电力谐波和间谐波参数估计算法研究
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摘要
随着大量非线性、冲击性负荷在电力系统中投入使用,给电网带来了严重的谐波污染,现代电网中不仅含有整数次谐波而且还存在非整数次谐波,即间谐波。谐波和间谐波治理的前提是对其参数准确估计,本文主要从傅立叶变换、小波变换、现代谱估计和自适应神经网络等几个方面探讨电力谐波和间谐波的参数估计算法。
傅立叶变换是最基本的谐波和间谐波分析方法,已被IEC 61000-4-7标准采用。利用傅立叶变换进行谐波分析的缺点是在非同步采样时存在频谱泄露和栅栏效应,频率分辨率与采样数据长度成反比。加窗插值傅立叶变换是抑制频谱泄漏和消除栅栏效应的有效方法,然而现有的加窗插值傅立叶变换方法在分析精度和计算量之间存在着矛盾,例如,Hanning窗插值算法简单,但分析精度低,Blackman-Harris窗插值算法分析精度高,但计算量大。因此,提出3项3阶Nuttall窗和4项5阶Nuttall窗插值傅立叶变换方法及其改进策略,其插值系数求解简单,计算量小,同时谐波分析精度可媲美Blackman窗和Blackman-Harris窗插值傅立叶变换方法。通过消除基波对二次谐波或基波和谐波对其附近间谐波的频谱泄漏,提高了Nuttall窗插值傅立叶变换方法的总体分析精度,而计算量增加不大。
小波变换克服了傅立叶变换在频域完全局部化而在时域完全无局部性的缺点,可以同时提取信号的时频信息,近年来也被用于谐波分析,但利用小波变换方法分析稳态谐波信号时,频谱混叠比较严重,分析精度不高。提出一种基于递归滤波器的谐波和间谐波分析方法,该方法有效克服了小波变换的频谱混叠现象,能够准确估计谐波和间谐波的频率和幅值,并且递归滤波器的输出值可按采样点来逐点更新,仅由信号的前六个采样值和递归滤波器的前七个输出值决定,计算复杂性与采样频率无关。
针对傅立叶变换在短数据条件下频率分辨率低的缺点,将现代谱估计方法用于谐波和间谐波的频率估计,提出最优加权Burg算法和基于传播算子的MUSIC算法。最优加权Burg算法能够减小Burg算法的谱峰偏移和消除其谱线分裂。利用传播算子估计噪声子空间时不需要估计自相关矩阵和特征分解,计算复杂度低,并且信号源数的适当过估计将会使基于传播算子的MUSIC算法的频率估计性能媲美MUSIC算法。利用基于多级维纳滤波器的TLS-ESPRIT算法估计正弦信号频率时同样能减小计算量。通过多个仿真算例,从不同角度验证了所提算法具有频率分辨率高的优点,适用于非同步采样、短数据条件下的谐波和间谐波频率估计。
将Adaline神经元用于谐波和间谐波分析,提出复数域Adaline神经网络谐波分析模型和增强型Adaline神经网络的频率学习率自适应选择方法。复数域Adaline神经网络模型的输入向量和权向量仅为Adaline神经元的一半,简化了网络结构。对各谐波和间谐波的频率学习率根据频率的变化量进行自动调整,能够改善增强型Adaline神经网络的收敛性和分析精度。将LMS牛顿算法、变步长LMS算法、RLS算法等自适应算法应用于Adaline神经网络,能够大大提高Adaline神经网络的收敛速度。仿真算例表明,所提出的Adaline神经网络模型和算法具有分析精度高、收敛速度快的优点。
最后利用基于传播算子的求根MUSIC和Adaline神经网络相结合的方法对计算机用电、微波炉用电、球磨机电流和杭州某锻造厂电流的实测数据进行分析,验证了所提出谐波和间谐波自适应分析算法的有效性,并得出各自的谐波和间谐波参数及用电特点。
With extensive applications of nonlinear or impact loads in power system, that causes serious harmonics contamitation to the electric network. There are not only integer harmonics but also many non-integer harmonics which are interharmonics in modern electric network. The accurate estimation of harmonics and interharmonics parameters is the premise for their compensation. The paper mainly investigated the parameters estimation algorithm of harmonics and interharmonics in Fourier transform, wavelet transform, modern spectral estimation and Adaline neural network.
