基于小波变换和支持向量机的电能质量扰动分析方法
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摘要
近年来电能质量问题已引起人们广泛关注。这主要是因为:一方面,大量非线性、波动性、冲击性和不平衡性负荷的广泛使用导致电能质量日益下降;另一方面,以计算机和微处理器为核心的对电能质量扰动敏感的高自动化和高智能化的电子设备和精密工业对电能质量提出了越来越高的要求。电力系统供电的电能质量是电力工业产品的重要指标,涉及发电、供电、用电各方面的利益。电能质量指标若偏离正常水平过大,会给发电、输电、变电、配电和用电带来不同程度的危害。因此,电能质量问题已经成为电能供应市场的核心问题之一,电能质量检测与分析技术和电能质量控制技术亦成为电力系统领域中新的研究热点。电能质量检测与分析是电能质量控制的基础,建立电能质量监测与分析系统并对电能质量扰动进行正确检测、评估和分类均是十分必要的。本文深入研究了基于复小波变换的动态电能质量扰动检测与定位方法、基于支持向量机的动态电能质量扰动自动识别方法和基于提升小波变换的电能质量扰动数据压缩方法。其应用可提高电能质量监测与分析系统的准确性、实时性及智能化、自动化和网络化水平。
为解决常用正交实小波变换不能提取信号相位信息的缺陷,在分析小波相频特性对小波分析效果影响的基础上,提出利用复小波变换的复合信息对动态电能质量扰动进行分析可获得更好的分析效果。由于现有的复小波均为连续小波,为克服其计算复杂等缺陷,深入研究了一种通过改变相频特性由现有正交紧支实小波构造正交紧支复小波的方法。该方法基于多分辨率分析思想,仅要求正交紧支实小波具有低通滤波器即可,由该方法构造的正交紧支复小波具有正交性和紧支性,仍可采用Mallat快速算法。选择Db4正交紧支实小波构造出一种Db4正交紧支复小波,并将其用于动态电能质量扰动检测与定位。所构建的Db4正交紧支复小波滤波器组与原Db4正交紧支实小波滤波器组的长度相同,支集相同,同时具有与Db4正交紧支小波相同的特性:正交性、紧支性、消失矩和正则性。通过仿真,对Db4正交紧支复小波变换与Db4正交紧支实小波变换的分析效果和Db4正交紧支复小波的复合信息与简单信息的分析效果进行了对比分析。
鉴于小波变换优秀的时频局部化特性和支持向量机优秀的统计学习能力,提出一种基于复小波变换和多类支持向量机分类器的动态电能质量扰动识别与分类方法:复小波变换主要用于提取动态电能质量扰动的特征向量;多类支持向量机分类器主要用于根据提取的特征向量对动态电能质量扰动进行识别与分类。为克服现有多类支持向量机分类器算法本身存在的一些缺陷,在借鉴模糊聚类分析思想的基础上,提出一种新的多类SVM分类器算法,即分级聚类SVM算法,同时构造了一种基于分级聚类SVM算法的动态电能质量扰动分类树。为验证所提出方法的正确性和有效性,对基于复小波变换和多类支持向量机分类器的动态电能质量扰动识别与分类方法和基于人工神经网络的分类方法进行了对比分析,同时也对分级聚类SVM算法和常用的几种多类SVM分类器算法进行了对比分析。
为减少电能质量扰动数据的存储空间、传输数据量以及提高电能质量监测与分析系统的实时性,在深入研究提升小波变换基本理论的基础上,给出一种基于提升小波变换的电能质量扰动数据压缩方法:首先通过提升小波变换对电能质量扰动信号进行多尺度分解;然后根据相应的施加阈值策略对每个尺度上的高频系数进行阈值量化与编码处理,并保存与扰动相关的系数值而抛弃其它与扰动无关的系数值,从而实现电能质量扰动数据压缩;最后可利用提升小波逆变换由压缩后的数据对原始电能质量扰动信号进行重构。在阈值量化与编码步骤采取各个尺度下使用不同软阈值的策略,阈值估计采用极大极小阈值算法。为了更好地验证基于提升小波变换的电能质量扰动数据压缩方法的正确性和有效性,给出了四个数据压缩性能评价指标,并选用Db4正交紧支实小波的提升算法对几种常见电能质量扰动的数据压缩效果进行了仿真测试。
设计了一种基于电能质量监测与分析系统,其主站由工控机和PCI CAN板卡构成,从站即为各个电能质量监测装置。同时给出了基于复小波变换和支持向量机的电能质量分析方法在该系统中的软件实现流程。提出一种基于DSP+双口RAM+ARM的电能质量监测装置的硬件设计方案,DSP主要用于电力信号采集、基本电力参数计算、电能质量参数计算与分析,此外还要实现事件记录、故障报警、遥信/遥控等功能;ARM主要用于实现本地显示、CAN通信、系统参数设置、键盘操作等;DSP和ARM之间通过双口RAM进行数据交换。为解决ARM和CAN控制器之间地址与数据总线复用问题,设计了ARM与CAN控制器之间的接口时序电路,该时序电路通过CPLD实现;为提高系统的实时性、稳定性和可靠性,采用了嵌入式实时操作系统μC/OS-II用于ARM软件开发。
In recent years, power quality problem have drawn extensive attention of people. One reason is that power quality has been being disturbed heavily with the increasing number of polluting loads such as non-linear loads, time-variant loads, fluctuating loads, unbalanced loads, etc.; the other is that intelligent electrical devices have put forward more rigorous requirements for power quality. As an important index of the power industry product, power quality concerns the interests of generating power, supplying power and utilizing power. In the event that the power quality index departs the normal level too much, it will endanger the electric power generation, electric power transmission, electric power transform, electric power distribution and electric power consumption to a different extent. Therefore, power quality has become one of the primary problems in the electric power market. Power quality monitroing and analysis technology and power quality control technology have become new researching focuses of the electric power system field. Power Quality monitoring and analysis is the basis and premise of power quality control. Therefore, it is very necessary to build a power quality monitoring and analysis system to examine, evaluate and classify the power quality disturbances correctly. This dissertation makes a deep research on methods with regard to power quality analysis which include detection and location method of dynamic power quality disturbances based on complex wavelet transform, automatic recognition and classification method of dynamic power quality disturbances based on multi-class support vector machine classifier; data compression method of power quality disturbances based on lifting wavelet transform. Application of these methods may improve the power quality monitoring and analysis system in aspects of accuracy, real-time performance, automation, etc.
