A Fast Harmonic Detection Algorithm for Three-Phase Symmetric Systems
Ye Zongbin1, Hou Bo1, Zhang Yan’ao1, Qin Jiasheng1, Zhang Xulong2
1. School of Electrical Engineering China University of Mining and Technology Xuzhou 221116 China; 2. School of Electrical and Control Engineering Xuzhou University of Technology Xuzhou 221018 China
Abstract：The active power filter (APF) can compensate harmonics caused by nonlinear equipment such as high-frequency power electronic devices. Whether its harmonic detection algorithm can detect the harmonic component quickly and accurately largely determines the dynamic response and harmonic compensation performance of APF. The traditional discrete Fourier transform (DFT) was a frequency domain harmonic detection method, which can detect specific harmonics. However, it had large computation and long delay and, hence, can not detect harmonics quickly and compensate them in time. This was insufficient to support fast harmonic compensation of APF. Recently, some methods introduced the sliding window iterative algorithm into DFT, but there was still delay of a fundamental period. To address these issues, this paper proposes a new sliding-window discrete Fourier transform (SDFT) algorithm for three-phase symmetric systems. By using the symmetry of three-phase signals, it effectively detects harmonics within 1/6 fundamental cycle. This method is based on DFT and sliding window iterative algorithm. Firstly, the DFT algorithm needs N complex multiplications to detect a specific order harmonic. The sliding window iterative algorithm updates the datas using cyclic sliding pointer, reducing the calculation to one complex multiplication, thus leading to the delay of one fundamental period. Secondly, the z-domain transfer function of DFT is composed of a comb filter, a complex resonator and gain coefficient. The method proposed in this paper uses a new comb filter, which makes use of the characteristic that the sampling value of B and C phase signals in three-phase symmetric signals can replace the partial sampling value of phase A as the input sequence of DFT calculation. It only needs 1/6 fundamental period to obtain the output sequence of the harmonic components. This way, the problem that SDFT requires one fundamental cycle delay is addressed, and APF can detect and compensate harmonics more quickly. The test results in the simulation model with the fundamental frequency of 50Hz and sampling frequency of 15kHz show that both SDFT and the proposed method can effectively detect the target frequency components. However, it takes about 20ms to obtain detection results by using SDFT. The proposed method only needs about 3.3ms, that is, 1/6 SDFT delay time. The proposed method and SDFT are applied to the system composed of three-phase shunt APF and three-phase uncontrolled rectifier bridge with resistive load. The negative sequence 5th harmonic current components generated by three-phase uncontrolled rectifier circuit are detected and extracted respectively, and the detection results are used as the reference value of harmonic current in current loop to compensate the negative sequence 5th harmonic current components. The experimental results show that both SDFT and the proposed method can achieve specific harmonic detection, but the proposed method has better dynamic response performance and requires less storage space than SDFT. After the compensation by APF system using SDFT and the proposed method, the 5th harmonic current content in grid current decreases from 23.56% to 0.64% and 0.77% respectively. The experimental results show that the grid-connected current of the APF system with the proposed method can reach the steady state faster. The following conclusions can be drawn from the simulation and experimental results: The proposed fast harmonic detection algorithm, which is suitable for three-phase symmetric systems, can achieve fast and effective detection of specific harmonics. Compared with SDFT harmonic detection algorithm, the proposed method obtains faster dynamic response, and only needs 1/6 fundamental cycle to detect specific harmonics. Applying the proposed method to APF system can improve the dynamic performance of the system and compensate specific harmonics faster.
