基于双分数阶快速重复控制的有源电力滤波器电流控制策略
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摘要
首先介绍了传统重复控制结构,建立dq坐标系下的快速化改进方法,并分析指出其存在电网频率偏移时的适应性、重复控制快速化改进后周期延时环节点数为非正整数以及低采样频率下相位超前补偿环节难以取到合适的整数阶拍次的难题。为解决上述问题,进一步引入分数思想,提出一种具有频率变化适应性的双分数阶快速重复控制策略。通过将传统内模重塑为有限个阶次相邻、不同权重系数的整数阶内模,得到基于分数阶周期延时环节的新型内模,同时将传统的单个固定拍次相位补偿环节改造为有限个阶次相邻的整数阶超前环节模型并联,实现分数阶超前环节的相位补偿。算法上利用数学上经典的拉格朗日插值法实现双环节分数化,并分析了不同插值点和插值长度对拟合效果的影响。通过两个算例从频率特性角度分析对比了和传统方法的性能差异。最后在搭建的16.5kV·A实验样机上验证了所提策略的有效性。
This paper firstly introduces the structure of traditional repetitive control and the rapid improvement method in dq coordinates is established. Then the adaptability problems of traditional repetitive control with frequency varying, non-integer value of cycle delay points of improved rapid repetitive control, and the difficulty to get proper integer phase compensating order under low sample frequency are analyzed. To solve these problems, fractional thought is introduced and a double fractional-order repetitive control strategy with frequency adaptability is proposed. By remoulding the traditional internal model into a finite number of adjacent integer-order internal models, novel internal model based on fractional-order cycle delay link is obtained. Meanwhile, finite number of adjacent integer-order phase-lead links are used to replace the traditional single fixed integer-order phase-lead link, to achieve the fractional-order phase compensation. In the algorithm, the classical Lagrange interpolation method is adopted to achieve the fractionization of two links. The influence of interpolation points and interpolation length on fitting effect is analyzed. Two case studies are implemented and performance differences between the proposed method and traditional methods are analyzed and compared from the perspective of frequency characteristics. Finally, experiments on the established 16.5 kV·A prototype have verified the validity of proposed strategy.
This paper firstly introduces the structure of traditional repetitive control and the rapid improvement method in dq coordinates is established. Then the adaptability problems of traditional repetitive control with frequency varying, non-integer value of cycle delay points of improved rapid repetitive control, and the difficulty to get proper integer phase compensating order under low sample frequency are analyzed. To solve these problems, fractional thought is introduced and a double fractional-order repetitive control strategy with frequency adaptability is proposed. By remoulding the traditional internal model into a finite number of adjacent integer-order internal models, novel internal model based on fractional-order cycle delay link is obtained. Meanwhile, finite number of adjacent integer-order phase-lead links are used to replace the traditional single fixed integer-order phase-lead link, to achieve the fractional-order phase compensation. In the algorithm, the classical Lagrange interpolation method is adopted to achieve the fractionization of two links. The influence of interpolation points and interpolation length on fitting effect is analyzed. Two case studies are implemented and performance differences between the proposed method and traditional methods are analyzed and compared from the perspective of frequency characteristics. Finally, experiments on the established 16.5 kV·A prototype have verified the validity of proposed strategy.
引文
[1]肖湘宁,廖坤玉,唐松浩,等.配电网电力电子化的发展和超高次谐波新问题[J].电工技术学报,2018,33(4):707-720.Xiao Xiangning,Liao Kunyu,Tang Songhao,et al Development of power-electronized distribution grids and the new supraharmonics issues[J].Transactions of China Electrotechnical Society,2018,33(4):707-720.
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[14]周娟,郑婉玉,刘刚,等.一种具有频率适应性的nk±m次谐波重复控制策略及其在四桥臂APF中的应用[J].电源学报,2017,15(4):10-16.Zhou Juan,Zheng Wanyu,Liu Gang,et al.Frequency adaptive nk±m order harmonic repetitive controller and its application in four-leg APF[J].Journal of Power Supply,2017,15(4):10-16.
[15]孙高阳,刘亚静,李秉格,等.一种消除反馈延迟的全数字锁相环[J].电工技术学报,2017,32(20):171-178.Sun Gaoyang,Liu Yajing,Li Bingge,et al.An alldigital phase-locked loop with compensating feedback unit delay[J].Transactions of China Electrotechnical Society,2017,32(20):171-178.
[16]郁祎琳,徐永海,刘晓博.滑窗迭代DFT的谐波电流检测方法[J].电力系统保护与控制,2011,39(13):78-82.Yu Yilin,Xu Yonghai,Liu Xiaobo.Study of harmonic current detection based on sliding-window iterative algorithm of DFT[J].Power System Protection and Control,2011,39(13):78-82.
[17]郑诗程,徐礼萍,郎佳红,等.基于重复PI控制和前馈控制的静止无功发生器[J].电工技术学报,2016,31(6):219-225.Zheng Shicheng,Xu Liping,Lang Jiahong,et al.Static var generator based on repetitive PI control and feedforward control[J].Transactions of China Electrotechnical Society,2016,31(6):219-225.
[18]Jeffreys H,Jeffreys B S.Lagrange’s interpolation formula[J].Methods of Mathematical Physics,1988:260.
[19]Oetken G.A new approach for the design of digital interpolating filters[J].IEEE Transactions on Acoustics,Speech,and Signal Processing,1979,27(6):637-643.
[20]Laakso T I,V?lim?ki V,Karjalainen M,et al.Splitting the unit delay tools for fractional delay filter design[J].IEEE Signal Processing Magazine,1996,13(1):30-60.
