基于分数阶滤波器的三相锁相环技术
|
摘要
采用复数滤波器(CCF)研究电网同步锁相技术是目前比较流行的方法。为进一步提高锁相环(PLL)的动态性能,利用分数阶控制可以改善系统动态品质这一特性,提出一种将CCF-PLL改为分数阶滤波器(FOF)的PLL算法。设计的前级多重FOF结构会在电网基波正负序(FPC/FNC)及各次谐波处产生谐振尖峰,通过闭环控制,可以精确分离出FPC、FNC和谐波,从而使后级的同步旋转坐标系PLL提取出纯净的频率、相位等信息。为分析所提PLL的动态特性,推导了其线性化数学模型,并在此基础上对系统进行设计,确定其相关参数。研究发现,在相同开环截止频率下,提出的PLL比CCF-PLL具备更优异的动态性能。最后,通过Matlab/Simulink仿真和相关实验验证了该PLL的正确性和良好的动态品质。
Using complex coefficient filter(CCF) to study grid synchronization is a popular method at present. In order to further improve the dynamic performance of phase-locked loop(PLL), a new PLL algorithm that changes the CCF-PLL to fractional-order filter(FOF) is put forward by using the characteristic of fractional-order control that can improve the dynamic quality of the system. The designed pre-stage multiple FOF structure can generate the resonance peaks in the positive-/negative-sequence component(FPC/FNC) and harmonics of the grid fundamental wave. Through the closed-loop control, FPC/FNC and harmonics are precisely separated, so that the pure frequency and phase are extracted by the post-stage synchronous rotating frame PLL. To analyze the dynamic performance of the proposed PLL, its linearized mathematical model is derived, thereby the corresponding system and related parameters are designed. The study shows that with the same open-loop cut-off frequency, the proposed PLL has better dynamic performance than the CCF-PLL.Finally, the proposed PLL is tested by Matlab/Simulink simulation and related experiments, which shows good dynamic behavior.
Using complex coefficient filter(CCF) to study grid synchronization is a popular method at present. In order to further improve the dynamic performance of phase-locked loop(PLL), a new PLL algorithm that changes the CCF-PLL to fractional-order filter(FOF) is put forward by using the characteristic of fractional-order control that can improve the dynamic quality of the system. The designed pre-stage multiple FOF structure can generate the resonance peaks in the positive-/negative-sequence component(FPC/FNC) and harmonics of the grid fundamental wave. Through the closed-loop control, FPC/FNC and harmonics are precisely separated, so that the pure frequency and phase are extracted by the post-stage synchronous rotating frame PLL. To analyze the dynamic performance of the proposed PLL, its linearized mathematical model is derived, thereby the corresponding system and related parameters are designed. The study shows that with the same open-loop cut-off frequency, the proposed PLL has better dynamic performance than the CCF-PLL.Finally, the proposed PLL is tested by Matlab/Simulink simulation and related experiments, which shows good dynamic behavior.
引文
[1]Sonti V,Jain S,Bhattacharya S.Analysis of the modulation strategy for the minimization of the leakage current in the PV grid-connected cascaded multilevel inverter[J].IEEE Transactions on Power Electronics,2017,32(2):1156-1169.
[2]朱永强,贾利虎,谢文超,等.一种用于单相/三相变换的新型电力电子变换技术[J].电工技术学报,2018,33(7):1433-1439.Zhu Yongqiang,Jia Lihu,Xie Wenchao,et al.A new power electronic transformation technology for singlephase and three-phase[J].Transactions of China Electrotechnical Society,2018,33(7):1433-1439.
[3]Lee K J,Lee J P,Shin D,et al.A novel grid synchronization PLL method based on adaptive low-pass notch filter for grid-connected PCS[J].IEEE Transactions on Industrial Electronics,2014,61(1):292-301.
[4]Zhu Ye,Xu Dehong,He Ning,et al.A novel RPV(reactive-power-variation)antiislanding method based on adapted reactive power perturbation[J].IEEETransactions on Power Electronics,2013,28(11):4998-5012.
