基于S变换的电能质量扰动分析
摘要
电能质量扰动会导致设备过热、电机停转、保护失灵以及计量不准等严重后果,因此电能质量问题引起了广泛的关注。电能质量扰动类型较多,单一的时域或频域方法难以胜任所有类型的电能质量扰动分析,因而时频分析方法成了电能质量扰动分析的常用工具。S变换作为小波变换和短时傅立叶变换的继承和发展,省却了对基小波的选择,同时克服了小波变换受噪声影响大以及短时傅立叶变换窗宽固定的缺陷,近年成了电能质量扰动分析的热点工具。本文依据国内外相关电能质量标准,结合电能质量研究现状和工程实际需要,重点研究了利用S变换进行电能质量扰动分析的一系列方法。
针对电能质量扰动信号的噪声水平估计问题,利用改进S变换提出了电能质量扰动信号的白噪声方差估计方法。根据电能质量扰动信号在改进S变换域的时频特性,提出了能量聚集度概念,即扰动信号能量在改进S变换时频面的聚集程度。通过使扰动信号的能量聚集度达到最小确定改进S变换的窗宽因子,保证扰动信号和白噪声在时频面的混叠区域最小,便于扰动信号和噪声的分离。进而根据白噪声在改进S变换域的分布特性检测时频面的噪声和非噪声区域,利用噪声区域估计白噪声的方差。仿真实验验证了采用所提方法估计的白噪声方差有很高的可信度,有望应用于电能质量扰动信号的降噪。
针对电能质量扰动信号的降噪问题,基于改进S变换的能量聚集度概念和噪声估计方法提出了两种电能质量扰动信号的降噪方法。方法一利用白噪声估计过程中确定的非噪声区域,通过硬阈值方法实现降噪。方法二通过简单的迭代算法实现,首先反复计算信号的改进S变换能量聚集度及由其确定阈值采用硬阈值算法进行降噪后得到的修正S变换,直至由能量聚集度二次变化率最小值确定的迭代次数为止,然后对修正S变换进行反变换得到降噪后的扰动信号。通过与小波降噪方法的降噪效果进行比较,证明了所提的两种降噪方法有一定的优势。
针对电能质量扰动分类问题,利用改进S变换和决策树提出了电能质量扰动分类的新方法。首先讨论了改进S变换的特征向量,阐明了频率-幅值包络和时间-幅值向量能够反映扰动信号的主要频域和时域特征,并从中提取了4个统计特征量,然后采用简单的分类二叉树实现了9种电能质量扰动的分类。仿真结果表明,所提的分类方法识别正确率高,对噪声不敏感。
针对S变换计算量大的问题,提出了不完全S变换以改善其在电能质量扰动分析应用中的计算速度。电能质量扰动的检测通常只需要利用扰动信号S变换主要频率分量,因此,在计算S变换的过程中仅计算对应于扰动信号主要频率的S变换时间分量,就可以减少S变换的运算时间,而主要频率是由扰动信号功率谱包络的动态测度方法确定的。仿真结果证明,在保证检测精度的基础上,不完全S变换能大大缩短计算时间。
针对电能质量扰动参数估计问题,结合改进S变换时频分辨率可调和不完全S变换计算速度快的优点,提出了基于改进不完全S变换的电能质量扰动参数估计方法。算法根据不同扰动类型自适应地选择窗宽因子,进而计算扰动信号的改进不完全S变换的各主要频率分量,最后利用这些分量实现各种扰动参数的估计。仿真结果证明了所提方法具有估计精度高,计算速度快的特点。
针对电容器投切扰动源的定位问题,利用S变换的相位与扰动信号具有直接联系的特点,提出了基于交叉S变换的电容器投切扰动源定位的新方法。算法首先通过计算瞬时扰动电压和电流信号的不完全S变换得到相应的两个扰动频率分量,然后求它们的向量积得到交叉S变换的相位差谱,最后利用扰动起始时刻的相位差极性确定投切电容器相对于监测点的位置,结合多处监测点确定投切电容器的准确位置。仿真结果证明了算法的有效性。
根据上述提出的基于S变换的系列电能质量扰动分析方法,设计了综合电能质量扰动分析系统。系统由前处理单元、电力参数测量及电能计量单元、扰动触发单元、电能质量分析系统和评估系统等功能单元组成。在各功能单元的阐述中,主要提出了基于动态测度的基波频率精确测量方法,扰动检测触发信号的动态测度产生方法以及基于上位机的电能质量扰动的专家分析系统,将提出的基于S变换的系列电能质量扰动分析方法有效地整合于该系统中。
本文提出的基于S变换的电能质量扰动分析的系列方法和综合电能质量扰动分析系统,为电能质量实时检测和离线分析提供了有效的工具。
Power Quality disturbances cause several problems, such as overheating, failure of motors, disoperation of protective equipment and inaccurate metering. As a consequence, more concern about different issues that relate to the power quality has been raised in recent years. It is failed to accomplish analysis of all the types of power quality disturbances utilizing single time or frequency means because of the diversity of power quality disturbances. Therefore, the time-frequency analysis methods become the hot tools. The S-transform can be seen either as an extension of ideas of wavelet or short-time Fourier transform, and it has characteristics superior to them because it has no use for the choice of base function. S-transform is more robust to noise than wavelet and it is essentially a short-time Fourier-transform whose window width varies inversely with the frequency. In accordance with national and international power quality standard and research situations, systematic and in-depth researches about power quality disturbances analysis approaches are carried out. The main contributions of this dissertation are listed as follows:
A modified S-transform based method for noise level estimation of power quality signal is proposed. According to the time-frequency property of power quality in modified S-transform, the concept of energy congregation level is defined. The time-frequency resolution is determined by making the value of energy congregation level minimum, so there has the minimal aliasing area to facilitate the separation of disturbances signal and noise. By use of white noise distribution characteristic the area of power quality signal’s energy and noise in modified S-transform plane is detected. Based on the time-frequency plane only contains the power spectrum in noise area the estimation of noise variance is implemented. Simulation results show that the estimation results of noise variance are of high degree of confidence while the sampling rate achieves a certain extent.