Fourier transform is the most elementary method for the analysis of harmonics and interharmonics, which has been adopted by IEC 61000-4-7 standard. The disadvantage of applying Fourier transform to harmonics analysis is that it exists the spectral leakage and fence effect, its frequency resolution is inversely proportional to the sample data length in asynchronous sampling. The windowed interpolating Fourier transform is the effective method to restrain spectral leakage and eliminate fence effect, however there are conflicts between the measurement precision and the computational burden for the current windowed interpolating Fourier transform methods. For example, Hanning window interpolating algorithm is simple, but its accuracy is low; Blackman-Harris window interpolating algorithm has high precision, but its computational amount is large. Therefore, the interpolating Fourier transform algorithm and its improved strategy based on three-term third derivative and four-term fifth derivative Nuttall window were proposed in this paper. The solution of their interpolating coefficients is simple, while the analytical accuracy of harmonics are comparable to Blackman or Blackman-Harris window interpolating algorithm. The improved method which eliminated the spectral leakage on the second hamonic generated by the fundamental component or the interharmonics near the fundamental component and harmonics promoted the orerall analytical accuracy of the Nuttall interpolating Fourier transform with a small amount of additional computation.
Wavelet transform which overcomes the faults of Fourier transform complete localization in frequency domain and no localization in time domain and can extract time-frequency information of signal is used to harmonics analysis recently. However, for the stationary harmonic signal, the analytical accuracy of wavelet transform is not high because of its serious spectral aliasing. An analytical method of haromnics and interharmonics based on recursive filter was proposed in this paper. The method which overcomes spectral aliasing of wavelet transform can accurately estimate amplitudes and phases of harmonics and interharmonics. Moreover, the recursive filter output is only decided by six previous sample values and seven previous recursive filter outputs, that computational complexity is independent of the sampling frequency.
Modern spectral estimation was used to frequency estimation of harmonics and interharmonics to overcome the disadvantage of Fourier transform of low frequency resolution in short sample data. An optimal weighted Burg algorithm and a MUSIC algorithm based on propagator method (PM) were proposed. The optimal weighted Burg algorithm can reduce spectral peak excursion and eliminate spectral line splitting of Burg algorithm. The estimation of noise subspace based on PM doesn't require estimation of covariance and eigenvalue decomposition, and computational load is low. Moreover the appropriate overestimation of signal numbers will make frequency estimation performance of MUSIC based on PM be comparable to MUSIC. The frequency estimation using TLS-ESPRIT based on Multi-stage wiener filter can reduce computational burden too. The multiple simulation examples showed the proposed method had the advantages of high frequency resolution, and was applicable for harmonics and interhamonics frequency estimation of asynchronous sampling and short data length.
The paper introduced Adaline neuron in the analysis of harmonics and interharmonics, complex Adaline neural network harmonic analysis model and an adaptive selecting method of frequency learning rates on enhanced Adaline neural network were proposed. The complex Adaline neural network model reduced input vectors and weights to half that of Adaline neuron. The frequency learning rates of harmonics and interharmonics were automatic adjustment according to change frequency, that could improve convergence performance and analytical precision of enhanced Adaline neural network. Several adaptive algorithms such as least mean square (LMS) Newton algorithm, variable step size LMS algorithm, recursive least square algorithm were used to Adaline neural network, that could greatly improve the convergence speed. The simulation examples demonstrated that the proposed Adaline neural network and learning algorithm achieved high precision and rapid convergence.