[1] 王保帅, 肖勇, 胡珊珊, 等. 适用于非整数次幂的高精度混合基FFT谐波测量算法[J]. 电工技术学报, 2021, 36(13): 2812-2820, 2843. Wang Baoshuai, Xiao Yong, Hu Shanshan, et al.High precision mixed radix FFT algorithm for harmonic measurement under non-integer power sequence[J]. Transactions of China Electrotechnical Society, 2021, 36(13): 2812-2820, 2843. [2] 陈杰, 章新颖, 闫震宇, 等. 基于虚拟阻抗的逆变器死区补偿及谐波电流抑制分析[J]. 电工技术学报, 2021, 36(8): 1671-1680. Chen Jie, Zhang Xinying, Yan Zhenyu, et al.Dead-time effect and background grid-voltage harmonic suppression methods for inverters with virtual impedance control[J]. Transactions of China Elec-trotechnical Society, 2021, 36(8): 1671-1680. [3] 孟令辉, 舒泽亮, 闫晗, 等. 基于特征次谐波补偿的单相统一电能质量调节器并联变换器控制策略[J]. 电工技术学报, 2020, 35(24): 5125-5133. Meng Linghui, Shu Zeliang, Yan Han, et al.Control strategy for single-phase unified power quality conditioner of parallel converter based on specific order harmonics compensation[J]. Transactions of China Electrotechnical Society, 2020, 35(24): 5125-5133. [4] 王雪, 高云广, 吝伶艳, 等. 有源电力滤波器的研究现状与展望[J]. 电力系统保护与控制, 2019, 47(1): 177-186. Wang Xue, Gao Yunguang, Lin Lingyan, et al.Research status and prospect of active power filter[J]. Power System Protection and Control, 2019, 47(1): 177-186. [5] 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, 90. Yu Yilin, Xu Yonghai, Liu Xiaobo.Study of harmonic current detection based on sliding-window iterative algorithm of DFT[J]. Power System Pro-tection and Control, 2011, 39(13): 78-82, 90. [6] 刘聪, 戴珂, 张树全, 等. RDFT算法在有源电力滤波器中的应用[J]. 电力自动化设备, 2011, 31(7): 96-100. Liu Cong, Dai Ke, Zhang Shuquan, et al.Application of RDFT algorithm in active filters[J]. Electric Power Automation Equipment, 2011, 31(7): 96-100. [7] Jiang Weidong, Ding Xingxing, Ni Youyuan, et al.An improved deadbeat control for a three-phase three-line active power filter with current-tracking error compensation[J]. IEEE Transactions on Power Elec-tronics, 2018, 33(3): 2061-2072. [8] 张国澎, 周犹松, 郑征, 等. 有源电力滤波器指定次谐波补偿优化限流策略研究[J]. 电力系统保护与控制, 2018, 46(16): 46-53. Zhang Guopeng, Zhou Yousong, Zheng Zheng, et al.Research on current-limiting optimization strategy for specific harmonic compensation of active power filter[J]. Power System Protection and Control, 2018, 46(16): 46-53. [9] 张俊敏, 田微. 基于瞬时无功功率理论谐波检测方法的研究[J]. 电力系统保护与控制, 2008, 36(18): 33-36. Zhang Junmin, Tian Wei.Study on harmonic detection methods based on instantaneous reactive power theory[J]. Power System Protection and Control, 2008, 36(18): 33-36. [10] 王丽, 刘会金, 王陈. 瞬时无功功率理论的研究综述[J]. 高电压技术, 2006, 32(2): 98-100, 103. Wang Li, Liu Huijin, Wang Chen.Summary of the instantaneous reactive power theory[J]. High Voltage Engineering, 2006, 32(2): 98-100, 103. [11] Soares V, Verdelho P, Marques G D.An instan-taneous active and reactive current component method for active filters[J]. IEEE Transactions on Power Electronics, 2000, 15(4): 660-669. [12] 王希文, 杜川. 瞬时无功功率理论与谐波检测方案[J]. 电气技术, 2014, 15(4): 38-41. Wang Xiwen, Du Chuan.Instantaneous reactive power theory and the measurement methods for detecting harmonics[J]. Electrical Engineering, 2014, 15(4): 38-41. [13] 朱鹏程, 李勋, 康勇, 等. 统一电能质量控制器控制策略研究[J]. 