣泰．采用有源滤波器实现平衡变换的供电系统研究[J]．铁道学报，2003，25(1)：48—54．
[25] 曾国宏，郝荣泰．有源滤波器滞环电流控制的矢量方法[J] ．电力系统自动化，2003，27(5)：31—35．
[26] 曾江，焦连伟，倪以信等．有源滤波器定频滞环电流控制新方法[J] ．电网技术，2000，24(6)：1—8．
[27] 李卫国，曾国宏，郝荣泰．基于状态优化的单相有源滤波器边带控制方案[J] ．电力系统自动化，2002，26(10)：36—40．
[28] 舒欣梅，张代润．一种消除有源电力滤波器系统震荡的控制方法[J] ．电源技术应用，2003，6(5)：34—36．
[29] 唐卓尧，任震．并联型混合滤波器及其滤波特性分析[J] ．中国电机工程
学报，2000，20(5)：25—29．
[30] 李民，王兆安，卓放．基于瞬时无功功率理论的高次谐波和无功功率检测[J] ．电力电子技术，1992，26(2)：14—17．
[31] 唐中琦，谢运祥．有源滤波器补偿电流的检测与控制[J] ．电工电能新技术，1998，17(4)：28—31．
[32] Bred D M, Novotny D W. Current control of VSI-PWM Inverters[J]. IEEE Trans on IA, 1985, 21(4):562—570.
[33] Malesani L, Tenti P.A novel hysteresis control method for current-controlled voltage-source PWM inverters with constant modulation frequency[J]. IEEE Trans on IA, 1990, 26(1):88—92.
[34] Kazmier-Kowski M P, Dzieniakowsld M A, Sulkowski W. Novel space vector controller for PWM-inverter[J]. IEEE Trans on PE, 1991, 6(1):158—166.
[35] Kwon B H, Kim TW, Youn J H. A novel SVM-Based hysteresis current controlled[J]. IEEE Trans on PE, 1998, 13(2):297—307.
[36] Sale M, Tuusa H. A novel open-loop control method for a current-source active power filter[J]. IEEE Transactions on, 2003, 50(2):313-321.
[37] Thomas T, Haddad K, Joos G. Design and performance of active power filters[H]. IEEE Industry Applications 1998, 4 (5):38-46.
[38] Woo-Cheol Lee, Taeck-Kie Lee, Dong-Seok Hyun. A three-phase parallel active power filter operating with PCC voltage compensation with consideration for an unbalanced load[J]. IEEE Transactions on, 2002, 17(5): 807-814.
[39] Dastfan A, Gosbell V J, Platt D. Control of a new active power filter using 3-D vector control[J]. IEEE Transactions on, 2000, 15(1):5-12.
[40] Chang G W. A new method for determining reference compensating currents of the three-phase shunt active power filter[J]. IEEE Power Engineering Review, 2001, 21(3):63-65.
[41] Luowei Zhou, Zicheng Li. A novel active power filter based on the least compensation current control method[J].IEEE Transactions on, 2000, 15(4): 655-659.
[42] Shyh-Jier Huang, Jinn-Chang Wu. A control algorithm for three-phase
three-wired active power filters under nonideal mains voltages[J]. IEEE Transactions on, 1999, 14 (4):753-760.
[43] Vcrdclho P, Marques G D. An active power filter and unbalanced current compensator[J]. IEEE Transactions on, 1997, 44(3): 321-328.
[44] Harrier J, Aredes M, Heumann K. A shunt active power filter applied to high voltage distribution lines[J]. IEEE Transactions on, 1997, 12(1):266-272.
[45] Dixon J W, Garcia J J, Moran L. Control system for three-phase active power filter which simultaneously compensates power factor and unbalanced loads[J]. IEEE Transactions on, 1995, 42 (6):636-641.
[46] Moran L A, Dixon J W, Wallace R R. A three-phase active power filter operating with fixed switching frequency for reactive power and current harmonic compensation[J]. IEEE Transactions on, 1995, 42(4): 402-408.
[47] Shen D, Lehn PW. Fixed-frequency space-vector-modulation control for three-phase four-leg active power filters[J]. IEE Proceedings, 2002, 149(4):268-274.
