小波能量熵的研究及其在电力系统谐波检测中的应用外文文献包括翻译

1、Research on Wavelet Energy Entropy and Its Application to Harmonic Detection in Power SystemNa Wu and Yong-Qin WeiAbstractAiming at the problem that FFT cant detect the transient signal, and wavelet analysis is easy to produce energy leakage and frequency aliasing in power harmonic detection, the pa

2、per gives a new algorithm which combined wavelet with information entropy in order to design a new function that is wavelet energy entropy, it is used to extract informations of transient signal effectively in power system. According to the harmonic characters in power system, a mathematic model is

3、done based on it. The simulation results in Matlab indicate that the new algorithm is validated in transient signal detection.Index TermsWavelet energy entropy, transient signal, power harmonic, matlab simulationI. INTRODUCTIONThe traditional algorithm in power harmonic detection is based on FFT or

4、improved FFT, and it can detect the amplitude and phase of steady signal, but it cant detect the transient signal. Wavelet analysis has high distinguish ability whether in time domain or in frequency domain, it can extract mutational signal effectively in power system, and wavelet analysis is very s

5、uitable to detect transient signal in power system. But wavelet analysis has some shortcomings: such as power transient signal has so many datas and calculated amounts after wavelet analysis, and it has energy leakage and frequency aliasing, the extraction result of transient characters is unexpecte

6、d1. The paper gives a new algorithm which combines wavelet with information entropy to produce wavelet energy entropy(WEE) ,it can overcome the disadvantages of wavelet analysis. And it has both the characteristics of multi-resolution in wavelet analysis and entropy being good at indicating the chao

7、s degree of system. So the new algorithm can detect either steady or transient signal comprehensively.II. WAVELET ENERGYA. Multi-Resolution Wavelet AnalysisIn 1989 S. Mallat applied the theory of multi-resolution to wavelet analysis, and he put forward a new fast algorithm of wavelet analysis, that

8、is Mallat Fast Wavelet Algorithm2.The fast wavelet algorithm based on the multi-resolution is to divide the signal into multiple components of different scales by orthogonal wavelet, its implementation is equivalent to the repeated use of a group of high and low pass filter, the time sequence signal

9、s were decomposed step by step, the high pass filter generates signals of high frequency components, the low pass filter generates signals of low frequency approximation component. The two components of pass filter are equal in the width of the frequency band, and each accounts for1/2 spectral band.

10、 After each decomposition, the sampling frequency of signals reduces the times. And aiming at the low frequency component, it repeats the above decomposition process fatherly, thus gets the two components of the next level. After a signal is converted by fast wavelet analysis, we define high frequen

11、cy coefficients which are at K moment of J decomposition scale as cDj(K) ,and define low frequency coefficients as cAj(K). The signal component of Dj(k) and Aj(k) are reconstructed of single branch, and the frequency range of the information contained in them is as follows.In the above formula fs is

12、 the sampling frequency of signal, and the original signal sequence x(n) can be expressed as the sum of the ms components, that is:For convenience, Am(n) is expressed as Dm+1(n), thenMallat algorithm improves the speed of discrete wavelet greatly, but almost all of the wavelet functions have frequen

13、cy aliasing, and that is easy to lead to the adjacent scale energy leakage and produce frequency aliasing phenomenon3.So if all wavelet coefficients of high frequency or single branch signal which is reconstructed are directly used as criteria of extraction in transient harmonic signal, that is easy

14、 to lead to inaccurate results inevitably.B. Information EntropyIn 1948, C. E. Shannon put forward the concept of information entropy firstly; he put the entropy as the uncertainty of a random event or the amount of information. For a system with uncertainty, if we use a random variable X with value

15、s of limited numbers, it represents the state of the system. Let its probability space as:Then the average uncertainty of the whole probability space, also as information entropy, is defined as:Information entropy H is an information measurement which is used to locate a system under certain conditi

16、ons, it is a measurement to unknown degree of a sequence, and it can be used to estimate the complexity of random signal.C. Wavelet Energy Entropy (WEE)Wavelet analysis has good ability of time-frequency localization. Multi-resolution analysis make construction and implement of wavelet into a unifie

17、d framework, and it has a corresponding practical and fast algorithm. So with combining multi-resolution wavelet and information entropy, we can get the wavelet entropy definition of a signal and its calculating method 4.Let E=E1,E2,Em be equal to the wavelet energy entropy spectrum of ms decomposit

18、ion scale of signal x(t) , and then it can be formed into a division of the signals energy in the scale of E. From the properties of orthogonal wavelet, its known that the total power E is equal to the sum of the components power Ej within a time window (the width of the window is ,N). Letpj=Ej/E, t