[5]沈虹,周文飞,王怀宝,等.基于无功电流控制的并网逆变器孤岛检测[J].电工技术学报,2017,32(16):294-300.Shen Hong,Zhou Wenfei,Wang Huaibao,et al.Islanding detection for grid-connected inverter based on reactive current control[J].Transactions of China Electrotechnical Society,2017,32(16):294-300.
[6]Guo Xiaoqiang,Liu Wenzhao,Lu Zhigang.Flexible power regulation and current-limited control of the grid-connected inverter under unbalanced grid voltage faults[J].IEEE Transactions on Industrial Electronics,2017,64(9):7425-7432.
[7]Hans F,Schumacher W,Harnefors L.Small-signal modeling of three-phase synchronous reference frame phase-locked loops[J].IEEE Transactions on Power Electronics,2018,33(7):5556-5560.
[8]曾正,邵伟华,刘清阳,等.并网逆变器数字锁相环的数学物理本质分析[J].电工技术学报,2018,33(4):808-816.Zeng Zheng,Shao Weihua,Liu Qingyang,et al.Mathematical and physical fundaments of digital phase-locked loop for grid-connected inverters[J].Transactions of China Electrotechnical Society,2018,33(4):808-816.
[9]Rodríguez P,Pou J,Bergas J,et al.Decoupled double synchronous reference frame PLL for power converters control[J].IEEE Transactions on Power Electronics,2007,22(2):584-592.
[10]González-Espín F,Figueres E,GarceráG.An adaptive synchronous-reference-frame phase-locked loop for power quality improvement in a polluted utility grid[J].IEEE Transactions on Industrial Electronics,2012,59(6):2718-2731.
[11]Zamani H,Karimi-Ghartemani M,Mojiri M.Analysis of power system oscillations from PMU data using an EPLL-based approach[J].IEEE Transactions on Instrumentation and Measurement,2018,67(2):307-316.
[12]张纯江,赵晓君,郭忠南,等.二阶广义积分器的三种改进结构及其锁相环应用对比分析[J].电工技术学报,2017,32(22):42-49.Zhang Chunjiang,Zhao Xiaojun,Guo Zhongnan,et al Three improved second order generalized integrators and the comparative analysis in phase locked loop application[J].Transactions of China Electrotechnical Society,2017,32(22):42-49.
[13]涂娟,汤宁平.基于改进型DSOGI-PLL的电网电压同步信号检测[J].中国电机工程学报,2016,36(9):2350-2356.Tu Juan,Tang Ningping.Synchronizing signal detection for grid voltage based on modified DSOGI-PLL[J].Proceedings of the CSEE,2016,36(9):2350-2356.
[14]Rodríguez P,Luna A,Candela I,et al.Multiresonant frequency-locked loop for grid synchronization of power converters under distorted grid conditions[J].IEEE Transactions on Industrial Electronics,2011,58(1):127-138.
[15]Guo Xiaoqiang,Wu Weiyang,Chen Zhe.Multiplecomplex coefficient-filter-based phase-locked loop and synchronization technique for three-phase gridinterfaced converters in distributed utility networks[J].IEEE Transactions on Industrial Electronics2011,58(4):1194-1204.
[16]Li Weiwei,Ruan Xinbo,Bao Chenlei,et al.Grid synchronization systems of three-phase gridconnected power converters:a complex-vector-filter perspective[J].IEEE Transactions on Industrial Electronics,2014,61(4):1855-1870.
[17]Golestan S,Monfared M,Freijedo F D,et al.Performance improvement of a prefiltered synchronousreference-frame PLL by using a PID-type loop filter[J].IEEE Transactions on Industrial Electronics,2014,61(7):3469-3479.
[18]Ramezani M,Golestan S,Li S,et al.A simple approach to enhance the performance of complexcoefficient filter-based PLL in grid-connected applications[J].IEEE Transactions on Industrial Electronics,2018,65(6):5081-5085.
