A practical, precise method for frequency tracking and phasor estimation

Comprehensive analysis of discrete Fourier transform (DFT) error is given in this paper, including why it is accurate when used in the case of synchronous sampling and how error rises when sampling frequency does not synchronized to signal frequency. Simple but precise expressions of phase angle error and amplitude error are given. Practical formulas to calculate the true phase angle and amplitude are presented. The formulas are very simple and precise. Based on the formula to calculate true phase angle, a new frequency tracking method is developed. The proposed method can be calculated recursively. And, with notable accuracy improvement, the calculation burden is little more than the traditional DFT method. Also, an adaptive method to suppress the effect of harmonics is presented, which adds very little calculation burden with satisfying performance. The most distinguished feature of the proposed method is that it is not only precise, but also simple. Some examples are given to demonstrate the feasibility, precision, simpleness and robustness of the proposed method.     

Voltage phasor and local system frequency estimation using Newtontype algorithm

A new approach to the design of a digital algorithm for voltage phasor and local system frequency estimation is presented. The estimation problem is considered as an unconstrained optimization problem. The algorithm is derived using Newton's iterative method, very commonly used in load-flow studies. The algorithm showed a very high level of robustness as well as high measurement accuracy over a wide range of frequency changes. The algorithm convergence of order two provided fast response and adaptability. To demonstrate the performance of the algorithm developed, computer simulated, experimentally obtained and real-life data records are processed. The presented work is a part of a project concerning the application of microprocessors in frequency relaying     

一种适用于同步相量测量的新算法

在异步采样的情况下,离散傅里叶变换(DFT)由于频谱泄漏及栅栏效应,计算结果不够精确,不能满足同步相量测量精度的要求。对现有的同步采样及误差消除方法进行了分析,提出了一种新的相量测量算法。通过线性插值计算,得到采样序列两相邻过零点进行频率跟踪,由所测频率对采样序列进行同步修正得到满足同步采样的新序列,采用DFT进行相量估计。仿真结果表明:该算法具有高精度、计算量小等特点,能够满足同步相量测量对精度及实时性的要求。     

一种适用于同步相量测量的新算法

在异步采样的情况下,离散傅里叶变换(DFT)由于频谱泄漏及栅栏效应,计算结果不够精确,不能满足同步相量测量精度的要求.对现有的同步采样及误差消除方法进行了分析,提出了一种新的相量测量算法.通过线性插值计算,得到采样序列两相邻过零点进行频率跟踪,由所测频率对采样序列进行同步修正得到满足同步采样的新序列,采用DFT进行相量估计.仿真结果表明:该算法具有高精度、计算量小等特点,能够满足同步相量测量对精度及实时性的要求.     

低频采样下基于卡尔曼滤波的同步相量测量算法的研究

各种基于定间隔采样的传统相量测量算法在跟踪速度和测量精度上不能很好地统一,在低频采样情况(每周波4~8个采样点)下提出一种基于线性卡尔曼滤波技术的10状态卡尔曼滤波模型,用于实时跟踪电力系统的电压有效值、频率、频率变化率和初相角,为系统提供精确的参数。结合二元泰勒展开公式,推导出各个参数的计算公式,并依据信号模型选取合适的时间区间保证算法对突变信号的响应速度。从采样频率、数据窗持续时间和算法对突变信号的跟踪精度方面对算法进行了讨论,结果表明使用该算法可以在低频采样下获得较高的参数估计精度。     

A novel short-window algorithm of phasor computation for EHV line protection

A novel phasor computation algorithm is presented in this paper. The real and imaginary part filters of this algorithm have identical magnitude frequency characteristic (IMFC) at all the frequencies and orthogonal phase frequency characteristic (PFC) at fundamental frequency. Considering the conditions of the same magnitude frequency characteristic (MFC) and the orthogonal PFC, the two-sample algorithm is derived. Once two-sample orthogonal filters with IMFC are obtained, the algorithm design is just to select proper shapes and lengths of windows, which determine the filtering performance and response-time, respectively. This method could be applied to design filter in any window-length, especially in short-window. Therefore, this class of phasor algorithms is suitable for EHV transmission line protection where a short-window is crucial for fast response and better operation performance. The proposed algorithm has been applied to a series of EHV relay devices by China Xuchang Relay Group.     

