基于线性卡尔曼滤波器的三相锁频环设计
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摘要
电网同步算法对提升并网控制器的性能有重要意义。该文基于线性卡尔曼滤波器提出一种三相锁频环技术(frequency-locked-loopbasedonlinearKalmanfilter,LKF-FLL),首先分析卡尔曼滤波器关于含直流偏置的电压畸变信号正交分解的有效性,分析表明当频率为已知量时可采用线性卡尔曼滤波器估计电网状态,包括频率、正/负序和直流偏置;接着针对基频观测采用三相锁频环,通过误差分析提出自适应三相锁频环结构;然后利用状态观测器的思想设计成本函数求取优化增益系数,逆推卡尔曼滤波参数,避免按照经验选取,最后通过和已有技术对比,显示所提三相锁频环在三相电压信号含直流偏置的畸变情况下的有效性和优越性,并通过仿真实验进行验证。
The effectiveness of grid synchronization algorithm is of great importance to improve the performance of grid-connected controller. A three-phase frequency-lockedloop based on linear Kalman filter(LKF-FLL) was proposed. Firstly, the validity of Kalman filter for orthogonal decomposition of voltage distortion signal with DC bias was analyzed. The analysis shows that when the frequency is a known quantity, the linear Kalman filter can be used to estimate the grid status, including frequency, positive/negative sequence and DC bias. Then the adaptive three-phase frequency-locked-loop structure was proposed through error analysis for the fundamental frequency observation. Next, using the state observer′s idea to design cost function for the optimal gain coefficient, and inversely calculate Kalman filter parameters, which can avoid choosing the filter parameters according to experience only. Finally, by comparing with the existing technology, such as second-order generalized integrator(SOGI), adaptive victoria filter(AVF), the effectiveness and superiority of the proposed three-phase FLL were shown in the case of distorted three-phase voltage with DC bias.
The effectiveness of grid synchronization algorithm is of great importance to improve the performance of grid-connected controller. A three-phase frequency-lockedloop based on linear Kalman filter(LKF-FLL) was proposed. Firstly, the validity of Kalman filter for orthogonal decomposition of voltage distortion signal with DC bias was analyzed. The analysis shows that when the frequency is a known quantity, the linear Kalman filter can be used to estimate the grid status, including frequency, positive/negative sequence and DC bias. Then the adaptive three-phase frequency-locked-loop structure was proposed through error analysis for the fundamental frequency observation. Next, using the state observer′s idea to design cost function for the optimal gain coefficient, and inversely calculate Kalman filter parameters, which can avoid choosing the filter parameters according to experience only. Finally, by comparing with the existing technology, such as second-order generalized integrator(SOGI), adaptive victoria filter(AVF), the effectiveness and superiority of the proposed three-phase FLL were shown in the case of distorted three-phase voltage with DC bias.
引文
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[22]Deng Zhe,Zhou Fengwu,Lin Huipin,et al.A novel fast grid-synchronization method under grid failure based on dual-input SOGI-FLL[J].Transactions of China Electrotechnical Society,2013,28(12):32-43(in Chinese).
[23]Rodriguez P,Luna A,Candela I,et al.Multiresonant frequency-locked loop for grid synchronization of power converters under distorted grid conditions[J].IEEETransactions on Industrial Electronics,2011,58(1):127-138.
[24]Vazquez S,Sanchez J A,Reyes M R,et al.Adaptive vectorial filter for grid synchronization of power converters under unbalanced and/or distorted grid conditions[J].IEEE Transactions on Industrial Electronics,2014,61(3):1355-1367.
[25]Reza S,Ciobotaru M,Agelidis V G.Accurate estimation of single-phase grid voltage fundamental amplitude and frequency by using a frequency adaptive linear Kalman filter[J].IEEE Journal of Emerging and Selected Topics in Power Electronics,2016,4(4):1226-1235.
[26]Yazdanian M,Mojiri M,Sheikholeslam F.An extended Kalman filter for identification of biased sinusoidal signals[C]//Proceedings of the 20th Iranian Conference on Electrical Engineering(ICEE2012).Tehran:IEEE,2012.
[27]Hajimolahoseini H,Taban M R,Abutalebi HR.Improvement of Extended Kalman Filter frequency tracker for nonstationary harmonic signals[C]//Proceedings of 2008 International Symposium on Telecommunications.Tehran:IEEE,2008.