19、hen jpj=1, so the corresponding WEE is defined as follows.In the above formula, Ej=kDjk2Along with the sliding of time window, we can get the rule of wavelet energy changing with time.III. DETECTION METHOD AND SIMULATION OF POWER SYSTEM HARMONIC SIGNALA. The Construction of a Power System SignalA co

20、mplex continuous power signal of time x(t) is constructed that x(t) contains fundamental wave,3 、5、7 odd steady harmonic,17 odd steady harmonic, and the process is accompanied with random disturbance signal.The mathematical expressions of x(t) is as follows.In the above formula, f 0 = 50Hz , rand(t)

21、 is the random noise signal of normal distribution function.The waveform of original signal is shown in Fig. 1.B. Wavelet AnalysisSelecting the sampling frequency as 12800Hz, discrete time series as analysis object, Mallat DB4 wavelet is selected, and is decomposed of 3 layer wavelet. Steps are as f

22、ollows in Fig. 2.The occupied frequency of cA3 is 0800 Hz. According to the characteristic of harmonic in power system, less than 17 times of harmonic is considered as steady-state harmonic, more than 17 times of harmonic is considered as transient harmonic. Then cA3 contains all of the informations

23、 of steady-state harmonic, and traditional FFT can be used to analyses the informations of its frequency entropy.cD1, cD2 and cD3 contain all of informations of transient harmonic, it can be reconstructed by wavelet analysis. Letting the reconstructed signal be cD1, cD2, cD3, the sum of cD1, cD2, cD

24、3 is transient harmonic signal. The waveform of cD1+ cD2+ cD3 is shown in Fig. 3.From the above Fig.3, we can see that wavelet analysis cant distinguish the transient harmonic signal from noise signal, but Wavelet energy entropy can be used to distinguish it.C. Wavelet Energy Entropy AnalysisThe for

25、mula (6) is used to solve the WEE of transient harmonic signal. Because the signal is divided into 3 layers by wavelet analysis, j is equal to 3. Selecting the moving window be equal to 100, step length be equal to 1, the calculated waveform of WEE is shown in Fig. 4.From the analysis of Fig. 4, the

26、 value of WEE increased suddenly, that is the time that 17 times transient harmonic occurring. After several periods, the value of WEE returned to the state before 0.2s, it shows that the attenuation of transient harmonic is in end. Thus the time of WEE mutation is the time of appearing or disappear

27、ing of a harmonic. Compared to the time characteristics of wavelet analysis, it is more convenient for analysis.In addition, WEE can reflect variations of the signal energy in different times, and also express the degree of harmonic complexity in some time.IV. CONCLUSIONThis paper studies the mechan

28、ism of applying WEE into harmonic dictions of power system. By wavelet, signal can be separated into two parts of high frequency and low frequency. About low frequency, its amplitude-frequency characteristic can be extracted by traditional FFT; about high frequency, we can make full use of the advan

29、tages of WEE. And extract the characteristics of transient signal effectively. Simulation experiments indicate that wavelet cant extract transient signal from the high frequency signal including noise, but WEE can extract characteristic informations of transient signal successfully.ACKNOWLEDGMENTThe

30、 paper is supported by the project of National Natural Science Foundation of China (No. 61071087)REFERENCES1 G. M. Luo, Z. Y. He, and S. Lin, “Discussion on Using Discrepancy Among Wavelet Relative Entropy Values to Recognize Transient Signals in Power Transmission Line,” Power System Technology, vo

31、l. 32, vol. 15, pp. 47-51, 2008.2 J. W. Sweldens and P. Schroder, “Building Your Own Wavelets at Home,” Wavelets in Computer Graphics, ACM SIGGRAPH Course Notes, 1996.3 R. Q, Quiroga, O. ARosso, and E. Basar, “Wavelet entropy in eventralated potential: a new method shows ordering of EEG oscillations

32、,” Biological Cybernetics, vol. 84, no. 4, pp 291-299, 2001.4 Z. Y. He, Y. M. Cai, and Q. Q. Qian, “A study of wavelet entropy theory and its application in electric power system fault detection,” in Proc. of the CSEE, 2005, vol. 25, no. 5, pp. 23-43.小波能量熵的研究及其在电力系统谐波检测中的应用吴娜 卫永琴摘要：在FFT不能检测瞬态信号的问题和小