[48] Zeng J, Ni Y, Diao Q. Current controller for active power filter based on optimal voltage space vector[J]. IEE Proceedings, 2001, 148(2): 111-116.
[49] Fu Zhongwen, Li Haishan, Huang Wenling. A new current detecting method based on d-q transformation for active power filter[J]. Power System Technology, International Conference on 2002, 4: 2265-2268.
[50] Gong Maozhong, Liu Hankui, Gu Jianjun. A novel method of calculating current reference for shunt active power filters without hardware synchronization[J]. Power Conversion Conference, 2002, 2: 795-799.
[51] 卓放，王兆安．有源电力滤波器技术的发展与电能质量的提高[J] ．电工技术杂志，2002，21(6)：1—7．
[52] 吴竞昌，孙树琴，宋文南等编著．电力系统谐波[M]．水利电力出版社，1988．
[53] 夏道止，沈赞陨编著．高压直流输电系统的谐波分析及滤波[M] ．水利电力出版社，1994．
[54] 胡广书编著．数字信号处理——理论、算法与实现[M] ．清华大学出版社，1997．
[55] 罗世国．有源电力滤波器的研究[D] ．重庆大学博士学位论文，1995．
[56]曾国宏．基于三/单相平衡变换的铁道新型牵引供电系统研究[D] ．北方交通大学博士学位论文，2002．
[57] 王璐．基于DSP的有源电力滤波器研究[D] ．西南交通大学硕士学位论文，2003．
[58] 唐敏．牵引变电所混合电力滤波器及其控制器的研究[D] ．西南交通大学硕士学位论文，2003．
[59] 徐俊起．新型静止无功发生器的研究[D]．西南交通大学硕士学位论文，2003．
[60] 李海山．有源电力滤波器电流检测新方法与实验系统开发[D]．河北工业大学硕士学位论文，2002．
[61] 王晓毛．基于DSP有源电力滤波器的研究[D] ．广东工业大学硕士学位论文，2000．
[62] 苏金明，阮沈勇．MATLAB6.1实用指南(下)[M] ．电子工业出版社，2002．
[63] 黄中霖．控制系统MATLAB计算及仿真[M] ．国防工业出版社，2003．
[64] MATLAB/SIMULINK Online Help
[2] Shiguo Luo, Zhencheng Hou. An Adaptive Detecting Method for Harmonic and Reactive Currents[J]. IEEE Trans On Ind Electron, 1995, 42(1):85-89.
[3] 王群，吴宁等．有源电力滤波器谐波电流检测的一种新方法[J]．电工技术学报，1997，12(1)：1—5．
[4] 陈建业．有源滤波器——结构、原理和应用[D]．2003．
[5] Akagi H. Trends in Active Power Line Conditioners[J]. IEEE Trans Power Election, 1994, 9(3): 263—268.
[6] 查晓明，王瑾，伍晓风等．基于PWM控制的并联型有源电力滤波器的MATLAB仿真研究[J] ．电力系统及其自动化学报，2001，13(3)：30—33．
[7] 谢运祥，唐中琦．电力有源滤波器及其应用技术的发展[J] ．电工技术杂志，2000，19(4)：1—3．
[8] 曾江，刁勤华，倪以信等．基于最优电压矢量的有源滤波器电流控制新方法[J]．电力系统自动化，2000，24(6)：25—31．
[9] Bhim Singh, Kamal Al-Haddad, Ambrish Chandra. A new control approach to three-phase active filter for harmonics and reactive power compensation[J]. IEEE Transactions on Power Systems, 1998, 13(1): 133-138.
[10] Akagi H, Kanazawa Y, Nabae A. Generalized theory of the instantaneous reactive power in three-phase circuits[J]. IEEE & JIEE, 1983:1375—1386.