Finally, the actual sampling data of the electrical comsuptions of computer and microwave oven, the current of ball mill and a forging plant in Hangzhou were analyzed by Root-MUSIC based on PM and Adaptive neural network method. The analysis results further verified the validity of the proposed adaptive analysis algorithm for harmonics and interharmonics, as well as obtained their parameters of harmonics (interharmonics) and electricity comsuption characteristics.
傅立叶变换是最基本的谐波和间谐波分析方法,已被IEC 61000-4-7标准采用。利用傅立叶变换进行谐波分析的缺点是在非同步采样时存在频谱泄露和栅栏效应,频率分辨率与采样数据长度成反比。加窗插值傅立叶变换是抑制频谱泄漏和消除栅栏效应的有效方法,然而现有的加窗插值傅立叶变换方法在分析精度和计算量之间存在着矛盾,例如,Hanning窗插值算法简单,但分析精度低,Blackman-Harris窗插值算法分析精度高,但计算量大。因此,提出3项3阶Nuttall窗和4项5阶Nuttall窗插值傅立叶变换方法及其改进策略,其插值系数求解简单,计算量小,同时谐波分析精度可媲美Blackman窗和Blackman-Harris窗插值傅立叶变换方法。通过消除基波对二次谐波或基波和谐波对其附近间谐波的频谱泄漏,提高了Nuttall窗插值傅立叶变换方法的总体分析精度,而计算量增加不大。
小波变换克服了傅立叶变换在频域完全局部化而在时域完全无局部性的缺点,可以同时提取信号的时频信息,近年来也被用于谐波分析,但利用小波变换方法分析稳态谐波信号时,频谱混叠比较严重,分析精度不高。提出一种基于递归滤波器的谐波和间谐波分析方法,该方法有效克服了小波变换的频谱混叠现象,能够准确估计谐波和间谐波的频率和幅值,并且递归滤波器的输出值可按采样点来逐点更新,仅由信号的前六个采样值和递归滤波器的前七个输出值决定,计算复杂性与采样频率无关。
针对傅立叶变换在短数据条件下频率分辨率低的缺点,将现代谱估计方法用于谐波和间谐波的频率估计,提出最优加权Burg算法和基于传播算子的MUSIC算法。最优加权Burg算法能够减小Burg算法的谱峰偏移和消除其谱线分裂。利用传播算子估计噪声子空间时不需要估计自相关矩阵和特征分解,计算复杂度低,并且信号源数的适当过估计将会使基于传播算子的MUSIC算法的频率估计性能媲美MUSIC算法。利用基于多级维纳滤波器的TLS-ESPRIT算法估计正弦信号频率时同样能减小计算量。通过多个仿真算例,从不同角度验证了所提算法具有频率分辨率高的优点,适用于非同步采样、短数据条件下的谐波和间谐波频率估计。
将Adaline神经元用于谐波和间谐波分析,提出复数域Adaline神经网络谐波分析模型和增强型Adaline神经网络的频率学习率自适应选择方法。复数域Adaline神经网络模型的输入向量和权向量仅为Adaline神经元的一半,简化了网络结构。对各谐波和间谐波的频率学习率根据频率的变化量进行自动调整,能够改善增强型Adaline神经网络的收敛性和分析精度。将LMS牛顿算法、变步长LMS算法、RLS算法等自适应算法应用于Adaline神经网络,能够大大提高Adaline神经网络的收敛速度。仿真算例表明,所提出的Adaline神经网络模型和算法具有分析精度高、收敛速度快的优点。
最后利用基于传播算子的求根MUSIC和Adaline神经网络相结合的方法对计算机用电、微波炉用电、球磨机电流和杭州某锻造厂电流的实测数据进行分析,验证了所提出谐波和间谐波自适应分析算法的有效性,并得出各自的谐波和间谐波参数及用电特点。
With extensive applications of nonlinear or impact loads in power system, that causes serious harmonics contamitation to the electric network. There are not only integer harmonics but also many non-integer harmonics which are interharmonics in modern electric network. The accurate estimation of harmonics and interharmonics parameters is the premise for their compensation. The paper mainly investigated the parameters estimation algorithm of harmonics and interharmonics in Fourier transform, wavelet transform, modern spectral estimation and Adaline neural network.