33、波分析很容易产生能量泄漏和频率混淆在电力谐波检测上，提出了一种新的算法，它结合小波与信息熵来设计一个新函数，小波能量熵，它是用来提取电力系统暂态信号有效信息的。根据电力系统中的谐波，数学模型是在此基础上完成的，Matlab仿真结果表明，新算法在暂态信号检测上得到验证。关键词：小波能量熵、暂态信号、谐波检测、matlab仿真1.简介传统的电力系统谐波检测算法是基于FFT或改进的FFT的，而且它可以检测稳态信号的振幅和相位,但它不能检测暂态信号。小波分析具有较高的时间和频率分辨率，它在电力系统能有效地提取突变信号，小波分析非常适合检测电力系统中的暂态信号。但小波分析有一些缺点：如电力暂态信号有很多

34、数据和计算量小波分析后，以及能量泄漏和频率混叠，瞬态特征提取的结果无法预测。提出了一种新的算法，小波与信息熵相结合生成小波能量熵，它可以克服了小波分析的不足。并在小波多分辨率分析的特性和熵善于表示系统的混乱程度。因此，新算法可以全面检测稳态或暂态信号。2.小波能量熵（1）小波多分辨率分析 1989年S.Mallat对于小波分析提出了一种新的快速算法，小波分析多分辨率的理论，即Mallat快速小波算法。基于多分辨率的快速小波算法信号划分为多个不同尺度的正交小波，其实现相当于一组的重复使用的高和低通滤波器。一步一步分解时间序列信号，高通滤波器生成信号的高频成分，低通滤波器产生低频近似分量的信号。滤

35、波器的两个组件在频带上宽度相等,并且每个账户占1/2光谱带。每次分解后,信号的采样频率降低。针对低频分量,重复上面的分解过程,从而得到下一个层次的两个组件。快速小波分析的信号转换后，我们定义了高频系数K时刻的J分解规模cDj(K)和低频系数定义为cAj (K)。信号组件的Dj(k)和Aj (k)的重构,以及频率范围中包含的信息如下。在上面的公式fs信号的采样频率,和原始信号序列x(n)可以表示为m的组件的总和，即：为了方便起见， Am(n)表示为Dm+1(n)，然后：Mallat算法大大提高了离散小波的速度，但几乎所有的小波函数频率混淆，这很容易导致相邻尺度能量泄漏和产生频率混叠现象3。所以如

36、果所有小波系数重构的高频信号或单一分支直接用作标准暂态谐波信号的提取，不可避免地且很容易导致不准确的结果。（2）信息熵1948年，C. E. Shannon首先提出信息熵的概念，他把熵作为一个随机的不确定性事件或信息的数量表示系统的不确定性，如果我们使用一个随机变量X的值有限的数字,它代表了国家的制度。其概率空间：然后整个的平均不确定性概率空间也为信息熵，定义为：信息熵H是一个用于测量定位系统在一定条件下，它是一个测量未知程度的序列，它可以用来估计随机信号的复杂性。（3）小波能量熵小波分析具有良好的时频局部化能力。建设和实施小波多分辨率分析成一个统一的框架，它有一个相应的实用快速算法。小波多分

37、辨率和信息熵相结合，我们可以得到一个小波熵的定义及其计算方法4。E=E1,E2,Em等于m的小波能量熵谱分解的信号x(t),然后它可以形成一个部门的信号的能量e的规模从正交小波的性质,众所周知,总功率等于总和组件的功率在一个时间窗口(窗宽,N)。pj=Ej/E，所以相应的极小的定义如下。在上面的公式中，Ej=kDjk2随着滑动时间窗口,我们可以得到小波能量随时间变化的规律。3.电力系统谐波的检测方法和SIGNALDET模拟电力系统谐波信号仿真检验方法（1）创建电力系统信号复杂的连续电力信号的时间x(t)是构造,x(t)包含基波，3、5、7次的稳定谐波，17次的稳定谐波，这个过程是伴随着随机干扰信号。x(t)的数学表达式如下。在上面的公式中， f 0 = 50Hz，rand(t)是正态分布的随机噪声信号的功能。原始信号的波形如图1所示。（2）小波分析选择采样频率为12800 Hz，离散时间序列为分析对象，Mallat DB4小波被选中时，3层小波分解。步骤如图2。被占领的cA3是0 800 Hz的频率。根据电力系统中谐波的特点,不到17倍的谐波被认为是稳态谐波,超过17倍的谐波被认为是暂态谐波。然后cA3包含所有信息的稳态谐波，传统的FFT可以用来分析其频率的信息熵。cD1,cD2和暂态谐波cD3包含所有的信息,它可以通过小波重构分析。重构