应用小波变换提取变压器保护特征量的研究
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摘要
电力变压器是电力系统中重要的电气设备，它的安全运行直接关系到电力系统连续稳定的工作，因此对变压器保护算法的研究具有重要意义。微机保护利用计算机的信息处理功能，采用灵活的算法来获得保护的高速度和高灵敏度。本文围绕将小波变换应用到变压器的微机保护算法中，为保护算法提取所需的电气特征量方面进行了探讨。
本文设计了以小波变换为基础的数字滤波器，对小波变换在微机变压器保护算法方面的应用进行了研究。针对一定谐波含量的信号，设计了将谐波分量分离的滤波过程，在此过程中引入采样率转换环节，配合小波滤波器实现不同频段信号的分离。同时对不同频段信号的分离采用不同的小波滤波器——共轭正交滤波器(CQF)与Daubechies(Daub)小波滤波器的滤波效果进行了比较和分析。如对于基波与二次谐波的分频，Daub6和CQF12滤波器对基波的滤波效果较好，而Daub6和Daub5对于二次谐波的滤波效果较好。为了验证滤波器的滤波效果，用半周傅氏算法对滤波前后的基波及各次谐波幅值的计算精度进行比较，滤波以后半周傅氏算法的精度有明显提高，计算误差在10%以内。
本文提出了短窗Morlet复小波计算基波与各次谐波信号幅值的算法，并运用于变压器电气量特征提取。在电网频率波动情况下，通过比较说明短窗Morlet复小波算法在频率波动过程中具有比傅氏算法更稳定的特点，同时也可以达到1～3周波内完成的快速性。本文将短窗Morlet复小波的幅值算法应用于实际故障信号的特征量提取，证明了该算法的优越性。
以Borland Delphi6.0为开发平台，开发了用于变电站自动化系统的可视化录波分析软件。该软件具有数据的图形显示、谐波分析、差动特性分析、阻抗特性分析和多功能计算器等功能，有助于用户根据需要观察保护特性曲线，为进一步的分析故障类型和判断保护动作正确与否提供依据。
Power transformers are an important equipment in power system, the safe operation of power transformers has much effect on the continuous running of power system. So it's valuable to research the algorithms of relay protection for transformer. Microcomputer-based protection uses the computer's advanced signal processing function, which gives help in enhancing the protection algorithms' operational speed and precision. This paper mainly focuses on the implement of wavelet to the Microcomputer-based protection for power transformer, especially to extract some useful information for the protection algorithms.
A wavelet-based digital filter is designed in this paper, and the applications of wavelet to the protection for transformer are discussed. Aiming at extracting harmonic components of signals, a filter progress is designed. During the progress, the technology of sampling rate alteration worked as an aid in dividing different frequency signals. The wavelet filters adopted in the progress are the conjugate quadrature filter bank(CQF) and the Daubechies (Daub)based filter. Analysis and comparison of the results are made when different wavelet filters work. For example, to the frequency splitting between fundamental wave and second harmonics, the filter Daub6 and CQF12 do well in extract the fundamental wave, whereas the filter Daub5 and Daub6 do well in extract the second harmonics. To test the filter's effect, the half-wave Fourier algorithm is used to calculate the amplitudes of harmonics. Through the filter progress, the errors of results are reduced compared with that are before the filter. The errors are less than 10%.
An algorithm that can extract harmonics' amplitudes using Morlet wavelets is put forward. Compared with the full-wave Fourier algorithm, the algorithm proposed in this article is more stable when the frequency of electric network flutters. Meanwhile the algorithm has the rapidity of giving out the
results in one to three periodic times. This algorithm works effectively in extracting harmonics' amplitudes of currents when transformer occurs exciting in-rush.
A visual signal analyzing software that serves in transformer substation automation system is developed based on the programming language of Borland Delphi 6.0. The function of the software can be an aid to the field engineer in judging the working condition of transformers.
