Removal of DC offset in current and voltage signals using a novelFourier filter algorithm

Protecting transmission lines frequently involves adopting distance relays. Protective relays must filter their inputs to reject unwanted quantities and retain signal quantities of interest. Accuracy and convergent speed of the filter algorithm are essential for protective relays. A widely applied filter algorithm, the discrete Fourier transform (DFT) can easily erase harmonics using simple calculation. However, the voltage and current signals contain large harmonics and DC offset during the fault interval. The DC offset heavily influences the precision and convergence speed of the fundamental frequency signal from DFT. In this investigation, the authors present a novel Fourier algorithm to remove the DC offset in a voltage or current signal. Applying a full-cycle DFT (FCDFT) requires one cycle plus two samples to calculate and compensate for the DC offset. Half-cycle DFT (HCDFT) only requires half of a cycle plus two or three samples to accomplish the algorithm when the input signal has no even order harmonics. Adopting the proposed algorithm in distance relays effectively suppresses the DC offset and quickly decomposes the accurate fundamental frequency components     

Removal of dc offset and subsynchronous resonance in current signals for series compensated transmission lines using a novel Fourier filter algorithm

In this paper, a novel Fourier filter algorithm for high-accuracy and high-convergence-speed fundamental frequency component calculation of series compensated transmission line is proposed. The performance of digital relaying is highly reliant on the algorithm of digital filtering, especially involving the dc offset and subsynchronous resonance. Input signals of protective relays must be filtered in advance to reject unwanted quantities and retain signal quantities of interest. Accuracy and convergence speed of filter algorithms are essential for protective relays. However, the voltage and current signals contain large harmonics and dc offset during fault intervals. A widely applied filter algorithm, the Discrete Fourier Transform (DFT), can easily eliminate harmonics via simple calculations. The dc offset heavily influences the precision and convergence speed of fundamental frequency component from DFT. Under high resistive fault conditions, the current signals will have subsynchronous resonance. The subsynchronous resonance current and voltage signals influence the performance of DFT much more than the dc offset. Although capable of erasing high order harmonics, the low pass filter cannot remove the dc offset and subsynchronous resonance. The Alternative Transient Program (ATP) of the Electromagnetic Transients Program (EMPT) is utilized to simulate the transient responses of series compensated transmission lines during the fault period. Adopting the proposed algorithm in distance relays effectively locks the dc offset and subsynchronous resonance signals and quickly estimates the accurate fundamental frequency components.     

一种提取基波分量的高精度快速滤波算法

为满足微机继电保护速动性的要求,短数据窗傅里叶算法得到了广泛应用.在系统发生故障期间,电压电流信号中包含大量的非周期分量与谐波分量,这将极大地延迟传统半波傅里叶算法的收敛速度.为此提出了基于狭窄带通滤波与半波傅里叶算法相结合的快速滤波算法,该算法充分利用了狭窄带通滤波算法对低频和高次谐波良好的抑制作用,同时结合了半波傅里叶算法计算实部受衰减直流分量影响小的特点,计算速度快,且滤波效果明显优于传统算法.     

故障电流中衰减直流分量的滤波算法研究

在电力系统中,任何故障或扰动都会使得系统中出现衰减直流分量,它将影响继保装置的测量精度。该文通过引入一组滤波算子,实现了衰减直流分量参数的在线计算,并在此基础上说明了信号基波和谐波分量的计算方法。该算法的数据窗只需要一个基波周期,具有很好的快速性,理论上是一种精确算法。对传统DFT算法和本文算法的仿真结果表明了这种算法的有效性。     

