基于映射与双谱的绝缘子信息提取故障诊断的理论与方法
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摘要
本文关于输电线绝缘子的场量和电量,深入研究了二个方面：场量数值解误差和减小,绝缘子劣化和污秽的电敏感特征量及诊断。
场量数值解误差和减小。计算绝缘子场量常采用软件ANSYS,但是ANSYS数值解有误差和只适用于有界场。针对绝缘子静电场ANSYS数值解误差,因难以得到实际绝缘子静电场解析解,研究的文献不多。为此,本文根据构造的单个理想针式绝缘子,对比其解析法和ANSYS解得出结论：负电极曲率半径越小,绝缘子每点电位和电场强度的ANSYS解误差越大；越靠近负尖电极,绝缘子电位和电场强度ANSYS解误差越大。
针对计算绝缘子串无界静电场,已有若干文献提出若干方法结合ANSYS计算无界场量。为更好地减小误差,本文提出映射与ANSYS相结合,高精度快速计算无界静电场。该方法利用复指数函数将二维无界静电场映射到二维有界静电场,并应用ANSYS计算该有界场,因边值问题相同,有界场某点电位就是无界场映射点电位。实例表明映射结合ANSYS的方法显著提高ANSYS求解二维无界静电场的精度,并加快了计算速度。
绝缘子劣化和污秽的电敏感特征量及诊断。针对泄漏电流监测绝缘子劣化和污秽的高误判率,本文查阅大量文献后提出高误判率在于未找出仅与被监测状态有关而与其它状态无关的量即敏感特征量。为找出绝缘子劣化和污秽的敏感特征量,本文基于试验采集的单个良好或单个劣化的染污绝缘子在不同污秽、湿度、温度、含谐波市电电压作用下的198+17+78+14个弱起晕泄漏电流时间序列(良好染污绝缘子的198+17个,劣化染污绝缘子的78+14个)的分析处理得出：
基波电阻是绝缘子劣化的敏感特征量。在198+78个时间序列中,良好和劣化绝缘子基波电阻值范围分别是222.39-2841.93MΩ和0.23-4.97MΩ。
双谱幅值特征量β是绝缘子劣化的敏感特征量。理论证明双谱强敏感于绝缘子劣化,弱敏感于污秽、湿度和温度；数据验证在198+17+78+14个时间序列中良好和劣化绝缘子双谱幅值特征量β值范围分别是1.2290×10-3-1.5026×10-1和7.5520×10-5-1.2660×10-3。
波峰因子是轻度污秽敏感特征量；1562.5Hz以上高频电流分量波形因子是重度污秽敏感特征量。这是根据每个泄漏电流时间序列多个时域特征量值对比得出具有实际判别意义的结论。
双谱幅值特征量β、波峰因子、Shannon熵组成的三维向量是绝缘子劣化的敏感特征向量。该向量使198+78个时间序列分成两个无重叠且远离的区域即绝缘子良好和劣化两个区域,使Euclide距离、灰关联和神经网络三种分类器均能100%诊断在198+78个训练序列和17+14测试序列中的劣化绝缘子。这是根据泄漏电流时间序列多个时域和频域特征量数值在空间定位得出又一具有理论和实用意义的结论。
About the quantities of electrostatics and electricity of insulators, two aspects are in-depth researched and discussed:the calculation and improvement of the error of the discrete value of the quantities of electrostatic field; finding the electrical quantities sensitive either to fault or to contamination and diagnosing insulators.
First, the calculation and improvement of the error of numerical solution of the quantities of electrostatic field are researched and discussed. Calculating the quantities of the electrostatic field of insulator often uses software ANSYS that has two problems:the error of numerical solution, and only bounded field. To the error of ANSYS solution of electrostatic field of insulator, there are few papers to research because it is difficult to find the analytical solution of the electrostatic field of a actual insulator. Thus a single ideal pin insulator is constructed, and the electric potential and the electric field intensity of any point in insulator are calculated with software ANSYS and analytical method. Two conclusions are reached:the sharper the negative electrode is, the bigger the error of the electrical potential and electric field of any point in insulator are; the more the point in insulator close with negative sharp electrode, the bigger the error of the electric potential of the point is, and the more the point in insulator close with positive electrode or negative electrode, the bigger the error of the electric field of the point is. To calculate the unbounded electrostatic field of insulator strings, some papers present methods so as to apply ANSYS to the unbounded electrostatic field of insulator strings. To decrease error more, this thesis presents that combining map and ANSYS solve unbounded electrostatic field with high accuracy. The method uses a complex exponential function to establish a map between unbounded and bounded electrostatic fields of two-dimension. Then ANSYS is used in bounded fields. As the boundary value problems are same, the electric potential of each point in bounded fields equals the electric potential of each mapping point in unbounded fields. An example indicates that the accuracy obviously increase when solving unbounded field with map and ANSYS.
