一种三相对称系统快速谐波检测算法

A Fast Harmonic Detection Algorithm for Three-Phase Symmetric Systems

有源电力滤波器(APF)在谐波治理方面有着广泛应用,其谐波补偿性能在很大程度上取决于谐波检测环节的性能。为了提升谐波检测速度,该文提出一种基于滑窗离散傅里叶变换(SDFT)的快速谐波检测算法。相较于传统滑窗离散傅里叶算法存在一个基波周期延时,该文提出的快速谐波检测算法利用三相系统的对称性,替换传统滑窗离散傅里叶变换谐波检测算法的梳状滤波器构成环节,能在1/6个基波周期内实现谐波的有效检测,降低检测延迟。该文首先分析传统滑窗离散傅里叶变换谐波检测算法的优缺点;其次推导所提出的快速谐波检测算法的Z域表达式并分析其特点;最后通过仿真及小功率缩比有源电力滤波器样机实验平台验证了所提出的快速谐波检测算法的有效性。

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.