In order to resolve the disadvantage of the common-used orthogonal real wavelet transform that it cannot draw the signal’s phase information, based on analyzing the impact of wavelets’phase-frequency characteristic on wavelet analyzing results, it is brought forward that analyzing power quality disturbances by use of compound information of the complex wavelet transform may acquire better analysis results. Since the existing complex wavelets are all continuous wavelets, in order to overcome the disadvantages of complex calculation, this dissertation deeply researches a method for constituting orthogonal compact support complex wavelets by the existing orthogonal compact support real wavelets through changing the phase-frequency characteristic. This method is based on multi-resolution analysis and as long as the orthogonal compact support real wavelet has low-pass filter, it will meet the requirements of this method. Since the orthogonal compact support complex wavelet constituted by means of this method is orthogonal and compact supported, it can adopt Mallat fast wavelet algorithm. In order to acquire much better analysis results, Db4 orthogonal compact support real wavelet is chosen here to constitute a kind of db4 orthogonal compact support complex wavelet,which is used to detect and locate dynamic power quality disturbances. The Db4 orthogonal compact support complex wavelet filter group constituted by means of this method has the same length and the same support set as the original Db4 orthogonal compact support real wavelet. It also has the same characters as the Db4 orthogonal compact support real wavelet , respectively orthogonal, compact support, vanishing moment and regularity. Through simulation, the analysis results of Db4 orthogonal compact support complex wavelet are compared with that of Db4 orthogonal compact support real wavelet, and the analysis results of compound information of orthogonal compact support complex wavelet are compared with that of simple information.
Whereas wavelet transform has the excellent characteristic of time-frequency localization, and support vector machine (SVM) has the excellent ability of statistic study, this dissertation brings forward a new method based on complex wavelet transform and multi-class SVM classifier for recognizing and classifying dynamic power quality disturbances. The complex wavelet transform is used to to extract the feature vector of dynamic power quality disturbances, and the multi-class SVM classifier is used to recognize and classify dynamic power quality disturbances according to the feature vector extracted. Based on the theory of structural risk minimization, SVM has stronger generalization ability, and can resolves several deficiencies of artificial neural network. In order to overcome the deficiencies of current multi-class SVM classifier algorithms, this dissertation brings forward a new multi-class SVM classifier algorithm based on fuzzy clustering analysis thought, i.e. hierarchical clustering SVM algorithm,and simultaneously constructs a classification tree for dynamic power quality disturbances based on hierarchical clustering SVM classifier algorithm. The hierarchical clustering SVM algorithm has the merits such as higher learning speed, lower error classification rate, less sub-classifier number, and requiring less memory, etc. In order to certify the correctness and validity of this method, through simulation this dissertation compares the recognition and classification method of dynamic power quality disturbances based on complex wavelet transform and multi-class SVM classifier with that based on artificial neural network, and also compares the hierarchical clustering SVM algorithm with several common-used multi-class SVM classifier algorithm.
In order to reduce the storage space and the transmission time of power quality disturbance data, and also in order to enhance the real-time performance of the power quality monitoring and analysis system, this dissertation brings forward a new data compression method of power quality disturbance based on lifting wavelet transform which is as follows: firstly confirm the decomposition scale and make multi-scale decomposition to power quality disturbance signal by lifting wavelet transform; secondly, according to the relevant threshold strategy, make the threshold quantization and encoding operation to the higher frequency coefficients of each scale, and simultaneously store the coefficients with connection to the disturbance and throw away the coefficients without connection to the disturbance, and in this way compression of power quality disturbance data is accomplished; finally according to the compressed data reconstruct the original power quality disturbance signal by use of inverse lifting wavelet transform. In order to evaluate the correctness and validity of the compression method based on lifting wavelet transform, four evaluation indexes of data compression performance, respectively compression ratio, mean square deviation percentage, signal-to-noise ratio and energy ratio, are introduced,. In addition, the lifting algorithm of Db4 orthogonal compact support real wavelet is chosen to make simulation experiments to the compression results of power quality disturbances. This dissertation designs a power quality monitoring and analysis system. The main station is composed of industrial computer and PCI CAN card, and the slave station is just the power quality monitoring device. In addition, the software implementation procedure of power quality analysis method based on complex wavelet transform and SVM in the system is proposed. This dissertation brings forward a hardware scheme for the power quality monitoring device which is based on the DSP+DARAM+ARM structure. DSP is mainly used to gather power signals, calculate basic power parameters, calculate and analyze the power quality parameters, and implement the functions of event recording, malfunction alarming and remote signalling/remote control; ARM is mainly used to implement local display, CAN communication, setting up system parameters and keyboard operation, etc.; DSP and ARM change the data via DARAM. In order to resolve the problem of address bus and data bus multiplexing between ARM and CAN controller, a sequence circuit between ARM and CAN controller, which is implemented via CPLD, is designed. In order to increase the real-time performance, stability and reliability of device, the embedded real-time operation systemμC/OS-II is adopted in ARM software development.