[11] 王兆安，李民，卓放．三相电路瞬时无功功率理论的研究[J] ．电工技术学报，1992，7(3)：55—59．
[12] 杨君，王兆安．三相电路谐波电流两种检测方法的对比研究[J] ．电工技术学报，1995，10(2)：43—48．
[13] 李圣青，罗飞，张昌凡．基于i_p及i_q运算方式的改进型谐波电流检测方法[J] ．电气传动，2003，23(2)：48—50．
[14] 李群湛著．电气化铁道并联综合补偿及其应用[M] ．北京：中国铁道出版社，1993．
[15] 刘进军，刘波，王兆安．基于瞬时无功功率理论的串联混合型单相电力有源滤波器[J] ．中国电机工程学报，1997，17(1)：37—41．
[16] 高明振，任震，唐卓尧，李群湛．无源—有源混合滤波器容量优化设计[J] ．铁道学报，1999，21(5)：43—46．
[17] 蒋平，王宝安，赵剑峰等．配电网串并联复合有源电力滤波器的仿真研究[J] ．电力系统自动化，2002，26(19)：36-40．
[18] 贾时平，李圣怡．并联有源滤波器的最优电压滞环电流控制[J] ．电力自动化设备，2002，22(4)：14—17．
[19] 曾国宏，郝荣泰．有源滤波器滞环电流控制的矢量方法[J]．电力系统自动化，2003，27(5)：31—35．
[20] 秦梅、周林，叶一麟．三相平衡和补平衡系统中有害电流的检测技术[J]．电工技术杂志，2000，19(6)：4—6．
[21] 史伟伟，蒋全，胡敏强等．串联型有源电力滤波器功率电路设计[J] ．电力自动化设备，2002，22(4)：5—9．
[22] Malesani L, Mattavalli P, Tomasin P. High-performance hysteresis modulation technique for active filers[J]. IEEE Trans on PE, 1997, 12(5):876—884.
[23] Habrouk M E, Darwish M K, Mehta P. Active Power Filets: A Review[J]. IEE Proc—Electr Power Appl, 2000, 147(5): 403—413.
[24] 曾国宏，郝荣泰．采用有源滤波器实现平衡变换的供电系统研究[J]．铁道学报，2003，25(1)：48—54．
[25] 曾国宏，郝荣泰．有源滤波器滞环电流控制的矢量方法[J] ．电力系统自动化，2003，27(5)：31—35．
[26] 曾江，焦连伟，倪以信等．有源滤波器定频滞环电流控制新方法[J] ．电网技术，2000，24(6)：1—8．
[27] 李卫国，曾国宏，郝荣泰．基于状态优化的单相有源滤波器边带控制方案[J] ．电力系统自动化，2002，26(10)：36—40．
[28] 舒欣梅，张代润．一种消除有源电力滤波器系统震荡的控制方法[J] ．电源技术应用，2003，6(5)：34—36．
[29] 唐卓尧，任震．并联型混合滤波器及其滤波特性分析[J] ．中国电机工程
学报，2000，20(5)：25—29．
[30] 李民，王兆安，卓放．基于瞬时无功功率理论的高次谐波和无功功率检测[J] ．电力电子技术，1992，26(2)：14—17．
[31] 唐中琦，谢运祥．有源滤波器补偿电流的检测与控制[J] ．电工电能新技术，1998，17(4)：28—31．
[32] Bred D M, Novotny D W. Current control of VSI-PWM Inverters[J]. IEEE Trans on IA, 1985, 21(4):562—570.
[33] Malesani L, Tenti P.A novel hysteresis control method for current-controlled voltage-source PWM inverters with constant modulation frequency[J]. IEEE Trans on IA, 1990, 26(1):88—92.
[34] Kazmier-Kowski M P, Dzieniakowsld M A, Sulkowski W. Novel space vector controller for PWM-inverter[J]. IEEE Trans on PE, 1991, 6(1):158—166.
[35] Kwon B H, Kim TW, Youn J H. A novel SVM-Based hysteresis current controlled[J]. IEEE Trans on PE, 1998, 13(2):297—307.
[36] Sale M, Tuusa H. A novel open-loop control method for a current-source active power filter[J]. IEEE Transactions on, 2003, 50(2):313-321.
[37] Thomas T, Haddad K, Joos G. Design and performance of active power filters[H]. IEEE Industry Applications 1998, 4 (5):38-46.