Secondly, finding the electrical quantities sensitive either to fault or to contamination and diagnosing insulators are researched and discussed. To the higher incorrect and missing judgement of instruments using leakage current (LC) to diagnose insulator and monitor contamination, having consulted many correlative papers the thesis presents that that the essential reason for higher incorrect and missing judgement is that the instruments have not found the eigenvalue only related to the monitored state and not related to other states. To find the sensitive eigenvalues of both faulty insulator and insulator contamination, based on experimental 198+17+78+14 LC time series(198+17 LC time series belong to perfect contaminated insulators; 78+14 LC time series belong to faulty contaminated insulators) of light discharge of single insulator which is at the state of various dirtiness, humidity, and temperature, and is applied non-sinusoidal voltages at different virtual values, this thesis reachs the following conclusions:
Fundamental resistance is the sensitive eigenvalue for faulty insulator. By 198+78 LC time series, the scopes of the fundamental resistance of perfect and faulty insulators are 222.39-2841.93MΩand 0.23～4.97MΩ, respectively. The bispectrum amplitude eigenvalueβof LC time series is sensitive eigenvalue for faulty insulators. It is validated in theory that the bispectrum of the LC time series is the eigenvalue sensitive to insulators, but not sensitive to insulator contamination, humidity and temperature. It is validated in datum that by 198+17+78+14 LC time series, the scopes ofβvalue of perfect and faulty insulators are 1.2290×10-3～1.5026×10-1, and 7.5520×10-5～1.2660×10-3. The wave crest factor of LC time series is sensitive eigenvalue for light contaminations. The waveform factor of 1562.5-25000Hz high frequency current component of LC time series is sensitive eigenvalue for heavy contaminations. These conclusions result from the contrast of many quantities of each LC time series, and have practical significance. A three-dimensional vector, which consists of theβof bispectrum, Shannon entropy, and wave crest factor is the sensitive eigenvector for faulty insulator. The eigenvector can divide all the insulators into two regions not only non-overlapping but far apart regions:the region of perfect contaminated insulators; the region of faulty contaminated insulators. Using above a three-dimensional vector as input vector, any of three classifiers, Euclide distance judgment, grey relational analysis of B-mode, and BP artificial neural network, can exactly distinguish between perfect and faulty insulators at various dirtiness, humidity, temperature and the virtual values of the voltage involving harmonics. This conclusion has both academic and practical significances.
场量数值解误差和减小。计算绝缘子场量常采用软件ANSYS,但是ANSYS数值解有误差和只适用于有界场。针对绝缘子静电场ANSYS数值解误差,因难以得到实际绝缘子静电场解析解,研究的文献不多。为此,本文根据构造的单个理想针式绝缘子,对比其解析法和ANSYS解得出结论：负电极曲率半径越小,绝缘子每点电位和电场强度的ANSYS解误差越大；越靠近负尖电极,绝缘子电位和电场强度ANSYS解误差越大。
针对计算绝缘子串无界静电场,已有若干文献提出若干方法结合ANSYS计算无界场量。为更好地减小误差,本文提出映射与ANSYS相结合,高精度快速计算无界静电场。该方法利用复指数函数将二维无界静电场映射到二维有界静电场,并应用ANSYS计算该有界场,因边值问题相同,有界场某点电位就是无界场映射点电位。实例表明映射结合ANSYS的方法显著提高ANSYS求解二维无界静电场的精度,并加快了计算速度。
绝缘子劣化和污秽的电敏感特征量及诊断。针对泄漏电流监测绝缘子劣化和污秽的高误判率,本文查阅大量文献后提出高误判率在于未找出仅与被监测状态有关而与其它状态无关的量即敏感特征量。为找出绝缘子劣化和污秽的敏感特征量,本文基于试验采集的单个良好或单个劣化的染污绝缘子在不同污秽、湿度、温度、含谐波市电电压作用下的198+17+78+14个弱起晕泄漏电流时间序列(良好染污绝缘子的198+17个,劣化染污绝缘子的78+14个)的分析处理得出：
基波电阻是绝缘子劣化的敏感特征量。在198+78个时间序列中,良好和劣化绝缘子基波电阻值范围分别是222.39-2841.93MΩ和0.23-4.97MΩ。
双谱幅值特征量β是绝缘子劣化的敏感特征量。理论证明双谱强敏感于绝缘子劣化,弱敏感于污秽、湿度和温度；数据验证在198+17+78+14个时间序列中良好和劣化绝缘子双谱幅值特征量β值范围分别是1.2290×10-3-1.5026×10-1和7.5520×10-5-1.2660×10-3。
波峰因子是轻度污秽敏感特征量；1562.5Hz以上高频电流分量波形因子是重度污秽敏感特征量。这是根据每个泄漏电流时间序列多个时域特征量值对比得出具有实际判别意义的结论。
双谱幅值特征量β、波峰因子、Shannon熵组成的三维向量是绝缘子劣化的敏感特征向量。该向量使198+78个时间序列分成两个无重叠且远离的区域即绝缘子良好和劣化两个区域,使Euclide距离、灰关联和神经网络三种分类器均能100%诊断在198+78个训练序列和17+14测试序列中的劣化绝缘子。这是根据泄漏电流时间序列多个时域和频域特征量数值在空间定位得出又一具有理论和实用意义的结论。
About the quantities of electrostatics and electricity of insulators, two aspects are in-depth researched and discussed:the calculation and improvement of the error of the discrete value of the quantities of electrostatic field; finding the electrical quantities sensitive either to fault or to contamination and diagnosing insulators.