为解决常用正交实小波变换不能提取信号相位信息的缺陷,在分析小波相频特性对小波分析效果影响的基础上,提出利用复小波变换的复合信息对动态电能质量扰动进行分析可获得更好的分析效果。由于现有的复小波均为连续小波,为克服其计算复杂等缺陷,深入研究了一种通过改变相频特性由现有正交紧支实小波构造正交紧支复小波的方法。该方法基于多分辨率分析思想,仅要求正交紧支实小波具有低通滤波器即可,由该方法构造的正交紧支复小波具有正交性和紧支性,仍可采用Mallat快速算法。选择Db4正交紧支实小波构造出一种Db4正交紧支复小波,并将其用于动态电能质量扰动检测与定位。所构建的Db4正交紧支复小波滤波器组与原Db4正交紧支实小波滤波器组的长度相同,支集相同,同时具有与Db4正交紧支小波相同的特性:正交性、紧支性、消失矩和正则性。通过仿真,对Db4正交紧支复小波变换与Db4正交紧支实小波变换的分析效果和Db4正交紧支复小波的复合信息与简单信息的分析效果进行了对比分析。
鉴于小波变换优秀的时频局部化特性和支持向量机优秀的统计学习能力,提出一种基于复小波变换和多类支持向量机分类器的动态电能质量扰动识别与分类方法:复小波变换主要用于提取动态电能质量扰动的特征向量;多类支持向量机分类器主要用于根据提取的特征向量对动态电能质量扰动进行识别与分类。为克服现有多类支持向量机分类器算法本身存在的一些缺陷,在借鉴模糊聚类分析思想的基础上,提出一种新的多类SVM分类器算法,即分级聚类SVM算法,同时构造了一种基于分级聚类SVM算法的动态电能质量扰动分类树。为验证所提出方法的正确性和有效性,对基于复小波变换和多类支持向量机分类器的动态电能质量扰动识别与分类方法和基于人工神经网络的分类方法进行了对比分析,同时也对分级聚类SVM算法和常用的几种多类SVM分类器算法进行了对比分析。
为减少电能质量扰动数据的存储空间、传输数据量以及提高电能质量监测与分析系统的实时性,在深入研究提升小波变换基本理论的基础上,给出一种基于提升小波变换的电能质量扰动数据压缩方法:首先通过提升小波变换对电能质量扰动信号进行多尺度分解;然后根据相应的施加阈值策略对每个尺度上的高频系数进行阈值量化与编码处理,并保存与扰动相关的系数值而抛弃其它与扰动无关的系数值,从而实现电能质量扰动数据压缩;最后可利用提升小波逆变换由压缩后的数据对原始电能质量扰动信号进行重构。在阈值量化与编码步骤采取各个尺度下使用不同软阈值的策略,阈值估计采用极大极小阈值算法。为了更好地验证基于提升小波变换的电能质量扰动数据压缩方法的正确性和有效性,给出了四个数据压缩性能评价指标,并选用Db4正交紧支实小波的提升算法对几种常见电能质量扰动的数据压缩效果进行了仿真测试。
设计了一种基于电能质量监测与分析系统,其主站由工控机和PCI CAN板卡构成,从站即为各个电能质量监测装置。同时给出了基于复小波变换和支持向量机的电能质量分析方法在该系统中的软件实现流程。提出一种基于DSP+双口RAM+ARM的电能质量监测装置的硬件设计方案,DSP主要用于电力信号采集、基本电力参数计算、电能质量参数计算与分析,此外还要实现事件记录、故障报警、遥信/遥控等功能;ARM主要用于实现本地显示、CAN通信、系统参数设置、键盘操作等;DSP和ARM之间通过双口RAM进行数据交换。为解决ARM和CAN控制器之间地址与数据总线复用问题,设计了ARM与CAN控制器之间的接口时序电路,该时序电路通过CPLD实现;为提高系统的实时性、稳定性和可靠性,采用了嵌入式实时操作系统μC/OS-II用于ARM软件开发。
In recent years, power quality problem have drawn extensive attention of people. One reason is that power quality has been being disturbed heavily with the increasing number of polluting loads such as non-linear loads, time-variant loads, fluctuating loads, unbalanced loads, etc.; the other is that intelligent electrical devices have put forward more rigorous requirements for power quality. As an important index of the power industry product, power quality concerns the interests of generating power, supplying power and utilizing power. In the event that the power quality index departs the normal level too much, it will endanger the electric power generation, electric power transmission, electric power transform, electric power distribution and electric power consumption to a different extent. Therefore, power quality has become one of the primary problems in the electric power market. Power quality monitroing and analysis technology and power quality control technology have become new researching focuses of the electric power system field. Power Quality monitoring and analysis is the basis and premise of power quality control. Therefore, it is very necessary to build a power quality monitoring and analysis system to examine, evaluate and classify the power quality disturbances correctly. This dissertation makes a deep research on methods with regard to power quality analysis which include detection and location method of dynamic power quality disturbances based on complex wavelet transform, automatic recognition and classification method of dynamic power quality disturbances based on multi-class support vector machine classifier; data compression method of power quality disturbances based on lifting wavelet transform. Application of these methods may improve the power quality monitoring and analysis system in aspects of accuracy, real-time performance, automation, etc.