本文设计了以小波变换为基础的数字滤波器，对小波变换在微机变压器保护算法方面的应用进行了研究。针对一定谐波含量的信号，设计了将谐波分量分离的滤波过程，在此过程中引入采样率转换环节，配合小波滤波器实现不同频段信号的分离。同时对不同频段信号的分离采用不同的小波滤波器——共轭正交滤波器(CQF)与Daubechies(Daub)小波滤波器的滤波效果进行了比较和分析。如对于基波与二次谐波的分频，Daub6和CQF12滤波器对基波的滤波效果较好，而Daub6和Daub5对于二次谐波的滤波效果较好。为了验证滤波器的滤波效果，用半周傅氏算法对滤波前后的基波及各次谐波幅值的计算精度进行比较，滤波以后半周傅氏算法的精度有明显提高，计算误差在10%以内。
本文提出了短窗Morlet复小波计算基波与各次谐波信号幅值的算法，并运用于变压器电气量特征提取。在电网频率波动情况下，通过比较说明短窗Morlet复小波算法在频率波动过程中具有比傅氏算法更稳定的特点，同时也可以达到1～3周波内完成的快速性。本文将短窗Morlet复小波的幅值算法应用于实际故障信号的特征量提取，证明了该算法的优越性。
以Borland Delphi6.0为开发平台，开发了用于变电站自动化系统的可视化录波分析软件。该软件具有数据的图形显示、谐波分析、差动特性分析、阻抗特性分析和多功能计算器等功能，有助于用户根据需要观察保护特性曲线，为进一步的分析故障类型和判断保护动作正确与否提供依据。
Power transformers are an important equipment in power system, the safe operation of power transformers has much effect on the continuous running of power system. So it's valuable to research the algorithms of relay protection for transformer. Microcomputer-based protection uses the computer's advanced signal processing function, which gives help in enhancing the protection algorithms' operational speed and precision. This paper mainly focuses on the implement of wavelet to the Microcomputer-based protection for power transformer, especially to extract some useful information for the protection algorithms.
A wavelet-based digital filter is designed in this paper, and the applications of wavelet to the protection for transformer are discussed. Aiming at extracting harmonic components of signals, a filter progress is designed. During the progress, the technology of sampling rate alteration worked as an aid in dividing different frequency signals. The wavelet filters adopted in the progress are the conjugate quadrature filter bank(CQF) and the Daubechies (Daub)based filter. Analysis and comparison of the results are made when different wavelet filters work. For example, to the frequency splitting between fundamental wave and second harmonics, the filter Daub6 and CQF12 do well in extract the fundamental wave, whereas the filter Daub5 and Daub6 do well in extract the second harmonics. To test the filter's effect, the half-wave Fourier algorithm is used to calculate the amplitudes of harmonics. Through the filter progress, the errors of results are reduced compared with that are before the filter. The errors are less than 10%.
An algorithm that can extract harmonics' amplitudes using Morlet wavelets is put forward. Compared with the full-wave Fourier algorithm, the algorithm proposed in this article is more stable when the frequency of electric network flutters. Meanwhile the algorithm has the rapidity of giving out the
results in one to three periodic times. This algorithm works effectively in extracting harmonics' amplitudes of currents when transformer occurs exciting in-rush.
A visual signal analyzing software that serves in transformer substation automation system is developed based on the programming language of Borland Delphi 6.0. The function of the software can be an aid to the field engineer in judging the working condition of transformers.