Two denoising approaches of power quality signals are proposed based on concept of energy congregation level and method of noise estimation respectively. One of the ways of denoising is realized just using iterative algorithm. The rectified S-transform is obtained by computing the energy congregation level and hard threshold denoising algorithm is carried out repeatedly. The quadratic change rate of energy congregation level is defined to find the optimal iterations number used in iterating algorithm to obtain satisfactory denoising results. Then the inverse rectified S-transform is performed to get the denoised power quality disturbances signals. The other way of denoising is realized by utilizing the power quality region of the time-frequency plane which is determined in the process of noise estimation and the hard threshold algorithm is used to verify the value of the modified S-transform matrix elements. The denoising results compared with wavelet-based method illustrate the advantage of the proposed approaches.
A classification method of power quality disturbances is proposed using modified S-transform and decision tree. The approach is realized by extracting 4 features from modified S-transform module matrix and employing binary classification tree. 9 types of disturbances are recognized effectively using the proposed method. The simulation results show that the proposed classification methods are feasible for real applications for their significant accuracy and immune to noise.
In order to overcome the defect of large amount calculation of S-transform, the definition of incomplete S-transform is proposed and applied to power quality disturbances detection. The detection methods of power quality based on S-transform usually use the major vectors of S-transform module time-frequency matrix instead of all of the vectors. If just the major vectors corresponding disturbances major frequency fractional are computed, much computation time will be saved. Dynamics is utilized to describe the envelope of power spectrum so as to detect the valid frequency samples of FFT. The simulation results illustrate that the proposed method increases speed of algorithm and has no loss of detection precision.
A new method of parameters estimation of power quality disturbances is proposed based on modified incomplete S-transform, which combine the modified S-transform with incomplete S-transform that have complementary advantages in time frequency resolutions and computation speed. The optimal windowing coefficients in connection with different disturbances are adaptively selected, and then the major vectors obtained using the modified incomplete S-transform and these vectors are utilized to estimate the parameters. Simulation results verified that the proposed method has characteristics of lower complexity, less computation and high precision.
On the basis of phase property of S-transform that it provides multi-resolution analysis while retaining the absolute phase of each frequency, a cross S-transform method for locating capacitor switching disturbances is proposed. The disturbance frequency vectors of S-transform of transient voltage and current, which are obtained by performing incomplete S-transform, are employed to perform cross S-transform and the phase difference spectrum is obtained. The phase difference of transient voltage and current is determined by extracting the value at disturbance start point from the phase spectrum. The relative location of switching capacitor is determined by the polarity of the value and the exact location can be obtained by combining with detection results of multiple monitoring stations. The proposed method has been verified by simulation experiments.
A comprehensive power quality analysis system is designed based on the series algorithm described above. The architecture is designed witch consists of pre- processing unit, power parameter and energy measurement unit, disturbance triggering unit, power quality analysis unit and assessment system. Some key algorithms are proposed in the process that elaborates the function units, including dynamic-based frequency measurement method, triggering signal generating approach and PC-based power quality analysis expert system. The series S-transform-based power quality analysis method are effectively integrated in the system.