In order to resolve the disadvantage of the common-used orthogonal real wavelet transform that it cannot draw the signal’s phase information, based on analyzing the impact of wavelets’phase-frequency characteristic on wavelet analyzing results, it is brought forward that analyzing power quality disturbances by use of compound information of the complex wavelet transform may acquire better analysis results. Since the existing complex wavelets are all continuous wavelets, in order to overcome the disadvantages of complex calculation, this dissertation deeply researches a method for constituting orthogonal compact support complex wavelets by the existing orthogonal compact support real wavelets through changing the phase-frequency characteristic. This method is based on multi-resolution analysis and as long as the orthogonal compact support real wavelet has low-pass filter, it will meet the requirements of this method. Since the orthogonal compact support complex wavelet constituted by means of this method is orthogonal and compact supported, it can adopt Mallat fast wavelet algorithm. In order to acquire much better analysis results, Db4 orthogonal compact support real wavelet is chosen here to constitute a kind of db4 orthogonal compact support complex wavelet,which is used to detect and locate dynamic power quality disturbances. The Db4 orthogonal compact support complex wavelet filter group constituted by means of this method has the same length and the same support set as the original Db4 orthogonal compact support real wavelet. It also has the same characters as the Db4 orthogonal compact support real wavelet , respectively orthogonal, compact support, vanishing moment and regularity. Through simulation, the analysis results of Db4 orthogonal compact support complex wavelet are compared with that of Db4 orthogonal compact support real wavelet, and the analysis results of compound information of orthogonal compact support complex wavelet are compared with that of simple information.
Whereas wavelet transform has the excellent characteristic of time-frequency localization, and support vector machine (SVM) has the excellent ability of statistic study, this dissertation brings forward a new method based on complex wavelet transform and multi-class SVM classifier for recognizing and classifying dynamic power quality disturbances. The complex wavelet transform is used to to extract the feature vector of dynamic power quality disturbances, and the multi-class SVM classifier is used to recognize and classify dynamic power quality disturbances according to the feature vector extracted. Based on the theory of structural risk minimization, SVM has stronger generalization ability, and can resolves several deficiencies of artificial neural network. In order to overcome the deficiencies of current multi-class SVM classifier algorithms, this dissertation brings forward a new multi-class SVM classifier algorithm based on fuzzy clustering analysis thought, i.e. hierarchical clustering SVM algorithm,and simultaneously constructs a classification tree for dynamic power quality disturbances based on hierarchical clustering SVM classifier algorithm. The hierarchical clustering SVM algorithm has the merits such as higher learning speed, lower error classification rate, less sub-classifier number, and requiring less memory, etc. In order to certify the correctness and validity of this method, through simulation this dissertation compares the recognition and classification method of dynamic power quality disturbances based on complex wavelet transform and multi-class SVM classifier with that based on artificial neural network, and also compares the hierarchical clustering SVM algorithm with several common-used multi-class SVM classifier algorithm.
In order to reduce the storage space and the transmission time of power quality disturbance data, and also in order to enhance the real-time performance of the power quality monitoring and analysis system, this dissertation brings forward a new data compression method of power quality disturbance based on lifting wavelet transform which is as follows: firstly confirm the decomposition scale and make multi-scale decomposition to power quality disturbance signal by lifting wavelet transform; secondly, according to the relevant threshold strategy, make the threshold quantization and encoding operation to the higher frequency coefficients of each scale, and simultaneously store the coefficients with connection to the disturbance and throw away the coefficients without connection to the disturbance, and in this way compression of power quality disturbance data is accomplished; finally according to the compressed data reconstruct the original power quality disturbance signal by use of inverse lifting wavelet transform. In order to evaluate the correctness and validity of the compression method based on lifting wavelet transform, four evaluation indexes of data compression performance, respectively compression ratio, mean square deviation percentage, signal-to-noise ratio and energy ratio, are introduced,. In addition, the lifting algorithm of Db4 orthogonal compact support real wavelet is chosen to make simulation experiments to the compression results of power quality disturbances. This dissertation designs a power quality monitoring and analysis system. The main station is composed of industrial computer and PCI CAN card, and the slave station is just the power quality monitoring device. In addition, the software implementation procedure of power quality analysis method based on complex wavelet transform and SVM in the system is proposed. This dissertation brings forward a hardware scheme for the power quality monitoring device which is based on the DSP+DARAM+ARM structure. DSP is mainly used to gather power signals, calculate basic power parameters, calculate and analyze the power quality parameters, and implement the functions of event recording, malfunction alarming and remote signalling/remote control; ARM is mainly used to implement local display, CAN communication, setting up system parameters and keyboard operation, etc.; DSP and ARM change the data via DARAM. In order to resolve the problem of address bus and data bus multiplexing between ARM and CAN controller, a sequence circuit between ARM and CAN controller, which is implemented via CPLD, is designed. In order to increase the real-time performance, stability and reliability of device, the embedded real-time operation systemμC/OS-II is adopted in ARM software development.