[28]Sun Ming,Sahinoglu Z.Extended Kalman filter based grid synchronization in the presence of voltage unbalance for smart grid[C]//Proceedings of ISGT 2011.Anaheim:IEEE,2011.
[29]Chen C I,Chang G W,Hong R C,et al.Extended real model of Kalman Filter for time-varying harmonics estimation[J].IEEE Transactions on Power Delivery,2010,25(1):17-26.
[30]江辉,谢兴,王志忠,等.基于优化无迹Kalman滤波的电网动态谐波估计[J].深圳大学学报:理工版,2015,32(2):188-195.
[31]Jiang Hui,Xie Xing,Wang Zhizhong,et al.Dynamic harmonic estimation based on optimized unscented Kalman filter model[J].Journal of Shenzhen University:Science and Engineering,2015,32(2):188-195(in Chinese).
[32]Bittanti S,Savaresi S M.Frequency tracking via extended Kalman filter:parameter design[C]//Proceedings of 2000American Control Conference.Chicago:IEEE,2000.
[33]Reza M S,Ciobotaru M,Agelidis V G.Frequency adaptive linear Kalman filter for fast and accurate estimation of grid voltage parameters[C]//Proceedings of2012 IEEE International Conference on Power System Technology(POWERCON).Auckland:IEEE,2012.
[34]Reza M S,Ciobotaru M,Agelidis V G.Instantaneous power quality analysis using frequency adaptive Kalman filter technique[C]//Proceedings of the 7th International Power Electronics and Motion Control Conference.Harbin,China:IEEE,2012.
[2]王宝诚,伞国成,郭小强,等.分布式发电系统电网同步锁相技术[J].中国电机工程学报,2013,33(1):50-55.
[3]Wang Baocheng,San Guocheng,Guo Xiaoqiang,et al.Grid synchronization and PLL for distributed power generation systems[J].Proceedings of the CSEE,2013,33(1):50-55(in Chinese).
[4]Darvish H,Wang Xin.Synchronization of unbalanced three phase voltages with nonlinear estimation[C]/Proceedings of 2015 IEEE Power&Energy Society Innovative Smart Grid Technologies Conference(ISGT).Washington:IEEE,2015.
[5]徐岩,张晓明,王瑜,等.基于离散傅里叶变换的频谱分析新方法[J].电力系统保护与控制,2011,39(11):38-43.
[6]Xu Yan,Zhang Xiaoming,Wang Yu,et al.A new method of spectrum analysis based on DFT[J].Power System Protection and Control,2011,39(11):38-43(in Chinese).
[7]荣海舟,粟时平,逯培兵,等.一种改进型FFT谐波分析方法[J].电力系统及其自动化学报,2009,21(1):124-128.
[8]Rong Haizhou,Su Shiping,Lu Peibing,et al.Improved FFT method for harmonic analysis base on least square method[J].Proceedings of the CSU-EPSA,2009,21(1):124-128(in Chinese).
[9]Quan Xiangjun,Dou Xiaobo,Wu Zaijun,et al.A concise discrete adaptive filter for frequency estimation under distorted three-phase voltage[J].IEEE Transactions on Power Electronics,2017,32(12):9400-9412.
[10]全相军,窦晓波,吴在军,等.基于离散谐振器的自适应数字锁频环设计[J].中国电机工程学报,2016,36(13):3620-3628.
[11]Quan Xiangjun,Dou Xiaobo,Wu Zaijun,et al.The design for digital adaptive frequency-locked-loop based on discrete resonators[J].Proceedings of the CSEE,2016,36(13):3620-3628(in Chinese).
[12]刘桂花,曹小娇,王卫.弱电网下单相光伏并网逆变器锁频环同步方法[J].中国电机工程学报,2015,35(19):5022-5029.
[13]Liu Guihua,Cao Xiaojiao,Wang Wei.A frequency locked loop grid synchronization method of single-phase gridconnected PV inverter under weak grid[J].Proceedings of the CSEE,2015,35(19):5022-5029(in Chinese).
[14]Sun Shaohua,Liu Bo,Ben Hongqi,et al.Adaptive frequency locked loop for grid synchronization based fast positive-negative sequence decomposition under distorted grid conditions[J].Proceedings of the CSEE,2014,34(27):4594-4604.
[15]全相军,窦晓波,吴在军,等.基于离散复变量自适应滤波器的三相电网同步算法[J].电力系统自动化,2017,41(16):158-164.