中国电机工程学报, 2004, 24(8): 67-73. Zhu Pengcheng, Li Xun, Kang Yong, et al.Study of control strategy for a unified power quality con-ditioner[J]. Proceedings of the CSEE, 2004, 24(8): 67-73. [14] Newman M J, Zmood D N, Holmes D G.Stationary frame harmonic reference generation for active filter systems[J]. IEEE Transactions on Industry Appli-cations, 2002, 38(6): 1591-1599. [15] Wang Yifei, Li Yunwei.Analysis and digital imple-mentation of cascaded delayed-signal-cancellation PLL[J]. IEEE Transactions on Power Electronics, 2011, 26(4): 1067-1080. [16] Wang Yifei, Li Yanwei.Grid synchronization PLL based on cascaded delayed signal cancellation[J]. IEEE Transactions on Power Electronics, 2011, 26(7): 1987-1997. [17] Wang Yifei, Li Yunwei.Three-phase cascaded delayed signal cancellation PLL for fast selective harmonic detection[J]. IEEE Transactions on Indu-strial Electronics, 2013, 60(4): 1452-1463. [18] Golestan S, Ramezani M, Guerrero J M, et al.dq-frame cascaded delayed signal cancellation-based PLL: analysis, design, and comparison with moving average filter-based PLL[J]. Power Electronics IEEE Transactions on, 2015, 30(3): 1618-1632. [19] McGrath B P, Holmes D G, Galloway J J H. Power converter line synchronization using a discrete Fourier transform (DFT) based on a variable sample rate[J]. IEEE Transactions on Power Electronics, 2005, 20(4): 877-884. [20] Gonzalez S A, Garcia-Retegui R, Benedetti M.Harmonic computation technique suitable for active power filters[J]. IEEE Transactions on Industrial Electronics, 2007, 54(5): 2791-2796. [21] 赵阳, 徐朝阳, 吴思敏, 等. SDFT算法在单相并联有源电力滤波器中的应用[J]. 电力电子技术, 2013, 47(2): 101-103. Zhao Yang, Xu Zhaoyang, Wu Simin, et al.Appli-cation of SDFT algorithm in single-phase shunt active power filter[J]. Power Electronics, 2013, 47(2): 101-103. [22] 刘华吾, 胡海兵, 邢岩. 有限字长对滑动窗DFT稳定性的影响研究[J]. 电工技术学报, 2016, 31(11): 22-31. Liu Huawu, Hu Haibing, Xing Yan.Research of finite-word-length effects on the stability of the sliding DFT[J]. Transactions of China Electro-technical Society, 2016, 31(11): 22-31. [23] Park C S.Fast, accurate, and guaranteed stable sliding discrete Fourier transform[sp Tips&Tricks][J]. Signal Processing Magazine IEEE, 2015, 32(4): 145-156. [24] Jacobsen E, Lyons R.An update to the sliding DFT[J]. IEEE Signal Processing Magazine, 2004, 21(1): 110-111. [25] Xia Tao, Zhang Xu, Tan Guojun, et al.Synchronous reference frame single-phase phase-locked loop (PLL) algorithm based on half-cycle DFT[J]. IET Power Electronics, 2020, 13(9): 1893-1900. [26] Farhang-Boroujeny B, Gazor S.Generalized sliding FFT and its application to implementation of block LMS adaptive filters[J]. IEEE Transactions on Signal Processing, 1994, 42(3): 532-538. [27] Yang Bingyuan, Dai Ke, Yang Chaowei, et al.Improvement of recursive DFT for APF with higher switching frequency to suppress wideband har-monics[J]. IEEE Access, 2021, 9: 144300-144312. [28] 陆秀令, 周腊吾, 张松华, 等. 电力谐波滑窗迭代DFT检测算法的研究与仿真[J]. 系统仿真学报, 2008, 20(14): 3652-3655. Lu Xiuling, Zhou Lawu, Zhang Songhua, et al.Study and simulation of harmonic detection based on sliding-window iterative algorithm of discrete fourier transform[J]. Journal of System Simulation, 2008, 20(14): 3652-3655. [29] 鲁挺, 赵争鸣, 张颖超, 等. 采样延迟和误差对三电平PWM整流直接功率控制性能的影响及其抑制方法[J]. 电工技术学报, 2010, 25(3): 66-72. Lu Ting, Zhao Zhengming, Zhang Yingchao, et al.Effect of sampling delay and error on direct power control performance of three-level PWM rectifier and its restraining method[J]. Transactions of China Elec-trotechnical Society, 2010, 25(3): 66-72.
2023, Vol. 38 