引文
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19 A. Bonner, T. Grebe, E. Gunther, et al. Modeling and Simulation of the Propagation of Harmonics in Electric Power Networks Ⅱ : Sample Systems and Examples. IEEE Transactions on Power Delivery, 1996, 11(1): 466~474
20 H. Qian, R. X. Zhao, T. Chen. Interharmonics Analysis Based on Interpolating Windowed FFT Algorithm. IEEE Transactions on Power Delivery, 2007, 22(2): 1064~1069
21 磨少清, 李啸骢. 一种高精度的改进傅里叶测频算法. 电力系统自动化, 2003, 27(12): 48~50
22 庞 浩, 李东霞, 俎云霄, 等. 应用FFT进行电力系统谐波分析的改进算法. 中国电机工程学报, 2003, 23(6): 50~54
23 向东阳, 王公宝, 马伟明, 等. 基于 FFT 和神经网络的非整数次谐波检测方法. 中国电机工程学报, 2005, 25(9): 35~39
24 张伏生, 耿中行, 葛耀中. 电力系统谐波分析的高精度 FFT 算法. 中国电机工程学报, 1999, 19(3): 63~66
25 R. M. Hidalgo, J. G. Fernandez, R. R. Rivera, et al. A simple Adjustable Window Algorithm to Improve FFT Measurements. IEEE Transactions on Instrumentation and Measurement, 2002, 51(1): 31~36
26 G. T. Heydt, P. S. Fjeld, C. C. Liu, et al. Application of the Windowed FFT to Electric Power Quality Assessment. IEEE Transactions on Power Delivery, 1999, 14(4): 1411~1416
27 H. Xue, R. Yang. Optimal Interpolating Windowed Discrete Fourier Transform Algorithms for Harmonic Analysis in Power Systems. IEE Proceedings: Generation, Transmission and Distribution, 2003, 150: 583~587
28 I. Daubechies. Ten Lectures on Wavelets. Philadelphia: SIAM Mathematical Analysis, 1992
29 S. G. Mallat. A Theory for Multiresolution Signal Decomposition: the Wavelet Representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989, 11(7): 674~693
30 A. W. Galli, G. T. Heydt, P. F. Ribeiro. Exploring the Power of Wavelet Analysis. IEEE Computer Applications in Power, 1996, 9(4): 37~41
31 王晶. 动态电能质量的分形指数小波分析方法. 中国电机工程学报, 2004,24(5): 40~45
32 胡铭, 陈珩. 基于小波变换模极大值的电能质量扰动检测与定位. 电网技术, 2001, (3): 12~16
33 D. G. Ece, O. N. Gerek. Power Quality Event Detection Using Joint 2-D-wavelet Subspaces. IEEE Transactions on Instrumentation and Measurement, 2004, 53(4): 1040~1046
34 S. Santoso, E. J. Powers, W. M. Grady. Electric Power Quality Disturbance Detection Using Wavelet Transform Analysis. Proceedings of the IEEE International Symposium on Time-frequency and Time-Scale Ajnalysis, 1994: 166~169
35 S. Santoso, E. J. Powers, W. M. Grady. Power Quality Assessment via Wavelet Transfrom Analysis. IEEE Transactions on Power Delivery, 1996, 11(2): 924~930
36 O. Poissson, P. Rioual, M. Meunier. New Signal Processing Tools Applied to Power Quality Ajnalysis. IEEE Transactions on Power Delivery, 1999, 14(2): 561~566
37 Y. H. Gu, M. H. J. Bollen. Time-frequency and Time Scale Domain Analysis of Voltage Disturbances. IEEE Transactions on Power Delivery, 2000, 15(4): 1279~1284
38 M. Albano, R. Caldon, R. Turn. Voltage Sag Analysis on Three Phase Systems Using Wavelet Transform and Probabilistic Neural Network. Proceedings of the 39th International Universities Power Engineering Conference, 2004, 3: 948~952
39 G. Zheng, X. M. Yan, H. W. Li, et al. Classification of Voltage Sag Based on Wavelet Transform and Wavelet Network. Proceedings of 2004 International Conference on Machine Learning and Cybernetics, 2004, 1: 466~470
40 N. S. D. Brito, B. A. Souza, F. A. C. Pires. Daubechies Wavelets in Quality of Electrical Power. Proceeding of IEEE ICHQP, Athens, Greece, 1998: 511~515
41 L. Angrisani, P. Daponte, M. D. Apuzzo. A Measurement Method Based on the Wavelet Transform for Power Quality Analysis. IEEE Transactions on Power Delivery, 1998, 13(4): 990~998
42 E. G. Mahmoud, A. G. Amr, E. S. Tarek. Detection, Localization andClassification of Power Quality Disturbances Using Discrete Wavelet Transform Technique. Alexandria Engineering Journal, 2003, 42(1): 17~23
43 O. Poisson, P. Rioual, M. Meunier. Detection and Measurement of Power Quality Disturbances Using Wavelet transform. IEEE Transactions on Power Delivery, 2000, 15(3): 1039~1044
44 S. Santoso, E. J. Powers, W. M. Grady. Power Quality Disturbance Data Compression Using Wavelet Transform Methods. IEEE Transactions on Power Delivery, 1997, 12(3): 1250~1257
45 O. N. Gerek, D. G. Ece. 2-D Analysis and Compression of Power Quality Event Data. IEEE Transactions on Power Delivery, 2004, 19(2): 791~798
46 T. B. Littler, D. J. Morrow. Wavelets for the Analysis and Compression of Power System Disturbances. IEEE Transactions on Power Delivery, 1999, 14(2): 358~364
47 郭彬彬, 黄纯. 基于小波包变换的电能质量扰动数据压缩. 电力自动化设备, 2005, 25(11): 34~37
48 D. C. Robertson, O. I. Camps, J. S. Mayer. Wavelets and Power System Transients: Feature Detection and Classification. Proceedings of SPIE - The International Society for Optical Engineering, 1994, 2242: 474~487