Strengths and limitations of a new phasor estimation technique to reduce CCVT impact in distance protection

This paper evaluates the performance of a new least squares approach that improves the accuracy and speed of convergence of the voltage phasors estimated during CCVT transient conditions. A justification of the validity of the linear mathematical model for the CCVT used is provided together with a short study about the risk of transient ferroresonance. Also, a discussion is presented about operating times of numerical distance relays and the importance of the new phasor estimation considered. The methodology followed to achieve a realistic evaluation in a variety of scenarios is presented. The results show the improvements achievable in most conditions, but also highlight an example scenario where the new method has limitations.     

基于频率测量值的相量及电气量的DFT修正算法

为解决频率偏移时电力系统相量及电气量的测量误差大的问题,提出了一种改进的离散傅里叶(DFT)修正算法。建立了相量的实部、虚部与幅值、初相角、频率偏移量之间的函数关系式,根据此关系式得到实部、虚部与频率之间所满足的一个恒等式。在频率已知条件下计算出修正后的相量幅值和相角,进一步推导出了修正后的相量实部与虚部,最后得到其他电气量的修正算法。仿真结果表明,当系统频率偏移时,在信号为纯正弦信号,或者含有高次谐波及随机噪声等情况下,算法均可有效地提高相量及电气量的计算精度。同时,该算法对采样频率和频率误差不敏感,计算量小,不增加额外的延迟时间。     

一种基于修正相角差的傅氏测频算法

基于相角差的传统傅氏测频算法所采用的相角差无法正确反映真实相角差,导致计算结果存在原理误差。提出了一种基于修正相角差的傅氏测频算法。利用相角差作为中间量,通过修正因子对相角差进行修正,消除传统傅氏算法的原理误差。算法保留了傅氏算法不敏感于噪声和谐波的良好特性。同时,采用基于二次插值技术的采样序列迭代修正方法,克服传统测频算法速度与精度无法兼得的矛盾。仿真结果表明相比于传统傅氏算法,在相同的硬件环境下,该算法的运算速度及测量精度均有提高。     

基于高精度测频的修正DFT相量及功率测量算法

为了提高频率偏移时电力系统相量及功率测量精度,提出了一种基于改进扩展卡尔曼滤波(IEKF)频率测量的修正离散傅里叶变换(DFT)相量及功率测量算法。分析了频率发生偏移时非同步采样下DFT的测量误差,建立了相角、幅值与频率偏移量和初相角之间的函数关系式。由IEKF得到频率偏移量,然后对DFT计算结果进行修正即可得到输入信号的真实相量和功率。仿真结果表明:该算法相比较于传统自适应DFT算法能有效消除或减弱谐波、噪声以及频率偏移对相量同步测量的影响,提高了相量及功率测量精度。     

Covariance management based RLS algorithm for phasor estimation inseverely noisy systems

This paper presents a new algorithm, derived from the recursive least squares (RLS), to estimate power system voltage and current harmonics for digital relay purposes. The algorithm is based on the RLS covariance matrix management, by making use of the covariance resetting in a different way. The approach provides a kind of attractor that absorbs all nonmodeled dynamics. In order to demonstrate its effectiveness, the proposed algorithm is applied to simulated signals and its performance is compared with other conventional methods     

基于相量量测的电力系统谐波状态估计算法的研究

基于相量量测单元的电力系统谐波状态估计技术,可选取电力网络的节点谐波电压为状态量,支路电流、节点注入电流和节点电压相量为量测量,从而使谐波状态方程成为线性方程.本文根据这个特点,再结合量测方案的不同情况,提出了在冗余量测和基本量测时,采用便于工程实际应用的乔累斯基算法来求解线性谐波状态方程,其计算量只是高斯消元法的一半,且不用考虑选主元,大大减少了计算的时间;在量测矩阵欠定时,采用奇异值分解算法,不仅可以为欠定的状态方程提供稳定的最小二乘解,而且该算法本身具有可观性分析的功能,不需要采用其它算法进行可观性分析,从而极大地简化了谐波状态估计分析的难度.最后通过仿真程序验证了这两种算法在谐波状态估计求解问题中的有效性和可靠性.     