引文
[1] 贺家李，宋从矩. 电力系统继电保护原理. 北京：中国电力出版社，1994
[2] 陈德树. 计算机继电保护原理与技术. 北京：中国电力出版社，1998
[3] 王国兴，张传利，黄益庄. 变压器励磁涌流判别方法的现状及发展. 中国电力，1998，31(10): 19~22
[4] 陈德树，张哲，尹相根. 微机继电保护. 北京：中国电力出版社，2000
[5] 吴运祥，沈国荣，朱声石. 重视并应用好变压器后备保护. 继电器，2000，28(7): 8~11
[6] 段玉倩，贺家李，贺继红. 基于人工神经网络方法的微机变压器保护. 中国电机工程学报，1998，18(3): 190~194
[7] 刘一江，车红卫. 变压器微机保护新方法. 湖南大学学报，1999，26(2):42~45
[8] Mom h J, R izy D T . Application of Wavelet Theory to Power Distribution Systems for Fault Detection. USA, ISAP'96: 345~350
[9] 王祁，钟生. 用小波变换提取高压变压器局部放电脉冲的研究. 电工技术学报，1997，12(4): 29~33
[10] 全玉生，高文胜. 小波变换在局部放电测量中的应用研究. 电网技术，1998，22(7): 35~37
[11] 王航，谈克雄. 用小波变换从窄带干扰中提取局部放电信号的实验研究. 高电压技术，1998，24(4): 3~5
[12] 黄群古，周有庆. 基于小波变换的微机保护数字滤波器. 继电器，1998，26(3): 11~13
[13] 张昊，石铁洪，刘沛. 基于B样条小波预处理的短窗算法. 中国电机工程学报，2000，20(10): 50~54
[14] 黄群古，任震，黄雯莹. 基于幅频特性的复值小波构造及其在电力系统信号分析中的应用. 继电器，2001，29(5): 1~4
[15] Tunaboylu N S , Collins E R. The Wavelet Transform Approach to Detect and Quantify Voltage Sags. In proc. Of the 1996 IEEE Int. Conf. On Harmonics and Quality of Power, Las Vegas, USA, 1996: 619~624
[16] Santoso S, Powers E J, Grady W M . Power Quality Disturbance Identification using Wavelet Transform and Artificial neural networks. In Proc. Of the 1996 IEEE Int. Conf. On Harmonics and Quality of Power, Las Vegas, USA, 1996: 615~618
[17] 操丰梅，苏沛浦. 小波变换在变压器差动保护中的应用. 中国电力，1998，31(11): 21~24
[18] 全玉生，李红杰，严璋. 应用小波变换测量间断角的新方法. 电力系统自动化，1998，22(1): 33~35
[19] 杨钟皓，董新洲. 基于小波变换的变压器励磁涌流识别方法. 清华大学学报，2002，42(9): 1184~1187
[20] 杨福生. 小波变换的工程分析与应用. 北京：科学出版社, 1999
[21] 宗孔德. 多抽样率信号处理. 北京：清华大学出版社，1996
[22] Pillay P, Bhhattacharjee A. Application of Wavelets to Model Short-Term Power System Disturbances. IEEE Trans. On Power Delivery, 1996,11(4): 2031~2037
[23] Santoso S, Powers E J, Grady W M , et al. Power Quality Assessment via Wavelet Transform Analysis. IEEE Trans. On Power System, 1996, 11(2): 924~930
[24] Santoso S, Powers E J, Grady W M . Electric Power Quality Disturbances Detection Using Wavelet Transform Analysis. In Proceeding of the IEEE-SP International Sym posium on Time-Frequency and Time-Scale Analysis, Philadephia, PA, 1994: 166~169
[25] 杨奇逊. 微型机继电保护基础. 北京：中国电力出版社，1988
[26] Shyh-Jier Huang, Cheng-Tao, Ching-Lien Huang. Application of Wavelets to Supervise Power System Disturbances. IEEE Trans. On Power Delivery, 1999,14(1): 235~243
[27] 何岭松，李巍华. 用Morlet小波进行包络检波分析. 振动工程学报，2002，15(1): 119~121
[28] T. Masters, Signal and Image Processing with Neural Networks, John Wiley&Sons , New York, USA, 1994
[29] 管霖，吴国沛，黄雯莹，任震，周宏. 小波变换在电力设备故障诊断中的应用研究. 中国电机工程学报，2000, 20(10):46~49
[30] 许超英，李海锋，赵建仓，王钢. 电力变压器励磁涌流和故障电流仿真研究. 继电器，2002，30(6): 29~32