49 A. M. Gaouda, M. M. A. Salama, M. R. Sultan, et al. Power Quality Detection and Classification Using Wavelet-multiresolution Signal Decomposition. IEEE Transactions on Power Delivery, 1999, 14(4): 1469~1476
50 M. Karimi, H. Mokhtari, M. R. Iravani. Wavelet Based On-line Disturbance Detection for Power Quality Applications. IEEE Transactions on Power Delivery, 2000, 15(4): 1212~1220
51 H. B. He, J. A. Starzyk. A Self-organizing Learning Array System for Power Quality Classification Based on Wavelet Transform. IEEE Transactions on Power Delivery, 2006, 21(1): 286~295
52 S. Santoso, J. Lamoree, W. M. Grady, et al. A Scalable PQ Event Identification System. IEEE Transactions on Power Delivery, 2000, 15(2): 738~743
53 D. C. Robertson, O. I. Camps, J. S. Mayer, et al. Wavelets and Electromagnetic Power System Transients. IEEE Transactions on PowerDelivery, 1996, 11(2): 1050~1056
54 S. Y. Yang, S. L. Ho, P. H. Ni, et al. A combined Wavelet-FE Method for Transient Electromagnetic-field Computations. IEEE Transactions on Magnetics, 2006, 42(4): 571~574
55 G. Ala, M. L. DiSilvestre, E. Francomano, et al. Wavelet-based Efficient Simulation of Electromagnetic Transients in a Lightning Protection System. IEEE Transactions on Magnetics, 2003, 39(3): 1257~1260
56 P. Pillay, A. Bhattacharjee. Application of Wavelets to Model Short-term Power System Disturbances. IEEE Transactions on Power Systems, 1996, 11(4): 2031~2037
57 G. T. Heydt, A. W. Galli. Transient Power Quality Problems Analyzed Using Wavelets. IEEE Transactions on Power Delivery, 1997, 12(2): 908~915
58 A. Geranmayeh, R. Moini, S. H. H. Sadeghi. Numerical Simulation of Electromagnetic Fields Radiated by Lightning Return Stroke Channels: A Wavelet-based Approach. IEEE Transactions on Electromagnetic Compatibility, 2006, 48(1): 225~233
59 A. P. S. Meliopoulos, H. L. Chien. An Alternative Method for Transient Analysis via Wavelets. IEEE Transactions on Power Delivery, 2000, 15(1): 114~121
60 T. X. Zheng, E. B. Makram, A. A. Girgis. Power System Transient and Harmonic Studies Using Wavelet Transform. IEEE Transactions on Power Delivery, 1999, 14(4): 1461~1468
61 刘应梅. 电能质量扰动检测和分析的研究. 中国电力科学研究院博士学问论文, 2003: 1-8
62 梅雪, 吴为麟. 基于小波和 ANN 的电能质量分类方法. 浙江大学学报, 2004, 38(10): 1383~1386
63 D. Borras, M. Castilla, N. Moreno, et al. Wavelet and Neural Structure: A New Tool for Diagnostic of Power System Disturbances. IEEE Transactions on Industry Applications, 2001, 37(1): 184~190
64 欧阳森, 王建华, 耿英三, 等. 基于小波和神经网络的电能质量识别方法. 电工电能新技术, 2003, 22(3): 32~36
65 王晶, 束洪春, 陈学允. 人工智能和数学变换用于电能质量的研究综述. 继电器, 2004, 32(2): 34~40
66 P. Janik, T. Lobos. Automated Classification of Power Quality Disturbances Using SVM and RBF Networks. IEEE Transactions on Power Delivery, 2006, 21(3): 1663~1669
67 W. M. Tong, X. L. Song, D. Z. Zhang. Recognition and Classification of Power Quality Disturbances Based on Self-adaptive Wavelet Neural Network. Lecture Notes in Computer Science, 2006, 3972: 1386~1394
68 S. Santoso, E. J. Power, W. M. Grady. Power Quality Disturbance Recognition Using Wavelet-based Neural ClassifierⅠ: Theoretical Function. IEEE Transactions on Power Delivery, 2000, 15(1): 222~228
69 S. Santoso, E. J. Power, W. M. Grady. Power Quality Disturbance Recognition Using Wavelet-based Neural ClassifierⅡ: Application. IEEE Transactions on Power Delivery, 2000, 15(1): 229~235
70 B. Perunicic, M. Mallini, Z. Wang, et al. Power Quality Disturbance Detection and Classification Using Wavelets and Artificial Neural Networks. Proceeding of IEEE ICHQP, Athens, Greece, 1998: 77~82
71 C. R. Pinnegar, M. V. Chilukuri, P. K. Dash. Discussion of "Multiresolution S-transform-based Fuzzy Recognition System for Power Quality Events". IEEE Transactions on Power Delivery, 2005, 20(1): 539~540
72 H. Kochukuttan, A. Chandrasekaran. Development of a Fuzzy Expert System for Power Quality Applications. Proceedings of the 29th Southeastern Symposium on System Theory, 1997: 239~243
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74 P. K. Dash, S. Mishra, M. Salama, et al. Classification of Power System Disturbances Using a Fuzzy Expert System and a Fourier Linear Combiner. IEEE Transactions on Power Delivery, 2000, 15(2): 472~477
75 T. X. Zhu, S. K. Tso, K. L. Lo. Wavelet-based Fuzzy Reasoning Approach to Power Quality Disturbance Recognition. IEEE Transactions on Power Delivery, 2004, 19(4): 1928~1935
76 M. V. Chilukuri, P. K. Dash. Multiresolution S-transform-based Fuzzy Recognition System for Power Quality Events. IEEE Transactions on Power Delivery, 2004, 19(1): 323~330