[19]Golestan S,Monfared M,Freijedo F D.Designoriented study of advanced synchronous reference frame phase-locked loops[J].IEEE Transactions on Power Electronics,2013,28(2):765-778.
[20]赵新,金新民,周飞,等.采用降阶谐振调节器的并网逆变器锁频环技术[J].中国电机工程学报,2013,33(15):38-44.Zhao Xin,Jin Xinmin,Zhou Fei,et al.A frequencylocked loop technology of grid-connected inverters based on the reduced order resonant controller[J].Proceedings of the CSEE,2013,33(15):38-44.
[21]何宇,漆汉宏,邓超,等.一种嵌入重复控制内模的三相锁相环的设计与实现[J].电工技术学报,2016,31(22):83-91.He Yu,Qi Hanhong,Deng Chao,et al.A novel three-phase phase-locked loop method based on internal model of repetitive control[J].Transactions of China Electrotechnical Society,2016,31(22):83-91.
[22]高哲.一类采用分数阶PIl控制器的分数阶系统可镇定性判定准则[J].自动化学报,2017,43(11):1993-2002.Gao Zhe.Stabilization criterion for a class of interval fractional-order systems using fractional-order PIlcontrollers[J].Acta Automatica Sinica,2017,43(11):1993-2002.
[23]Hristov J,El G M.Thermal impedance estimations by semi-derivatives and semi-integrals:1-D semi-infinite cases[J].Thermal Science,2013,17(2):581-589.
[24]Tang Shiqiang,Sun Yize,Chen Yujie,et al.An enhanced MPPT method combining fractional-order and fuzzy logic control[J].IEEE Journal of Photovoltaics,2017,7(2):640-650.
[25]Boukal Y,Darouach M,Zasadzinski M,et al.Robust H∞observerbased control of fractional-order systems with gain parametrization[J].IEEE Transactions on Automatic Control,2017,62(11):5710-5723.
[26]Jiang Yanwei,Zhang Bo.High-power fractionalorder capacitor with 1 [27]胡建兵,赵灵冬.分数阶系统稳定性理论与控制研究[J].物理学报,2013,62(24):5041-5047.Hu Jianbing,Zhao Lingdong.Stability theorem and control of fractional systems[J].Acta Physica Sinica,2013,62(24):5041-5047.
[28]Huang Qicheng,Rajashekara K.An improved delayed signal cancellation PLL for fast grid synchronization under distorted and unbalanced grid condition[J].IEEE Transactions on Industry Applications,2017,53(5):4985-4997.
[29]Kleinz M,Osler T J.A child's garden of fractional derivatives[J].College Mathematics Journal,2000,31(2):82-88.
[30]Teodorescu R,Liserre M,Rodríguez P.Grid converters for photovoltaic and wind power systems[M].Hoboken:John Wiley&Sons,2011.
[31]Chung S K.A phase tracking system for three phase utility interface inverters[J].IEEE Transactions on Power Electronics,2000,15(3):431-438.
[32]胡寿松.自动控制原理(第六版)[M].北京:科学出版社,2013.
[33]Xiong Linyun,Wang Jie,Mi Xiao,et al.Fractional order sliding mode based direct power control of grid-connected DFIG[J].IEEE Transactions on Power Systems,2018,33(3):3087-3096.
[34]Ivo Petrá?.Fractional-order nonlinear systems:modeling,analysis and simulation[M].Heidelberg:Springer-Verlag,2011.
[35]曲涛,任元,林海雪,等.GB/T 14549-1993电能质量-公用电网谐波[S].1993.
[36]潘艳,朱伟江,刘迅,等.GB/T 15945-2008电能质量-电力系统频率偏差[S].2008.
[37]侯铁信,卜正良,林海雪,等.GB/T 15543-2008电能质量-三相电压不平衡[S].2008.
[2]朱永强,贾利虎,谢文超,等.一种用于单相/三相变换的新型电力电子变换技术[J].电工技术学报,2018,33(7):1433-1439.Zhu Yongqiang,Jia Lihu,Xie Wenchao,et al.A new power electronic transformation technology for singlephase and three-phase[J].Transactions of China Electrotechnical Society,2018,33(7):1433-1439.
