输电线路雷电暂态综合建模及仿真算法研究
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摘要
输电线路防雷保护的根本目的就是尽可能地减少由于雷击引起的线路跳闸事故发生的次数并降低雷击事故引起的损失。输电线路的过电压保护和绝缘配合在很大程度上取决于其承受的过电压的幅值和波形,输电线路的绝缘水平以及各种设备(如绝缘子串、变压器和断路器等)的绝缘配合必须能够承受线路上可能出现的过电压。因此,对输电线路的雷击暂态特性进行研究,分析输电线路上可能出现的雷电过电压有利于可靠地设计输电线路及电气设备的绝缘配合,并且有利于实现经济上的最优化。
雷电过电压波在输电线路上传播时会发生衰减和变形,其原因主要是在雷电暂态情况下线路的电晕效应和线路参数的频变效应。本文分别针对这两个方面展开了研究和讨论。
当输电线路上承受的雷电过电压幅值超过电晕起始电压时,电晕开始发生。为减小误差,本文将发生电晕时输电线路的空间电场分成两部分之和,一部分是没有空间电荷时产生的标称场(拉普拉斯场):另一部分是引入空间电荷所产生的空间电荷场。在求解方程时,用模拟电荷法求解标称场,而用有限元法求解空间电荷场。其中在运用有限元法求解空间电荷场的过程中,首先利用给定的电荷密度初始值计算空间电场,再利用计算得到的合成电场反向计算空间电荷密度,通过逐步迭代计算得到雷击点处发生电晕时的Q-V曲线以及每一时刻输电线路对地的动态电容。对于线路上其它点的电晕过程的考虑,本文采用查表的思路,当该点处的电压达到某一幅值时,即查寻雷击点处的Q-V曲线,得到对应的电晕电荷和动态电容值进行计算。
在考虑参数频变时,输电线路径向参数的频率相关性可用一系列并联的电阻和电感的组合来描述。文中通过计算分析证明了该模型不仅能在很大的频率范围内较精确地表征输电线路的频率相关性,而且不必进行频域和时域的相互变换,节省了计算时间,更重要的是可以很方便地与电晕模型进行衔接。利用收敛速度更快的Newton-type迭代法计算了各RL模块的参数值。若在计算过程中同时考虑线路参数频变特性和电晕效应,则可将频变参数线路模型中描述线路的每一个π型单元的对地电容修改为电晕发生后的动态电容即可。
为了使本文所建立的输电线路暂态特性的分析模型更完整,文中用倾斜导体模型取代了现有的计算杆塔波阻抗时普遍采用的竖直导体模型,能够更好地反映杆塔的实际结构特征,进而建立了较为精确的输电线路杆塔的多波阻抗分析模型。该模型结合绝缘子闪络模型可分析杆塔遭受雷击,由于其电位的升高,引起绝缘子闪络,进而使线路上产生雷电过电压波的整个过程。对于所建立的暂态电路,采用暂态等值计算电路的方法,将电阻、电感以及电容组成的复杂网络转化为仅包含电阻及电流源并联的形式,利用节点电压法求解输电线路上每一点的电压波形。
根据所建立的模型和计算方法,文中计算了双指数雷电波、衰减振荡波和快速脉冲作用下的电晕效应,对其Q-V曲线各分支阶段的物理过程进行了阐述,并在此基础上分析了衰减振荡波作用下的次回环曲线的特性。文中设计了模拟实验,验证了本文所提出的计算方法的有效性。此外,本文分别对仅考虑冲击电晕效应、仅考虑线路参数频变效应以及同时考虑电晕和参数频变效应两方面影响的输电线路暂态特性进行了分析和比较。计算结果也显示电晕效应对于输电线路雷电过电压波形的衰减和畸变作用要大于参数频变效应,但是同时考虑这两方面影响更符合实际情况。文中还比较了不同因素对雷电过电压波的影响,如波头时间短的雷电波以及波尾时间短的雷电波在沿线路传播时其衰减和畸变作用更明显。文中运用matlab程序编写了输电线路过电压分析计算软件,文中的计算方法和结果可为实际线路的雷电防护和绝缘设计提供很好的参考依据。
The basic purpose of lightning protection of transmission line is to reduce lightning accident times and decrease the losses caused by lightning. The overvoltage protection and insulation coordination of transmission lines depend in great degree on the magnitude and waveform of the overvoltage. The insulation level of transmission line and the insulation coordination of different divices such as insulator, transformer and breaker, must endure the possible overvoltage. So doing research on lightning overvoltage of transmission line is propitious to the design of the insulaton coordination of transmission line and electrical devices and to the ecomic optimization of the system.