77 韩祯祥, 文福拴, 张琦. 人工智能在电力系统中的应用. 电力系统自动化,2000, 24(2): 2~10
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83 S. Mallat. A Wavelet Tour of Signal Processing. SanDiego, CA: Academic Press, 1997
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101 W. Sweldens. The Lifting Scheme: A Custom-design Construction of Biorthogonal Wavelets. Applied and Computational Harmonic Analysis, 1996, 3(2): 186~200
102 W. Sweldens. The Lifting Scheme: A Construction of Second Generation Wavelets. SIAM Journal of Mathematical Analysis, 1997, 29(2): 511~546
103 I. Daubechies, W. Sweldens. Factoring Wavelet Transform into Lifting Steps. Journal of Fourier Analysis and Application, 1998, 4(3): 245~267
2 O. N. Gerek, D. G. Ece. An Adaptive Statistical Method for Power Quality Analysis. IEEE Transactions on Instrumentation and Measurement, 2005, 54(1): 184~191
3 S. Chen. Open Design of Networked Power Quality Monitoring Systems. IEEE Transactions on Instrumentation and Measurement, 2004, 53(2): 597~601
4 薛蕙, 杨仁刚. 基于小波包除噪的电能质量扰动检测方法. 中国电机工程学报, 2004, 24(3): 85~90
5 肖湘宁. 电能质量分析与控制. 北京: 中国电力出版社, 2004
6 IEEE Std 1159-1995. IEEE Recommended Practice for Monitoring Electric Power Quality, 1995
7 IEEE Std 1159.3-2003. IEEE Recommended Practice for the Transfer of Power Quality Data, 2003
8 GB12325-2003.《电能质量 供电电压允许偏差》,1990
9 GB/T 15945-1995.《电能质量电力系统频率允许偏差》, 1995
10 GB/T 14549-1993.《电能质量 公用电网谐波》, 1993
11 GB/T 15543-1995.《电能质量 三相电压允许不平衡度》, 1995
12 GB12326-1990.《电能质量 电压波动和闪变》, 1990
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14 GB/T 18481-2001.《电能质量 暂时过电压和瞬态过电压》, 2001
15 杨汉生. 提升小波在电能质量分析中的应用研究. 南京理工大学博士学位论文, 2006: 4-16
16 胡铭, 陈珩. 电能质量分析方法综述. 电网技术, 2000, 24(2): 36~38
17 J. Arrillaga, D. A. Bradley, P. S. Bodger. Power System Harmonics. London: John Wiley & Sons. 1985
18 A. Bonner, T. Grebe, E. Gunther, et al. Modeling and Simulation of the Propagation of Harmonics in Electric Power Networks Ⅰ: Concepts, Modeland Simulation Techniques. IEEE Transactions on Power Delivery, 1996, 11(1): 452~465
19 A. Bonner, T. Grebe, E. Gunther, et al. Modeling and Simulation of the Propagation of Harmonics in Electric Power Networks Ⅱ : Sample Systems and Examples. IEEE Transactions on Power Delivery, 1996, 11(1): 466~474
20 H. Qian, R. X. Zhao, T. Chen. Interharmonics Analysis Based on Interpolating Windowed FFT Algorithm. IEEE Transactions on Power Delivery, 2007, 22(2): 1064~1069
21 磨少清, 李啸骢. 一种高精度的改进傅里叶测频算法. 电力系统自动化, 2003, 27(12): 48~50
22 庞 浩, 李东霞, 俎云霄, 等. 应用FFT进行电力系统谐波分析的改进算法. 中国电机工程学报, 2003, 23(6): 50~54
23 向东阳, 王公宝, 马伟明, 等. 基于 FFT 和神经网络的非整数次谐波检测方法. 中国电机工程学报, 2005, 25(9): 35~39
24 张伏生, 耿中行, 葛耀中. 电力系统谐波分析的高精度 FFT 算法. 中国电机工程学报, 1999, 19(3): 63~66
25 R. M. Hidalgo, J. G. Fernandez, R. R. Rivera, et al. A simple Adjustable Window Algorithm to Improve FFT Measurements. IEEE Transactions on Instrumentation and Measurement, 2002, 51(1): 31~36
26 G. T. Heydt, P. S. Fjeld, C. C. Liu, et al. Application of the Windowed FFT to Electric Power Quality Assessment. IEEE Transactions on Power Delivery, 1999, 14(4): 1411~1416
27 H. Xue, R. Yang. Optimal Interpolating Windowed Discrete Fourier Transform Algorithms for Harmonic Analysis in Power Systems. IEE Proceedings: Generation, Transmission and Distribution, 2003, 150: 583~587
28 I. Daubechies. Ten Lectures on Wavelets. Philadelphia: SIAM Mathematical Analysis, 1992
29 S. G. Mallat. A Theory for Multiresolution Signal Decomposition: the Wavelet Representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989, 11(7): 674~693
30 A. W. Galli, G. T. Heydt, P. F. Ribeiro. Exploring the Power of Wavelet Analysis. IEEE Computer Applications in Power, 1996, 9(4): 37~41
31 王晶. 动态电能质量的分形指数小波分析方法. 中国电机工程学报, 2004,24(5): 40~45
32 胡铭, 陈珩. 基于小波变换模极大值的电能质量扰动检测与定位. 电网技术, 2001, (3): 12~16
33 D. G. Ece, O. N. Gerek. Power Quality Event Detection Using Joint 2-D-wavelet Subspaces. IEEE Transactions on Instrumentation and Measurement, 2004, 53(4): 1040~1046
34 S. Santoso, E. J. Powers, W. M. Grady. Electric Power Quality Disturbance Detection Using Wavelet Transform Analysis. Proceedings of the IEEE International Symposium on Time-frequency and Time-Scale Ajnalysis, 1994: 166~169
35 S. Santoso, E. J. Powers, W. M. Grady. Power Quality Assessment via Wavelet Transfrom Analysis. IEEE Transactions on Power Delivery, 1996, 11(2): 924~930
36 O. Poissson, P. Rioual, M. Meunier. New Signal Processing Tools Applied to Power Quality Ajnalysis. IEEE Transactions on Power Delivery, 1999, 14(2): 561~566
37 Y. H. Gu, M. H. J. Bollen. Time-frequency and Time Scale Domain Analysis of Voltage Disturbances. IEEE Transactions on Power Delivery, 2000, 15(4): 1279~1284