[3]Lee K J,Lee J P,Shin D,et al.A novel grid synchronization PLL method based on adaptive low-pass notch filter for grid-connected PCS[J].IEEE Transactions on Industrial Electronics,2014,61(1):292-301.
[4]Zhu Ye,Xu Dehong,He Ning,et al.A novel RPV(reactive-power-variation)antiislanding method based on adapted reactive power perturbation[J].IEEETransactions on Power Electronics,2013,28(11):4998-5012.
[5]沈虹,周文飞,王怀宝,等.基于无功电流控制的并网逆变器孤岛检测[J].电工技术学报,2017,32(16):294-300.Shen Hong,Zhou Wenfei,Wang Huaibao,et al.Islanding detection for grid-connected inverter based on reactive current control[J].Transactions of China Electrotechnical Society,2017,32(16):294-300.
[6]Guo Xiaoqiang,Liu Wenzhao,Lu Zhigang.Flexible power regulation and current-limited control of the grid-connected inverter under unbalanced grid voltage faults[J].IEEE Transactions on Industrial Electronics,2017,64(9):7425-7432.
[7]Hans F,Schumacher W,Harnefors L.Small-signal modeling of three-phase synchronous reference frame phase-locked loops[J].IEEE Transactions on Power Electronics,2018,33(7):5556-5560.
[8]曾正,邵伟华,刘清阳,等.并网逆变器数字锁相环的数学物理本质分析[J].电工技术学报,2018,33(4):808-816.Zeng Zheng,Shao Weihua,Liu Qingyang,et al.Mathematical and physical fundaments of digital phase-locked loop for grid-connected inverters[J].Transactions of China Electrotechnical Society,2018,33(4):808-816.
[9]Rodríguez P,Pou J,Bergas J,et al.Decoupled double synchronous reference frame PLL for power converters control[J].IEEE Transactions on Power Electronics,2007,22(2):584-592.
[10]González-Espín F,Figueres E,GarceráG.An adaptive synchronous-reference-frame phase-locked loop for power quality improvement in a polluted utility grid[J].IEEE Transactions on Industrial Electronics,2012,59(6):2718-2731.
[11]Zamani H,Karimi-Ghartemani M,Mojiri M.Analysis of power system oscillations from PMU data using an EPLL-based approach[J].IEEE Transactions on Instrumentation and Measurement,2018,67(2):307-316.
[12]张纯江,赵晓君,郭忠南,等.二阶广义积分器的三种改进结构及其锁相环应用对比分析[J].电工技术学报,2017,32(22):42-49.Zhang Chunjiang,Zhao Xiaojun,Guo Zhongnan,et al Three improved second order generalized integrators and the comparative analysis in phase locked loop application[J].Transactions of China Electrotechnical Society,2017,32(22):42-49.
[13]涂娟,汤宁平.基于改进型DSOGI-PLL的电网电压同步信号检测[J].中国电机工程学报,2016,36(9):2350-2356.Tu Juan,Tang Ningping.Synchronizing signal detection for grid voltage based on modified DSOGI-PLL[J].Proceedings of the CSEE,2016,36(9):2350-2356.
[14]Rodríguez P,Luna A,Candela I,et al.Multiresonant frequency-locked loop for grid synchronization of power converters under distorted grid conditions[J].IEEE Transactions on Industrial Electronics,2011,58(1):127-138.
[15]Guo Xiaoqiang,Wu Weiyang,Chen Zhe.Multiplecomplex coefficient-filter-based phase-locked loop and synchronization technique for three-phase gridinterfaced converters in distributed utility networks[J].IEEE Transactions on Industrial Electronics2011,58(4):1194-1204.
[16]Li Weiwei,Ruan Xinbo,Bao Chenlei,et al.Grid synchronization systems of three-phase gridconnected power converters:a complex-vector-filter perspective[J].IEEE Transactions on Industrial Electronics,2014,61(4):1855-1870.