Fourier transform is the most elementary method for the analysis of harmonics and interharmonics, which has been adopted by IEC 61000-4-7 standard. The disadvantage of applying Fourier transform to harmonics analysis is that it exists the spectral leakage and fence effect, its frequency resolution is inversely proportional to the sample data length in asynchronous sampling. The windowed interpolating Fourier transform is the effective method to restrain spectral leakage and eliminate fence effect, however there are conflicts between the measurement precision and the computational burden for the current windowed interpolating Fourier transform methods. For example, Hanning window interpolating algorithm is simple, but its accuracy is low; Blackman-Harris window interpolating algorithm has high precision, but its computational amount is large. Therefore, the interpolating Fourier transform algorithm and its improved strategy based on three-term third derivative and four-term fifth derivative Nuttall window were proposed in this paper. The solution of their interpolating coefficients is simple, while the analytical accuracy of harmonics are comparable to Blackman or Blackman-Harris window interpolating algorithm. The improved method which eliminated the spectral leakage on the second hamonic generated by the fundamental component or the interharmonics near the fundamental component and harmonics promoted the orerall analytical accuracy of the Nuttall interpolating Fourier transform with a small amount of additional computation.
Wavelet transform which overcomes the faults of Fourier transform complete localization in frequency domain and no localization in time domain and can extract time-frequency information of signal is used to harmonics analysis recently. However, for the stationary harmonic signal, the analytical accuracy of wavelet transform is not high because of its serious spectral aliasing. An analytical method of haromnics and interharmonics based on recursive filter was proposed in this paper. The method which overcomes spectral aliasing of wavelet transform can accurately estimate amplitudes and phases of harmonics and interharmonics. Moreover, the recursive filter output is only decided by six previous sample values and seven previous recursive filter outputs, that computational complexity is independent of the sampling frequency.
Modern spectral estimation was used to frequency estimation of harmonics and interharmonics to overcome the disadvantage of Fourier transform of low frequency resolution in short sample data. An optimal weighted Burg algorithm and a MUSIC algorithm based on propagator method (PM) were proposed. The optimal weighted Burg algorithm can reduce spectral peak excursion and eliminate spectral line splitting of Burg algorithm. The estimation of noise subspace based on PM doesn't require estimation of covariance and eigenvalue decomposition, and computational load is low. Moreover the appropriate overestimation of signal numbers will make frequency estimation performance of MUSIC based on PM be comparable to MUSIC. The frequency estimation using TLS-ESPRIT based on Multi-stage wiener filter can reduce computational burden too. The multiple simulation examples showed the proposed method had the advantages of high frequency resolution, and was applicable for harmonics and interhamonics frequency estimation of asynchronous sampling and short data length.
The paper introduced Adaline neuron in the analysis of harmonics and interharmonics, complex Adaline neural network harmonic analysis model and an adaptive selecting method of frequency learning rates on enhanced Adaline neural network were proposed. The complex Adaline neural network model reduced input vectors and weights to half that of Adaline neuron. The frequency learning rates of harmonics and interharmonics were automatic adjustment according to change frequency, that could improve convergence performance and analytical precision of enhanced Adaline neural network. Several adaptive algorithms such as least mean square (LMS) Newton algorithm, variable step size LMS algorithm, recursive least square algorithm were used to Adaline neural network, that could greatly improve the convergence speed. The simulation examples demonstrated that the proposed Adaline neural network and learning algorithm achieved high precision and rapid convergence.
Finally, the actual sampling data of the electrical comsuptions of computer and microwave oven, the current of ball mill and a forging plant in Hangzhou were analyzed by Root-MUSIC based on PM and Adaptive neural network method. The analysis results further verified the validity of the proposed adaptive analysis algorithm for harmonics and interharmonics, as well as obtained their parameters of harmonics (interharmonics) and electricity comsuption characteristics.
引文
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