[16]Quan Xiangjun,Dou Xiaobo,Wu Zaijun,et al.Three-phase grid synchronization algorithm based on adaptive discrete complex-variable filter[J].Automation of Electric Power Systems,2017,41(16):158-164(in Chinese).
[17]王德玉,刘文钊,郭小强,等.非理想电网电压情况下并网变换器高阶解耦复数滤波并网同步技术[J].中国电机工程学报,2015,35(10):2576-2583.
[18]Wang Deyu,Liu Wenzhao,Guo Xiaoqiang,et al.Grid synchronization technique with high-order decoupled complex filters for grid-connected converters under non-ideal grid voltages[J].Proceedings of the CSEE,2015,35(10):2576-2583(in Chinese).
[19]唐轶,谢永强,王扬,等.基于解耦双同步坐标变换的三相锁相环研究[J].电测与仪表,2017,54(8):14-20.
[20]Tang Yi,Xie Yongqiang,Wang Yang,et al.Study on PLLbased on decoupled double synchronous reference frame[J].Electrical Measurement&Instrumentation,2017,54(8):14-20(in Chinese).
[21]邓哲,周峰武,林辉品,等.电网故障时基于双输入SOGI-FLL的新型电网快速同步方法[J].电工技术学报,2013,28(12):32-43.
[22]Deng Zhe,Zhou Fengwu,Lin Huipin,et al.A novel fast grid-synchronization method under grid failure based on dual-input SOGI-FLL[J].Transactions of China Electrotechnical Society,2013,28(12):32-43(in Chinese).
[23]Rodriguez P,Luna A,Candela I,et al.Multiresonant frequency-locked loop for grid synchronization of power converters under distorted grid conditions[J].IEEETransactions on Industrial Electronics,2011,58(1):127-138.
[24]Vazquez S,Sanchez J A,Reyes M R,et al.Adaptive vectorial filter for grid synchronization of power converters under unbalanced and/or distorted grid conditions[J].IEEE Transactions on Industrial Electronics,2014,61(3):1355-1367.
[25]Reza S,Ciobotaru M,Agelidis V G.Accurate estimation of single-phase grid voltage fundamental amplitude and frequency by using a frequency adaptive linear Kalman filter[J].IEEE Journal of Emerging and Selected Topics in Power Electronics,2016,4(4):1226-1235.
[26]Yazdanian M,Mojiri M,Sheikholeslam F.An extended Kalman filter for identification of biased sinusoidal signals[C]//Proceedings of the 20th Iranian Conference on Electrical Engineering(ICEE2012).Tehran:IEEE,2012.
[27]Hajimolahoseini H,Taban M R,Abutalebi HR.Improvement of Extended Kalman Filter frequency tracker for nonstationary harmonic signals[C]//Proceedings of 2008 International Symposium on Telecommunications.Tehran:IEEE,2008.
[28]Sun Ming,Sahinoglu Z.Extended Kalman filter based grid synchronization in the presence of voltage unbalance for smart grid[C]//Proceedings of ISGT 2011.Anaheim:IEEE,2011.
[29]Chen C I,Chang G W,Hong R C,et al.Extended real model of Kalman Filter for time-varying harmonics estimation[J].IEEE Transactions on Power Delivery,2010,25(1):17-26.
[30]江辉,谢兴,王志忠,等.基于优化无迹Kalman滤波的电网动态谐波估计[J].深圳大学学报:理工版,2015,32(2):188-195.
[31]Jiang Hui,Xie Xing,Wang Zhizhong,et al.Dynamic harmonic estimation based on optimized unscented Kalman filter model[J].Journal of Shenzhen University:Science and Engineering,2015,32(2):188-195(in Chinese).
[32]Bittanti S,Savaresi S M.Frequency tracking via extended Kalman filter:parameter design[C]//Proceedings of 2000American Control Conference.Chicago:IEEE,2000.
[33]Reza M S,Ciobotaru M,Agelidis V G.Frequency adaptive linear Kalman filter for fast and accurate estimation of grid voltage parameters[C]//Proceedings of2012 IEEE International Conference on Power System Technology(POWERCON).Auckland:IEEE,2012.
[34]Reza M S,Ciobotaru M,Agelidis V G.Instantaneous power quality analysis using frequency adaptive Kalman filter technique[C]//Proceedings of the 7th International Power Electronics and Motion Control Conference.Harbin,China:IEEE,2012.