[17]Golestan S,Monfared M,Freijedo F D,et al.Performance improvement of a prefiltered synchronousreference-frame PLL by using a PID-type loop filter[J].IEEE Transactions on Industrial Electronics,2014,61(7):3469-3479.
[18]Ramezani M,Golestan S,Li S,et al.A simple approach to enhance the performance of complexcoefficient filter-based PLL in grid-connected applications[J].IEEE Transactions on Industrial Electronics,2018,65(6):5081-5085.
[19]Golestan S,Monfared M,Freijedo F D.Designoriented study of advanced synchronous reference frame phase-locked loops[J].IEEE Transactions on Power Electronics,2013,28(2):765-778.
[20]赵新,金新民,周飞,等.采用降阶谐振调节器的并网逆变器锁频环技术[J].中国电机工程学报,2013,33(15):38-44.Zhao Xin,Jin Xinmin,Zhou Fei,et al.A frequencylocked loop technology of grid-connected inverters based on the reduced order resonant controller[J].Proceedings of the CSEE,2013,33(15):38-44.
[21]何宇,漆汉宏,邓超,等.一种嵌入重复控制内模的三相锁相环的设计与实现[J].电工技术学报,2016,31(22):83-91.He Yu,Qi Hanhong,Deng Chao,et al.A novel three-phase phase-locked loop method based on internal model of repetitive control[J].Transactions of China Electrotechnical Society,2016,31(22):83-91.
[22]高哲.一类采用分数阶PIl控制器的分数阶系统可镇定性判定准则[J].自动化学报,2017,43(11):1993-2002.Gao Zhe.Stabilization criterion for a class of interval fractional-order systems using fractional-order PIlcontrollers[J].Acta Automatica Sinica,2017,43(11):1993-2002.
[23]Hristov J,El G M.Thermal impedance estimations by semi-derivatives and semi-integrals:1-D semi-infinite cases[J].Thermal Science,2013,17(2):581-589.
[24]Tang Shiqiang,Sun Yize,Chen Yujie,et al.An enhanced MPPT method combining fractional-order and fuzzy logic control[J].IEEE Journal of Photovoltaics,2017,7(2):640-650.
[25]Boukal Y,Darouach M,Zasadzinski M,et al.Robust H∞observerbased control of fractional-order systems with gain parametrization[J].IEEE Transactions on Automatic Control,2017,62(11):5710-5723.
[26]Jiang Yanwei,Zhang Bo.High-power fractionalorder capacitor with 1
[28]Huang Qicheng,Rajashekara K.An improved delayed signal cancellation PLL for fast grid synchronization under distorted and unbalanced grid condition[J].IEEE Transactions on Industry Applications,2017,53(5):4985-4997.
[29]Kleinz M,Osler T J.A child's garden of fractional derivatives[J].College Mathematics Journal,2000,31(2):82-88.
[30]Teodorescu R,Liserre M,Rodríguez P.Grid converters for photovoltaic and wind power systems[M].Hoboken:John Wiley&Sons,2011.
[31]Chung S K.A phase tracking system for three phase utility interface inverters[J].IEEE Transactions on Power Electronics,2000,15(3):431-438.
[32]胡寿松.自动控制原理(第六版)[M].北京:科学出版社,2013.
[33]Xiong Linyun,Wang Jie,Mi Xiao,et al.Fractional order sliding mode based direct power control of grid-connected DFIG[J].IEEE Transactions on Power Systems,2018,33(3):3087-3096.
[34]Ivo Petrá?.Fractional-order nonlinear systems:modeling,analysis and simulation[M].Heidelberg:Springer-Verlag,2011.
[35]曲涛,任元,林海雪,等.GB/T 14549-1993电能质量-公用电网谐波[S].1993.
[36]潘艳,朱伟江,刘迅,等.GB/T 15945-2008电能质量-电力系统频率偏差[S].2008.
[37]侯铁信,卜正良,林海雪,等.GB/T 15543-2008电能质量-三相电压不平衡[S].2008.