The series S-transform-based power quality disturbances analysis methods and comprehensive analysis system expounded in the dissertation aim to provide effective theorem basis and algorithms for power quality on-line detection and off-line analysis, and may be used in engineering practice.
针对电能质量扰动信号的噪声水平估计问题,利用改进S变换提出了电能质量扰动信号的白噪声方差估计方法。根据电能质量扰动信号在改进S变换域的时频特性,提出了能量聚集度概念,即扰动信号能量在改进S变换时频面的聚集程度。通过使扰动信号的能量聚集度达到最小确定改进S变换的窗宽因子,保证扰动信号和白噪声在时频面的混叠区域最小,便于扰动信号和噪声的分离。进而根据白噪声在改进S变换域的分布特性检测时频面的噪声和非噪声区域,利用噪声区域估计白噪声的方差。仿真实验验证了采用所提方法估计的白噪声方差有很高的可信度,有望应用于电能质量扰动信号的降噪。
针对电能质量扰动信号的降噪问题,基于改进S变换的能量聚集度概念和噪声估计方法提出了两种电能质量扰动信号的降噪方法。方法一利用白噪声估计过程中确定的非噪声区域,通过硬阈值方法实现降噪。方法二通过简单的迭代算法实现,首先反复计算信号的改进S变换能量聚集度及由其确定阈值采用硬阈值算法进行降噪后得到的修正S变换,直至由能量聚集度二次变化率最小值确定的迭代次数为止,然后对修正S变换进行反变换得到降噪后的扰动信号。通过与小波降噪方法的降噪效果进行比较,证明了所提的两种降噪方法有一定的优势。
针对电能质量扰动分类问题,利用改进S变换和决策树提出了电能质量扰动分类的新方法。首先讨论了改进S变换的特征向量,阐明了频率-幅值包络和时间-幅值向量能够反映扰动信号的主要频域和时域特征,并从中提取了4个统计特征量,然后采用简单的分类二叉树实现了9种电能质量扰动的分类。仿真结果表明,所提的分类方法识别正确率高,对噪声不敏感。
针对S变换计算量大的问题,提出了不完全S变换以改善其在电能质量扰动分析应用中的计算速度。电能质量扰动的检测通常只需要利用扰动信号S变换主要频率分量,因此,在计算S变换的过程中仅计算对应于扰动信号主要频率的S变换时间分量,就可以减少S变换的运算时间,而主要频率是由扰动信号功率谱包络的动态测度方法确定的。仿真结果证明,在保证检测精度的基础上,不完全S变换能大大缩短计算时间。
针对电能质量扰动参数估计问题,结合改进S变换时频分辨率可调和不完全S变换计算速度快的优点,提出了基于改进不完全S变换的电能质量扰动参数估计方法。算法根据不同扰动类型自适应地选择窗宽因子,进而计算扰动信号的改进不完全S变换的各主要频率分量,最后利用这些分量实现各种扰动参数的估计。仿真结果证明了所提方法具有估计精度高,计算速度快的特点。
针对电容器投切扰动源的定位问题,利用S变换的相位与扰动信号具有直接联系的特点,提出了基于交叉S变换的电容器投切扰动源定位的新方法。算法首先通过计算瞬时扰动电压和电流信号的不完全S变换得到相应的两个扰动频率分量,然后求它们的向量积得到交叉S变换的相位差谱,最后利用扰动起始时刻的相位差极性确定投切电容器相对于监测点的位置,结合多处监测点确定投切电容器的准确位置。仿真结果证明了算法的有效性。
根据上述提出的基于S变换的系列电能质量扰动分析方法,设计了综合电能质量扰动分析系统。系统由前处理单元、电力参数测量及电能计量单元、扰动触发单元、电能质量分析系统和评估系统等功能单元组成。在各功能单元的阐述中,主要提出了基于动态测度的基波频率精确测量方法,扰动检测触发信号的动态测度产生方法以及基于上位机的电能质量扰动的专家分析系统,将提出的基于S变换的系列电能质量扰动分析方法有效地整合于该系统中。
本文提出的基于S变换的电能质量扰动分析的系列方法和综合电能质量扰动分析系统,为电能质量实时检测和离线分析提供了有效的工具。
Power Quality disturbances cause several problems, such as overheating, failure of motors, disoperation of protective equipment and inaccurate metering. As a consequence, more concern about different issues that relate to the power quality has been raised in recent years. It is failed to accomplish analysis of all the types of power quality disturbances utilizing single time or frequency means because of the diversity of power quality disturbances. Therefore, the time-frequency analysis methods become the hot tools. The S-transform can be seen either as an extension of ideas of wavelet or short-time Fourier transform, and it has characteristics superior to them because it has no use for the choice of base function. S-transform is more robust to noise than wavelet and it is essentially a short-time Fourier-transform whose window width varies inversely with the frequency. In accordance with national and international power quality standard and research situations, systematic and in-depth researches about power quality disturbances analysis approaches are carried out. The main contributions of this dissertation are listed as follows:
A modified S-transform based method for noise level estimation of power quality signal is proposed. According to the time-frequency property of power quality in modified S-transform, the concept of energy congregation level is defined. The time-frequency resolution is determined by making the value of energy congregation level minimum, so there has the minimal aliasing area to facilitate the separation of disturbances signal and noise. By use of white noise distribution characteristic the area of power quality signal’s energy and noise in modified S-transform plane is detected. Based on the time-frequency plane only contains the power spectrum in noise area the estimation of noise variance is implemented. Simulation results show that the estimation results of noise variance are of high degree of confidence while the sampling rate achieves a certain extent.