[2] 陈德树. 计算机继电保护原理与技术. 北京：中国电力出版社，1998
[3] 王国兴，张传利，黄益庄. 变压器励磁涌流判别方法的现状及发展. 中国电力，1998，31(10): 19~22
[4] 陈德树，张哲，尹相根. 微机继电保护. 北京：中国电力出版社，2000
[5] 吴运祥，沈国荣，朱声石. 重视并应用好变压器后备保护. 继电器，2000，28(7): 8~11
[6] 段玉倩，贺家李，贺继红. 基于人工神经网络方法的微机变压器保护. 中国电机工程学报，1998，18(3): 190~194
[7] 刘一江，车红卫. 变压器微机保护新方法. 湖南大学学报，1999，26(2):42~45
[8] Mom h J, R izy D T . Application of Wavelet Theory to Power Distribution Systems for Fault Detection. USA, ISAP'96: 345~350
[9] 王祁，钟生. 用小波变换提取高压变压器局部放电脉冲的研究. 电工技术学报，1997，12(4): 29~33
[10] 全玉生，高文胜. 小波变换在局部放电测量中的应用研究. 电网技术，1998，22(7): 35~37
[11] 王航，谈克雄. 用小波变换从窄带干扰中提取局部放电信号的实验研究. 高电压技术，1998，24(4): 3~5
[12] 黄群古，周有庆. 基于小波变换的微机保护数字滤波器. 继电器，1998，26(3): 11~13
[13] 张昊，石铁洪，刘沛. 基于B样条小波预处理的短窗算法. 中国电机工程学报，2000，20(10): 50~54
[14] 黄群古，任震，黄雯莹. 基于幅频特性的复值小波构造及其在电力系统信号分析中的应用. 继电器，2001，29(5): 1~4
[15] Tunaboylu N S , Collins E R. The Wavelet Transform Approach to Detect and Quantify Voltage Sags. In proc. Of the 1996 IEEE Int. Conf. On Harmonics and Quality of Power, Las Vegas, USA, 1996: 619~624
[16] Santoso S, Powers E J, Grady W M . Power Quality Disturbance Identification using Wavelet Transform and Artificial neural networks. In Proc. Of the 1996 IEEE Int. Conf. On Harmonics and Quality of Power, Las Vegas, USA, 1996: 615~618
[17] 操丰梅，苏沛浦. 小波变换在变压器差动保护中的应用. 中国电力，1998，31(11): 21~24
[18] 全玉生，李红杰，严璋. 应用小波变换测量间断角的新方法. 电力系统自动化，1998，22(1): 33~35
[19] 杨钟皓，董新洲. 基于小波变换的变压器励磁涌流识别方法. 清华大学学报，2002，42(9): 1184~1187
[20] 杨福生. 小波变换的工程分析与应用. 北京：科学出版社, 1999
[21] 宗孔德. 多抽样率信号处理. 北京：清华大学出版社，1996
[22] Pillay P, Bhhattacharjee A. Application of Wavelets to Model Short-Term Power System Disturbances. IEEE Trans. On Power Delivery, 1996,11(4): 2031~2037
[23] Santoso S, Powers E J, Grady W M , et al. Power Quality Assessment via Wavelet Transform Analysis. IEEE Trans. On Power System, 1996, 11(2): 924~930
[24] Santoso S, Powers E J, Grady W M . Electric Power Quality Disturbances Detection Using Wavelet Transform Analysis. In Proceeding of the IEEE-SP International Sym posium on Time-Frequency and Time-Scale Analysis, Philadephia, PA, 1994: 166~169
[25] 杨奇逊. 微型机继电保护基础. 北京：中国电力出版社，1988
[26] Shyh-Jier Huang, Cheng-Tao, Ching-Lien Huang. Application of Wavelets to Supervise Power System Disturbances. IEEE Trans. On Power Delivery, 1999,14(1): 235~243
[27] 何岭松，李巍华. 用Morlet小波进行包络检波分析. 振动工程学报，2002，15(1): 119~121
[28] T. Masters, Signal and Image Processing with Neural Networks, John Wiley&Sons , New York, USA, 1994
[29] 管霖，吴国沛，黄雯莹，任震，周宏. 小波变换在电力设备故障诊断中的应用研究. 中国电机工程学报，2000, 20(10):46~49
[30] 许超英，李海锋，赵建仓，王钢. 电力变压器励磁涌流和故障电流仿真研究. 继电器，2002，30(6): 29~32
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