[38] Woo-Cheol Lee, Taeck-Kie Lee, Dong-Seok Hyun. A three-phase parallel active power filter operating with PCC voltage compensation with consideration for an unbalanced load[J]. IEEE Transactions on, 2002, 17(5): 807-814.
[39] Dastfan A, Gosbell V J, Platt D. Control of a new active power filter using 3-D vector control[J]. IEEE Transactions on, 2000, 15(1):5-12.
[40] Chang G W. A new method for determining reference compensating currents of the three-phase shunt active power filter[J]. IEEE Power Engineering Review, 2001, 21(3):63-65.
[41] Luowei Zhou, Zicheng Li. A novel active power filter based on the least compensation current control method[J].IEEE Transactions on, 2000, 15(4): 655-659.
[42] Shyh-Jier Huang, Jinn-Chang Wu. A control algorithm for three-phase
three-wired active power filters under nonideal mains voltages[J]. IEEE Transactions on, 1999, 14 (4):753-760.
[43] Vcrdclho P, Marques G D. An active power filter and unbalanced current compensator[J]. IEEE Transactions on, 1997, 44(3): 321-328.
[44] Harrier J, Aredes M, Heumann K. A shunt active power filter applied to high voltage distribution lines[J]. IEEE Transactions on, 1997, 12(1):266-272.
[45] Dixon J W, Garcia J J, Moran L. Control system for three-phase active power filter which simultaneously compensates power factor and unbalanced loads[J]. IEEE Transactions on, 1995, 42 (6):636-641.
[46] Moran L A, Dixon J W, Wallace R R. A three-phase active power filter operating with fixed switching frequency for reactive power and current harmonic compensation[J]. IEEE Transactions on, 1995, 42(4): 402-408.
[47] Shen D, Lehn PW. Fixed-frequency space-vector-modulation control for three-phase four-leg active power filters[J]. IEE Proceedings, 2002, 149(4):268-274.
[48] Zeng J, Ni Y, Diao Q. Current controller for active power filter based on optimal voltage space vector[J]. IEE Proceedings, 2001, 148(2): 111-116.
[49] Fu Zhongwen, Li Haishan, Huang Wenling. A new current detecting method based on d-q transformation for active power filter[J]. Power System Technology, International Conference on 2002, 4: 2265-2268.
[50] Gong Maozhong, Liu Hankui, Gu Jianjun. A novel method of calculating current reference for shunt active power filters without hardware synchronization[J]. Power Conversion Conference, 2002, 2: 795-799.
[51] 卓放，王兆安．有源电力滤波器技术的发展与电能质量的提高[J] ．电工技术杂志，2002，21(6)：1—7．
[52] 吴竞昌，孙树琴，宋文南等编著．电力系统谐波[M]．水利电力出版社，1988．
[53] 夏道止，沈赞陨编著．高压直流输电系统的谐波分析及滤波[M] ．水利电力出版社，1994．
[54] 胡广书编著．数字信号处理——理论、算法与实现[M] ．清华大学出版社，1997．
[55] 罗世国．有源电力滤波器的研究[D] ．重庆大学博士学位论文，1995．
[56]曾国宏．基于三/单相平衡变换的铁道新型牵引供电系统研究[D] ．北方交通大学博士学位论文，2002．
[57] 王璐．基于DSP的有源电力滤波器研究[D] ．西南交通大学硕士学位论文，2003．
[58] 唐敏．牵引变电所混合电力滤波器及其控制器的研究[D] ．西南交通大学硕士学位论文，2003．
[59] 徐俊起．新型静止无功发生器的研究[D]．西南交通大学硕士学位论文，2003．
[60] 李海山．有源电力滤波器电流检测新方法与实验系统开发[D]．河北工业大学硕士学位论文，2002．
[61] 王晓毛．基于DSP有源电力滤波器的研究[D] ．广东工业大学硕士学位论文，2000．
[62] 苏金明，阮沈勇．MATLAB6.1实用指南(下)[M] ．电子工业出版社，2002．
[63] 黄中霖．控制系统MATLAB计算及仿真[M] ．国防工业出版社，2003．
[64] MATLAB/SIMULINK Online Help