一种新的三相状态估计算法

提出了一种新的三相状态估计算法 ,并详细地阐述了一种三相状态估计的处理策略。     

一种新的三相状态估计算法

提出了一种新的三相状态估计算法,并详细地阐述了一种三相状态估计的处理策略。     

A precise calculation of power system frequency and phasor

A series of precise digital algorithms based on discrete Fourier transforms (DFT) to calculate the frequency and phasor in real-time are proposed. These algorithms, called the smart discrete Fourier transforms (SDFT) family, not only keep all of the advantages of DFT but also smartly take frequency deviation and harmonics into consideration. These make the SDFT family more accurate than the other methods. Besides, the SDFT family is recursive and very easy to implement, so it is very suitable for use in real-time. The authors provide the simulation results compared with conventional DFT method and second-order Prony method to validate the claimed benefits of SDFT     

一种新型SOC估计算法的研究

在建立电池管理系统的过程中,动力电池荷电状态(SOC)的实时测量和估计很关键。分析了各种电池SOC估算方法的优缺点,提出了一种实时检测电池端电压作为判断电池充电状态的电压-安时计量算法。由该算法构成的电量计能实时、准确计算电池的电量和SOC,保证了动力电池在电动汽车应用中的安全、可靠运行。     

基于频数分布的防止变压器差动保护误动的新方法

为有效防止变压器区外故障因CT饱和引起的差动保护误动,提出了一种基于频数分布的检测CT饱和的新方法。该方法截取从故障发生到差流达到第一个极值之间的部分差流波形并经适当变换,利用频数分布直方图进行电流波形处理。根据频数分布特征,能够实现CT严重饱和、一般饱和、轻度饱和情况下变压器区内外故障的准确检测。该方法只需定位故障发生时刻,而不需定位差流出现时刻,算法简单,快速可靠。经大量仿真实验验证了新方法的可靠性和准确性。     

一种混合递推的DFT相量测量算法

电力系统的稳定、安全、经济的运行需要快速准确地采集实时的电压和电流的有效值（幅值）与相位。然而,电网的频率是波动的,使采样很难做到对被测信号进行整周期截断,FFT算法的栅栏效应和泄漏现象,将导致明显的测量误差。提出一种混合递推的DFT相量测量算法。首先,利用频谱修正法获得精确的电网频率,然后采用相量校正算法纠正误差。通过滑动数据窗的递推算法提高了计算效率和时间响应,仿真证实了所提算法是有效和可行的。     

一种混合递推的DFT相量测量算法

电力系统的稳定、安全、经济的运行需要快速准确地采集实时的电压和电流的有效值(幅值)与相位.然而,电网的频率是波动的,使采样很难做到对被测信号进行整周期截断,FFT算法的栅栏效应和泄漏现象,将导致明显的测量误差.提出一种混合递推的DFT相量测量算法.首先,利用频谱修正法获得精确的电网频率,然后采用相量校正算法纠正误差.通过滑动数据窗的递推算法提高了计算效率和时间响应,仿真证实了所提算法是有效和可行的.     

一种基于导数的实时频率跟踪算法

频率是电力系统监控和保护中的重要参数,为对其进行快速准确的测量,提出了一种实时的频率跟踪算法。利用交流信号的正弦特性,通过二阶求导并进行线性化近似处理,进而事后误差补偿。算法在二阶导数初始计算时,运用Lagrange多项式进行曲线拟合。为减小多项式拟合和线性近似带来的误差,引入了误差补偿量和误差修正因子,提高了算法的计算精度。同时,分析了拟合多项式的误差余项,从而应用等比定理并在半周期长度的数据窗内进行平滑滤波,在兼顾实时性的基础上提高了算法的鲁棒性。Matlab平台上的仿真结果表明:该算法计算精度较高,对二次谐波有一定抑制作用,能较好地满足电力系统实时频率跟踪的要求。