外文文献引言分析

Harmonic PhasorAnalysisBased on

ImprovedFFTAlgorithm

Bo Zeng, Zhaosheng Teng, Yulian Cai, Siyu Guo, and Baiyuan Qing

I.INTRODUCTION

N ONLINEAR loads can introduce large harmonic current into power systems, which may lead to severe problems(e.g., meter malfunctions, equipment overheat, overvoltage, and data loss) [1]. In researches on eliminating or at least reducing the impacts of harmonics on power systems, harmonic phasor analysis has been one of the most vital problems that attract most attentions.

译文：电力系统中由于非线性负荷的存在产生大量的谐波电流，导致出现例如仪表故障、设备过热、过压和数据丢失等严重问题[1]。在研究消除或至少减少谐波对电力系统的影响时,谐波相量分析已经成为较重要和热门的方法。

分析：第一层简述研究领域，确定研究对象—电力系统谐波(harmonic of power systems )及研究的主流研究方法—谐波相量分析（harmonic phasor analysis ）.

The existing harmonic phasor analysis methods utilize a variety of techniques, such as the least square algorithms [2], Kalman filter [3], artificial neural network [4], Newton’smethod [5], Prony’s method [6], and state estimation [7]. However, when real-time performances are required, these methods do not give satisfactory outcome, and in these sit- uations, the fast Fourier transform (FFT)-based methods are preferable for its availability, understandability, simplicity, and easiness to implement in DSP and advanced RISCmachineschips. Unfortunately, the fundamental frequency of a power system may vary, and fixed sampling rates are typical for most data acquisition systems [8]. Though a number of sampling synchronization methods, such as the adoption of discrete phase-locked loop [9] or adjustable sampling frequency [10], have been proposed, synchronous sampling is still difficult to achieve.

译文：现有的谐波相量分析理论有: 最小二乘法[2]、卡尔曼滤波[2]、人工神经网络(ANNs)[4]、Newton法[5]、Prony 法[6]及状态估计法[7]。但是，对于动态信号这些方法难以有满意的效果，在此情况下，快速傅里叶变换（FFT）因其有效性，易懂， DSP及RISC芯片的轻松实现，得到广泛应用。然而，由于电力系统基波频率实时变化，固定的采样率仅对大多数数据采集系统具有典型性[8]。尽管已经提出许多同步采样方法，如使用采用离散锁相环技术[9]，或修正采样频率法[10]，同步采样仍然很难实现。

分析：第一层，综述现有谐波相量分析方法理论，描述解决问题的方法——快速傅里叶变换（FFT）。

The FFT approaches under asynchronous sampling suffer from two serious drawbacks [11], namely, the spectral leakagedue to time limitation and the picket fence effect due to the frequency discretization of the calculated spectrum. As a con- sequence, the harmonic phasor of a signal cannot be obtained accurately. The common strategy to cope with these drawbacks is the windowing of the signal sequence for reducing the spectral leakage [12] and spectrum interpolation for reducing the picket fence effect [13], [14].

译文：在非同步采样条件下，FFT算法有两个严重的缺点[11]，即数据截断引起频谱泄漏，频谱离散化造成栅栏效应，最终导致不能准确获得谐波相量。解决这些缺点的最常见的方法是对信号序列加窗函数和差值来减少频谱泄露和栅栏效应 [13][14] 。

分析：第一层陈述目前FFT算法存在的不足及研究的关键点——减少频谱泄露和栅栏效应。

Windows with great sidelobe attenuation and high sidelobe decaying rate can sufficiently reduce the spectral leakage and the harmonic interference [15]. To achieve these desirable properties, different windows have been defined by adjusting coefficients of classical windows [16]–[19] or by convoluting parent windows [15], [20], and have been used in replacement of the rectangular window. Although the design of windows is thought to be a quite matured research area, new methods are still emerging, e.g., the new class of adjustable windows based on the cosine hyperbolic function proposed in [21] and the novel method for window parameterization in the frequency domain presented in [22]. Nuttall [23] categorized classical windows according to optimal sidelobe behaviors and intro- duced the family of optimal cosine-type windows.

To reduce the spectral error caused by the picket fence effect, windowed interpolation algorithms [12]–[15] are employed. Among these algorithms, the multipoint interpolation discrete Fourier transform (DFT) algorithms [24]–[29] are widely applied to promote the harmonic phasor analysis accuracy, i.e., the measurement accuracy of the harmonic frequencies, am- plitudes, and phases, or as called, the phasors. Unfortunately, for complicated windows such as the high-order combined cosine-type windows, the rectification is computationally ex- pensive due to the solution of high-order equations. Approaches have been proposed to deal with the problem, e.g., Yang et al.[30] proposed an accurate phasor estimation algorithm by using an FIR comb filter, and in [31], a method for exact calculation of harmonics using adaptive window width is presented.

译文：窗函数的旁瓣衰减和快速衰减特性可有效减少频谱泄露和间谐波[15]。为了获得满意的特性，不同的适应经典窗系数的窗函数[16-19]或卷积窗函数[15][20]被提出且已经取代了矩形窗。尽管窗函数已经是一个相当成熟的研究领域，新的理论依旧不断涌现，如在[21]基于余弦双曲线函数的可调窗函数，在[22]提出在频域中窗参数新方法，纳托尔在[23]根据最优窗旁瓣的行为将古典窗分类，并介绍了最优的余弦窗函数族。

为了减少栅栏效应所造成的的频谱误差，引入的加窗插值的方法[12]-[15]。在这些方法中,多点插值离散傅里叶变换(DFT)算法[24]–[29] 被广泛应用于提高谐波相量分析的精度，如测量谐波频率的参数，振幅，相位，即相量。然而，对于复杂的窗函数，例如高阶的余弦型窗，为了计算高阶方程的解，这种改进方法是计算复杂度很高的。Yang et al.在文献[30] 中通过使用FIR滤波器提出了一个准确的参数估计算法，在[31]中提出变矩形窗宽度的自适应谐波分析算法。

分析：第二层针对目前FFT算法出现的两个突出问题，对现有研究进行文献综述。

However, variations of the fundamental frequency are usually caused by faults in the power systems, which may leads to the uncertainty of the signal harmonics, and the phasor analysis of arbitrary harmonics under frequency variation is still an openproblem. Besides, interharmonics may exist in the measured signal. Accordingly, a frequency domain approach for power system