First, the calculation and improvement of the error of numerical solution of the quantities of electrostatic field are researched and discussed. Calculating the quantities of the electrostatic field of insulator often uses software ANSYS that has two problems:the error of numerical solution, and only bounded field. To the error of ANSYS solution of electrostatic field of insulator, there are few papers to research because it is difficult to find the analytical solution of the electrostatic field of a actual insulator. Thus a single ideal pin insulator is constructed, and the electric potential and the electric field intensity of any point in insulator are calculated with software ANSYS and analytical method. Two conclusions are reached:the sharper the negative electrode is, the bigger the error of the electrical potential and electric field of any point in insulator are; the more the point in insulator close with negative sharp electrode, the bigger the error of the electric potential of the point is, and the more the point in insulator close with positive electrode or negative electrode, the bigger the error of the electric field of the point is. To calculate the unbounded electrostatic field of insulator strings, some papers present methods so as to apply ANSYS to the unbounded electrostatic field of insulator strings. To decrease error more, this thesis presents that combining map and ANSYS solve unbounded electrostatic field with high accuracy. The method uses a complex exponential function to establish a map between unbounded and bounded electrostatic fields of two-dimension. Then ANSYS is used in bounded fields. As the boundary value problems are same, the electric potential of each point in bounded fields equals the electric potential of each mapping point in unbounded fields. An example indicates that the accuracy obviously increase when solving unbounded field with map and ANSYS.
Secondly, finding the electrical quantities sensitive either to fault or to contamination and diagnosing insulators are researched and discussed. To the higher incorrect and missing judgement of instruments using leakage current (LC) to diagnose insulator and monitor contamination, having consulted many correlative papers the thesis presents that that the essential reason for higher incorrect and missing judgement is that the instruments have not found the eigenvalue only related to the monitored state and not related to other states. To find the sensitive eigenvalues of both faulty insulator and insulator contamination, based on experimental 198+17+78+14 LC time series(198+17 LC time series belong to perfect contaminated insulators; 78+14 LC time series belong to faulty contaminated insulators) of light discharge of single insulator which is at the state of various dirtiness, humidity, and temperature, and is applied non-sinusoidal voltages at different virtual values, this thesis reachs the following conclusions:
Fundamental resistance is the sensitive eigenvalue for faulty insulator. By 198+78 LC time series, the scopes of the fundamental resistance of perfect and faulty insulators are 222.39-2841.93MΩand 0.23～4.97MΩ, respectively. The bispectrum amplitude eigenvalueβof LC time series is sensitive eigenvalue for faulty insulators. It is validated in theory that the bispectrum of the LC time series is the eigenvalue sensitive to insulators, but not sensitive to insulator contamination, humidity and temperature. It is validated in datum that by 198+17+78+14 LC time series, the scopes ofβvalue of perfect and faulty insulators are 1.2290×10-3～1.5026×10-1, and 7.5520×10-5～1.2660×10-3. The wave crest factor of LC time series is sensitive eigenvalue for light contaminations. The waveform factor of 1562.5-25000Hz high frequency current component of LC time series is sensitive eigenvalue for heavy contaminations. These conclusions result from the contrast of many quantities of each LC time series, and have practical significance. A three-dimensional vector, which consists of theβof bispectrum, Shannon entropy, and wave crest factor is the sensitive eigenvector for faulty insulator. The eigenvector can divide all the insulators into two regions not only non-overlapping but far apart regions:the region of perfect contaminated insulators; the region of faulty contaminated insulators. Using above a three-dimensional vector as input vector, any of three classifiers, Euclide distance judgment, grey relational analysis of B-mode, and BP artificial neural network, can exactly distinguish between perfect and faulty insulators at various dirtiness, humidity, temperature and the virtual values of the voltage involving harmonics. This conclusion has both academic and practical significances.
引文
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