考虑衰减直流分量的动态相量强跟踪测量算法

故障电流信号的频率变化以及包含的衰减直流分量会严重影响基于傅里叶变换的相量测量算法的精度和动态响应速度。文中提出了一种利用强跟踪滤波器滤除衰减直流分量的动态相量测量算法。首先,将衰减直流分量用其二阶泰勒展开多项式来表示,在状态变量中添加衰减直流分量及其一阶导数和二阶导数,建立含有基波角频率、幅值等参数和衰减直流分量参数的故障电流的非线性状态空间模型,减小信号估计的模型误差。其次,为了提高扩展卡尔曼滤波器在系统达到稳定时对系统参数突变的跟踪能力,利用强跟踪滤波器递推估计各状态变量。所提方法能够有效抑制衰减直流分量对相量测量精度的影响,对时变故障电流信号具有良好的动态响应能力。采用所提算法对加噪声的数值信号以及ATP-EMTP故障仿真信号进行相量测量,结果验证了算法的正确性与有效性。     

An Innovative Decaying DC Component Estimation Algorithm for Digital Relaying

We propose a new decaying dc component estimation algorithm for digital relaying. Fault currents tend to include a dc decaying component. This component decreases the accuracy and speed of the protection relay operation. The proposed algorithm can estimate and eliminate the dc decaying component from fault current signals after one cycle from the fault instant. Also, it can be applied to a conventional discrete Fourier transform to calculate phasor quantities of fault currents in a digital protection relay. In the proposed algorithm, the dc decaying magnitude and time constant are estimated exactly by integrating fault currents during one cycle. The dc decaying component is eliminated by subtracting the dc value at each sampling instant. To verify the performance of the proposed algorithm, we performed a dc component estimation test and distance protection test using PSCAD/EMTDC. The results of the PSCAD/EMTDC simulation showed that the proposed algorithm can estimate dc components exactly from fault currents and can be applied to digital protection relays for phasor extraction.      

交流1000kV特高压线路三相故障暂态过程分析

通过理论分析和仿真验证得到特高压线路三相故障后相关暂态电气量的特点:特高压线路故障电流中除有一很大的衰减直流分量外还存在高频分量:故障电压中也含有较大的高频分量但没有直流分量;故障高频分量的初始值与短路角(以电压角为基准)有关.当故障角为90°时.高频分量的初始值最大:高频谐波的频率与故障距离和系统运行方式有关.系统方...     

基于离散傅里叶变换的频谱分析新方法

针对现有的测频算法和频谱分析方法还存在一些不足之处,提出了基于离散傅里叶变换的频谱分析新方法,它能准确计算出信号中的基频分量,整次谐波和非整次谐波的幅值,频率和相角,以及衰减直流分量的幅值和衰减时间常数.公式推导的过程先从简单的单信号模型入手,得到单个余弦信号的幅值、频率和相角,再推广到一般情况下的复杂信号,采用牛拉法...     

A reiterative DFT to damp decaying DC and subsynchronous frequency components in fault current

This work presents a reiterative discrete Fourier transform (DFT) algorithm for fault current filtering. First, the short-windows DFT (SWDFT)-based mimic filter is developed to damp the measurement. Then, a reiterative scheme is proposed to reconstruct the damped measurement for further damping. The proposed algorithm can sufficiently damp the decaying dc as well as the subsynchronous frequency components. Thus, the proposed algorithm is appropriate to the filtering design on both the conventional and series-compensated transmission lines. Meanwhile, the recursive form is developed to reduce the computational burden. The simulation results illustrate that the algorithm significantly reduces the time to obtain the accurate fundamental phasor and that it has a better performance than the conventional DFT algorithm.     

基于改进型二阶广义积分器的同步信号检测

为了满足三相电压在不对称、直流分量及谐波畸变等情况下并网变换器的控制需求,需要准确地检测出电压信号的正序分量、幅值和基波频率。基于双二阶广义积分器锁频环的方法可实现电压在不对称和畸变下同步信号的提取。但当电压信号含有直流分量和多次谐波时,基本的SOGI结构滤波效果不理想,追踪的波形波动比较大,并降低了追踪速度。文中介绍一种改进的SOGI结构,该结构在SOGI的基础上增加求差节点和自适应滤波器,并保留SOGI-FLL的优势。电压的幅值和基波频率能准确快速被检测出来,很好的减小频率跳变后的波动、滤除谐波和消除直流分量。MATLAB仿真结果表明,其改进方法在电压信号不对称、直流分量及多次谐波存在条件下准确地检测出正序分量和基波频率。     