38 M. Albano, R. Caldon, R. Turn. Voltage Sag Analysis on Three Phase Systems Using Wavelet Transform and Probabilistic Neural Network. Proceedings of the 39th International Universities Power Engineering Conference, 2004, 3: 948~952
39 G. Zheng, X. M. Yan, H. W. Li, et al. Classification of Voltage Sag Based on Wavelet Transform and Wavelet Network. Proceedings of 2004 International Conference on Machine Learning and Cybernetics, 2004, 1: 466~470
40 N. S. D. Brito, B. A. Souza, F. A. C. Pires. Daubechies Wavelets in Quality of Electrical Power. Proceeding of IEEE ICHQP, Athens, Greece, 1998: 511~515
41 L. Angrisani, P. Daponte, M. D. Apuzzo. A Measurement Method Based on the Wavelet Transform for Power Quality Analysis. IEEE Transactions on Power Delivery, 1998, 13(4): 990~998
42 E. G. Mahmoud, A. G. Amr, E. S. Tarek. Detection, Localization andClassification of Power Quality Disturbances Using Discrete Wavelet Transform Technique. Alexandria Engineering Journal, 2003, 42(1): 17~23
43 O. Poisson, P. Rioual, M. Meunier. Detection and Measurement of Power Quality Disturbances Using Wavelet transform. IEEE Transactions on Power Delivery, 2000, 15(3): 1039~1044
44 S. Santoso, E. J. Powers, W. M. Grady. Power Quality Disturbance Data Compression Using Wavelet Transform Methods. IEEE Transactions on Power Delivery, 1997, 12(3): 1250~1257
45 O. N. Gerek, D. G. Ece. 2-D Analysis and Compression of Power Quality Event Data. IEEE Transactions on Power Delivery, 2004, 19(2): 791~798
46 T. B. Littler, D. J. Morrow. Wavelets for the Analysis and Compression of Power System Disturbances. IEEE Transactions on Power Delivery, 1999, 14(2): 358~364
47 郭彬彬, 黄纯. 基于小波包变换的电能质量扰动数据压缩. 电力自动化设备, 2005, 25(11): 34~37
48 D. C. Robertson, O. I. Camps, J. S. Mayer. Wavelets and Power System Transients: Feature Detection and Classification. Proceedings of SPIE - The International Society for Optical Engineering, 1994, 2242: 474~487
49 A. M. Gaouda, M. M. A. Salama, M. R. Sultan, et al. Power Quality Detection and Classification Using Wavelet-multiresolution Signal Decomposition. IEEE Transactions on Power Delivery, 1999, 14(4): 1469~1476
50 M. Karimi, H. Mokhtari, M. R. Iravani. Wavelet Based On-line Disturbance Detection for Power Quality Applications. IEEE Transactions on Power Delivery, 2000, 15(4): 1212~1220
51 H. B. He, J. A. Starzyk. A Self-organizing Learning Array System for Power Quality Classification Based on Wavelet Transform. IEEE Transactions on Power Delivery, 2006, 21(1): 286~295
52 S. Santoso, J. Lamoree, W. M. Grady, et al. A Scalable PQ Event Identification System. IEEE Transactions on Power Delivery, 2000, 15(2): 738~743
53 D. C. Robertson, O. I. Camps, J. S. Mayer, et al. Wavelets and Electromagnetic Power System Transients. IEEE Transactions on PowerDelivery, 1996, 11(2): 1050~1056
54 S. Y. Yang, S. L. Ho, P. H. Ni, et al. A combined Wavelet-FE Method for Transient Electromagnetic-field Computations. IEEE Transactions on Magnetics, 2006, 42(4): 571~574
55 G. Ala, M. L. DiSilvestre, E. Francomano, et al. Wavelet-based Efficient Simulation of Electromagnetic Transients in a Lightning Protection System. IEEE Transactions on Magnetics, 2003, 39(3): 1257~1260
56 P. Pillay, A. Bhattacharjee. Application of Wavelets to Model Short-term Power System Disturbances. IEEE Transactions on Power Systems, 1996, 11(4): 2031~2037
57 G. T. Heydt, A. W. Galli. Transient Power Quality Problems Analyzed Using Wavelets. IEEE Transactions on Power Delivery, 1997, 12(2): 908~915
58 A. Geranmayeh, R. Moini, S. H. H. Sadeghi. Numerical Simulation of Electromagnetic Fields Radiated by Lightning Return Stroke Channels: A Wavelet-based Approach. IEEE Transactions on Electromagnetic Compatibility, 2006, 48(1): 225~233
59 A. P. S. Meliopoulos, H. L. Chien. An Alternative Method for Transient Analysis via Wavelets. IEEE Transactions on Power Delivery, 2000, 15(1): 114~121
60 T. X. Zheng, E. B. Makram, A. A. Girgis. Power System Transient and Harmonic Studies Using Wavelet Transform. IEEE Transactions on Power Delivery, 1999, 14(4): 1461~1468
61 刘应梅. 电能质量扰动检测和分析的研究. 中国电力科学研究院博士学问论文, 2003: 1-8
62 梅雪, 吴为麟. 基于小波和 ANN 的电能质量分类方法. 浙江大学学报, 2004, 38(10): 1383~1386
63 D. Borras, M. Castilla, N. Moreno, et al. Wavelet and Neural Structure: A New Tool for Diagnostic of Power System Disturbances. IEEE Transactions on Industry Applications, 2001, 37(1): 184~190
64 欧阳森, 王建华, 耿英三, 等. 基于小波和神经网络的电能质量识别方法. 电工电能新技术, 2003, 22(3): 32~36
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