Two denoising approaches of power quality signals are proposed based on concept of energy congregation level and method of noise estimation respectively. One of the ways of denoising is realized just using iterative algorithm. The rectified S-transform is obtained by computing the energy congregation level and hard threshold denoising algorithm is carried out repeatedly. The quadratic change rate of energy congregation level is defined to find the optimal iterations number used in iterating algorithm to obtain satisfactory denoising results. Then the inverse rectified S-transform is performed to get the denoised power quality disturbances signals. The other way of denoising is realized by utilizing the power quality region of the time-frequency plane which is determined in the process of noise estimation and the hard threshold algorithm is used to verify the value of the modified S-transform matrix elements. The denoising results compared with wavelet-based method illustrate the advantage of the proposed approaches.
A classification method of power quality disturbances is proposed using modified S-transform and decision tree. The approach is realized by extracting 4 features from modified S-transform module matrix and employing binary classification tree. 9 types of disturbances are recognized effectively using the proposed method. The simulation results show that the proposed classification methods are feasible for real applications for their significant accuracy and immune to noise.
In order to overcome the defect of large amount calculation of S-transform, the definition of incomplete S-transform is proposed and applied to power quality disturbances detection. The detection methods of power quality based on S-transform usually use the major vectors of S-transform module time-frequency matrix instead of all of the vectors. If just the major vectors corresponding disturbances major frequency fractional are computed, much computation time will be saved. Dynamics is utilized to describe the envelope of power spectrum so as to detect the valid frequency samples of FFT. The simulation results illustrate that the proposed method increases speed of algorithm and has no loss of detection precision.
A new method of parameters estimation of power quality disturbances is proposed based on modified incomplete S-transform, which combine the modified S-transform with incomplete S-transform that have complementary advantages in time frequency resolutions and computation speed. The optimal windowing coefficients in connection with different disturbances are adaptively selected, and then the major vectors obtained using the modified incomplete S-transform and these vectors are utilized to estimate the parameters. Simulation results verified that the proposed method has characteristics of lower complexity, less computation and high precision.
On the basis of phase property of S-transform that it provides multi-resolution analysis while retaining the absolute phase of each frequency, a cross S-transform method for locating capacitor switching disturbances is proposed. The disturbance frequency vectors of S-transform of transient voltage and current, which are obtained by performing incomplete S-transform, are employed to perform cross S-transform and the phase difference spectrum is obtained. The phase difference of transient voltage and current is determined by extracting the value at disturbance start point from the phase spectrum. The relative location of switching capacitor is determined by the polarity of the value and the exact location can be obtained by combining with detection results of multiple monitoring stations. The proposed method has been verified by simulation experiments.
A comprehensive power quality analysis system is designed based on the series algorithm described above. The architecture is designed witch consists of pre- processing unit, power parameter and energy measurement unit, disturbance triggering unit, power quality analysis unit and assessment system. Some key algorithms are proposed in the process that elaborates the function units, including dynamic-based frequency measurement method, triggering signal generating approach and PC-based power quality analysis expert system. The series S-transform-based power quality analysis method are effectively integrated in the system.
The series S-transform-based power quality disturbances analysis methods and comprehensive analysis system expounded in the dissertation aim to provide effective theorem basis and algorithms for power quality on-line detection and off-line analysis, and may be used in engineering practice.
引文
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