Fast frequency and harmonic estimation in power systems using a new optimized adaptive filter

This paper presents an adaptive filter for fast estimation of frequency and harmonic components of a power system voltage or current signal corrupted by noise with low signal to noise ratio (SNR). Unlike the conventional linear combiner (Adaline) approach, the new algorithm is based on an objective function often used in independent component analysis for robust tracking under impulse noise conditions. However, the accuracy and speed of convergence of this algorithm depend on the choice of step size of the filter and its adaptation. Instead of choosing the step size η and the parameter β of the cost function by trial and error, an adaptive particle swarm optimization technique is used alternatively to obtain both η and β to reduce the error between the observed voltage or current samples and the estimated ones. Using the optimized values, the amplitude and phase of the fundamental and harmonic components are estimated. Further, the extracted fundamental component is used to estimate any frequency drift of the power system recursively using an optimized error function obtained from three consecutive voltage samples. To test the effectiveness of the algorithm, several time-varying power system signals are simulated with harmonics, interharmonics, and decaying dc components buried in noise with low signal-to-noise ratio (SNR) and are used to estimate the frequency and harmonic components. This approach will be useful in islanding detection of a distributed generating system.     

New Algorithms for Computer Relaying for Power Transmission Lines

Synopsis

This paper presents a new recursive discrete-time filter for calculating the impedance from digitized voltage and current samples from the relay location, The transmission line voltage and current signals during a fault are modelled as a sum of decaying dc, and components of fundamental frequency and higher harmonic frequency components. The recursive discrete-time filter interpolates the signal samples and generates filter coefficiencs either by using spectral observation or functional expansion techniques. Both the algorithms are tested by using the fault data recorded at the Saskatchewan Power Corporation producing fast and reliable tripping conditions.     

An analytic method for measuring accurate fundamental frequencycomponents

This paper proposes an analytic method for measuring the accurate fundamental frequency component of a fault current signal distorted with a DC-offset, a characteristic frequency component, and harmonics. The proposed algorithm is composed of four stages: sine filter, linear filter, Prony's method, and measurement. The sine filter and the linear filter eliminate harmonics and the fundamental frequency component, respectively. Then Prony's method is used to estimate the parameters of the DC-offset and the characteristic frequency component. Finally, the fundamental frequency component is measured by compensating the sine-filtered signal with the estimated parameters. The performance evaluation of the proposed method is presented for a-phase to ground faults on a 345 kV 200 km overhead transmission line. The electromagnetic transient program (EMTP) is used to generate fault current signals under different fault locations and fault inception angles. It is shown that the analytic method accurately measures the fundamental frequency component regardless of the characteristic frequency component as well as the DC-offset     

含分数次谐波环境下提取整数次谐波信息的新方法

提出了一种在含有分数次谐波环境下,以一定的规律逐渐降低的频率序列依次作为基频,利用傅里叶级数展开电力系统中实际的电压、电流信号,再通过迭代算法从中提取出工频量及其整数次谐波分量信息的新方法。该方法回避了现有的加窗DFT算法中选取窗函数困难的问题。新方法的原理进行了详细的数学推导和说明,并给出程序框图。为了验证方法的正确性,利用程序对一实际信号进行了分析。实例结果表明,与传统的FFT算法比较,新方法在富含间谐波和次谐波环境下依然能够提出基波和整数次谐波的幅值和相角,且精度满足工程需求。同时,该方法还具有实现简单等优点,易于在工程实际中应用。     

A discrete Fourier transform-based adaptive mimic phasor estimator for distance relaying applications

In protection relaying schemes, the digital filter unit plays the essential roles to calculate the accurate phasor. However, while the fault current contains plentiful decaying dc component, the over-reach of distance protection will cause sever problem. This work develops an adaptive mimic phasor estimator to remove the decaying dc oscillation between voltage and current and obtains the accurate apparent impedance. First, a discrete Fourier transform-based mimic phasor estimator is developed. Then, an adaptive scheme is proposed to obtain the decaying time constant. Unlike the fixed decaying dc time constant used in a digital mimic filter, the proposed algorithm adopts the transmission-line parameters information hiding in the voltage and current measurements to adaptively approximate the decaying dc time constant to the accurate value. Thus, the estimation error in the mimic filter due to the time constant mismatch can be eliminated. Both full-cycle and half-cycle versions are developed in this work. Simulations results illustrate the effectiveness of this new algorithm for distance relaying applications.     