[2]尹春杰,王芳,石磊,等.基于瞬时电压矢量定向的有源电力滤波器补偿电流检测[J].电工技术学报,2017,32(7):112-118.Yin Chunjie,Wang Fang,Shi Lei,et al.A novel compensation current detection method for APFbased on transient voltage space vector orientation[J].Transactions of China Electrotechnical Society,2017,32(7):112-118.
[3]Acuna P,Moran L,Rivera M,et al.Improved active power filter performance for renewable power generation systems[J].IEEE Transactions on Power Electronics,2014,29(2):687-694.
[4]Grino R,Cardoner R,Costa-CastellóR,et al.Digital repetitive control of a three-phase four-wire shunt active filter[J].IEEE Transactions on Industrial Electronics,2007,54(3):1495-1503.
[5]张宸宇,梅军,郑建勇,等.基于内置重复控制器改进无差拍的有源滤波器双滞环控制方法[J].电工技术学报,2015,30(22):124-132.Zhang Chenyu,Mei Jun,Zheng Jianyong,et al.Active power filter double hysteresis method with improved deadbeat control based on built-in repetitive controller[J].Transactions of China Electrotechnical Society,2015,30(22):124-132.
[6]贾要勤,王晓滨,杨强.并联有源电力滤波器的自适应重复控制[J].电工技术学报,2011,26(10):118-122.Jia Yaoqin,Wang Xiaobin,Yang Qiang.Adaptive repetitive control of parallel active power filter[J].Transactions of China Electrotechnical Society,2011,26(10):118-123.
[7]徐群伟,钟晓剑,胡健,等.基于误差迭代PI和改进重复控制的APF补偿电流控制[J].电力系统自动化,2015,39(3):124-131.Xu Qunwei,Zhong Xiaojian,Hu Jian,et al.Compensation current control of APF based on error iteration PI and improved repetitive control[J].Automation of Electric Power Systems,2015,39(3):124-131.
[8]姜泽旭,王海欣,黄海宏,等.三相三线制APF中半周期重复控制的研究[J].电器与能效管理技术,2018(13):1-5.Jiang Zexu,Wang Haixin,Huang Haihong,et al.Study on semi-periodic repetitive control of threephase three-wire APF[J].Electrical&Energy Management Technology,2018(13):1-5.
[9]陈东,张军明,钱照明.一种具有频率变化适应性的并网逆变器改进型重复控制方法[J].电工技术学报,2014,29(6):64-70.Chen Dong,Zhang Junming,Qian Zhaoming.An improved repetitive control scheme for gridconnected inverter with frequency-varying adaptability[J]Transactions of China Electrotechnical Society,2014,29(6):64-70.
[10]梁营玉,刘建政,李治艳.有源电力滤波器改进无差拍-重复控制策略[J].电工技术学报,2018,33(19):4573-4582.Liang Yingyu,Liu Jianzheng,Li Zhiyan.Improved deadbeat-repetitive control strategy for active power filter[J].Transactions of China Electrotechnical Society,2018,33(19):4573-4582.
[11]Hornik T,Zhong Q C.H∞repetitive voltage control of grid-connected inverters with a frequency adaptive mechanism[J].IET Power Electronics,2010,3(6):925-935.
[12]刘正春,朱长青,王勇,等.抗IPS频率波动的两种改进重复控制方法[J].电网技术,2018,42(9):3014-3023.Liu Zhengchun,Zhu Changqing,Wang Yong,et al.Two improved repetitive control methods against frequency fluctuation in IPS[J].Power System Technology,2018,42(9):3014-3023.
[13]高峰.变频电网三相有源电力滤波器重复控制策略[J].控制理论与应用,2018,35(4):447-456.Gao Feng.A repetitive control strategy for threephase active power filters in variable-frequency power grid[J].Control Theory&Applications,2018,35(4):447-456.
[14]周娟,郑婉玉,刘刚,等.一种具有频率适应性的nk±m次谐波重复控制策略及其在四桥臂APF中的应用[J].电源学报,2017,15(4):10-16.Zhou Juan,Zheng Wanyu,Liu Gang,et al.Frequency adaptive nk±m order harmonic repetitive controller and its application in four-leg APF[J].Journal of Power Supply,2017,15(4):10-16.
[15]孙高阳,刘亚静,李秉格,等.一种消除反馈延迟的全数字锁相环[J].电工技术学报,2017,32(20):171-178.Sun Gaoyang,Liu Yajing,Li Bingge,et al.An alldigital phase-locked loop with compensating feedback unit delay[J].Transactions of China Electrotechnical Society,2017,32(20):171-178.
[16]郁祎琳,徐永海,刘晓博.滑窗迭代DFT的谐波电流检测方法[J].电力系统保护与控制,2011,39(13):78-82.Yu Yilin,Xu Yonghai,Liu Xiaobo.Study of harmonic current detection based on sliding-window iterative algorithm of DFT[J].Power System Protection and Control,2011,39(13):78-82.
[17]郑诗程,徐礼萍,郎佳红,等.基于重复PI控制和前馈控制的静止无功发生器[J].电工技术学报,2016,31(6):219-225.Zheng Shicheng,Xu Liping,Lang Jiahong,et al.Static var generator based on repetitive PI control and feedforward control[J].Transactions of China Electrotechnical Society,2016,31(6):219-225.
[18]Jeffreys H,Jeffreys B S.Lagrange’s interpolation formula[J].Methods of Mathematical Physics,1988:260.
[19]Oetken G.A new approach for the design of digital interpolating filters[J].IEEE Transactions on Acoustics,Speech,and Signal Processing,1979,27(6):637-643.
[20]Laakso T I,V?lim?ki V,Karjalainen M,et al.Splitting the unit delay tools for fractional delay filter design[J].IEEE Signal Processing Magazine,1996,13(1):30-60.