利用基波相量变化率的快速选相方法

针对目前选相方法不能快速、可靠识别所有故障类型的问题,提出了利用基波相量变化率的故障选相方法。线路发生短路故障后,故障相基波电流相量变化率受衰减直流分量及工频故障分量影响,其值迅速增大,而非故障相基波电流相量变化率变化较小;如果发生接地故障,零序电流基波相量变化率受衰减直流分量及工频故障分量影响,其值也会迅速增大,否则其值在零附近波动。依据不同类型故障中基波电流相量变化率的特征能够快速、可靠识别故障相。利用PSCAD/EMTDC仿真数据对算法进行测试,仿真结果表明:算法能够在故障后四分之一周波内准确判断故障相,具有较高可靠性。     

基于二阶广义积分器的改进型ip-iq谐波检测算法*

针对电网直流分量和高次谐波对谐波电流检测精度的影响,提出了一种基于二阶广义积分器的改进型ip-iq谐波检测算法。该算法在传统ip-iq法的结构上加入了改进型SOGI滤波环节,有效滤除了输入信号中的直流分量同时还抑制了高次谐波,改进型SOGI的锁相环在电网电压含高次谐波和直流分量的情况下能提供稳定的电网电压频率,从而能够更准确检测出谐波电流。仿真算例对比分析了传统ip-iq法和基于一般SOGI的ip-iq法,验证了文中提出的谐波检测方法在电网含直流分量和高次谐波时的有效性和可靠性。     

一种滤除衰减直流分量的全波傅氏改进算法研究

全波傅氏算法在提取故障电流中基波分量时受衰减直流分量的影响较大。针对此问题,提出了一种滤除衰减直流分量的全波傅氏改进算法,给出新型衰减直流分量参数估算方法的公式推导。首先利用一个周波内的采样值求出故障电流中衰减直流分量的初始幅值和衰减时间常数,用采样值减去衰减直流分量值得到修正后的采样值,再利用全波傅氏算法计算出基波分量。分别采用静态模型信号、PSCAD/EMTDC仿真信号检验了该算法的性能。仿真结果表明,所提出的算法能够有效地减少衰减直流分量的影响。与一般改进算法相比,所提算法仅需要一个周波的采样数据,计算量小,计算的基波分量准确性高。     

基于自适应神经元的短路电流参数提取

真空断路器实现选相分闸的关键是快速提取短路电流参数。传统快速傅立叶(FFT)和最小二乘参数估计方法由于响应速度慢、计算量大难以满足选相分闸的实时要求；该文基于自适应神经元，给出了一种真空断路器同步开断短路电流时快速提取短路电流参数，预测电弧熄灭时电流零点的方法。介绍了自适应神经元估计短路电流参数的基本原理，采用正交滤波器消除衰减直流分量和误差自相关估计自适应改变学习步长，加快神经元的学习收敛速度和减少稳态误差。MATLAB仿真验证了所提方法的快速性和有效性。     

An advanced method for testing of distance relay operatingcharacteristic

This paper describes a test method for distance relays using an advanced open-loop digital simulator. Derivation of test signals during prefault and fault, and test procedure are introduced. It is demonstrated that the method of generating test signals and the procedure of applying them to a relay under test directly affect test results. Prefault voltage and current are also a very important factor. The decaying DC offset is considered as well. Test results for five different relays using this new method are presented in this paper. The results demonstrate practical benefits of the test method