Attenuation and distortion may occur on lighitning overvoltage when travling along the line and the main causations are corona effect and frequency dependent effect of transmission line in lighting transient situations. The two aspects are studied in this paper.
When the voltage on line exceeds corona inception voltage, corona occurs. In order to reduce calculation errors, the electric field is devided into two parts, one is the nominal field with no charge and the other is the field by space charge. When solving the equation, simulation charge method is used to solve the nominal field and finite element method to the space charge field. When solving the space charge field, the given initial value of charge density is applied to calculate the space electric field, and the calculated total field is then used to calculate the space charge density reversely. The Q-V curve and the dynamic capacitance of the line at corona can be obtained by iterative calculation. For the corona effects of other points on the line, the thinking of lookup is used in this paper, that is, when the voltage on some point reaches a certain value, the corona charge and dynamic capacitance are obtained by lookuping the Q-V curve on the lightning stroke point.
When considering the frequency dependent parameters of the line, its radial parameters are described by series and parallel of resistance and inductance. The calculation results verify that the model not only can describe the frequency dependent characteristics of the line in a large range of frequency, but also need not to do transformation between frequency domain and time domain which can save the calcualtiong time and the more important is that it can be connected to the corona model convinently. The paramenters of each RL module are evalued by Newton-type iteration method whose convergence rate is more rapid. If it is needed to consider the frequency dependent characteristics and the corona effects of the line synchronously, the capacitance in the frequency dependent model is changed to the dynamic capacitance.
In order to make the models established in this paper more complete, the general vertical conductor model to express the tower is replaced by the inclined conductor tower model, and the more accurate multiwave impedance tower model is proposed to analyze the lightning transients of transmission tower. The tower model combined with the insulator flash model can be used to analyze the total process that when the tower is stroked by lightning, the voltages on it are rised, and then the insulator flashes and lightning overvoltages are produced on the line. For the transient circuit model, the method of transient equivalent calculation circuit is applied, which converts the complex network composed of resistances, inductances and capacitances into the circuit made up of only parallel resistances and current sources. Node voltage method is used to solve the voltage on each point of the line.
According to models and calculation methods proposed in this paper, the corona effect under double exponential lightning waveform, damped oscillation waveform and fast surge are calculated, the physical process of each branch on the Q-V curve is described, and on the basis the characteristics of minor loop curve under damped oscillatory waves are also analyzed. A simulation experiment is made to verify the effectivemess of the model proposed in this paper. In addition, the situations of only considering impulse corona effect, only considering frequency dependent effect of line parameters and considering corona effects and frequency dependent characteristics synchronously are analyzed and compared with each other. The calculation results indicate that the attenuation and distortion of corona effects on transmission line are larger than those by frequency dependent effects, but it is more conforming to reality considering the two aspects synchronously. The influences of different aspects on lighting overvoltage are also compared in this paper, for example, it is more obvious for the attenuation and distortion functions of lighitning waveform with short wave fronts and wavetails on the travelling waves. Software for analyzing lightning overvoltages on transmission line is programmed by matlab, and the calculation method and results proposed in this paper can provide guidelines for the lightining protection and insulation design of practice lines.
雷电过电压波在输电线路上传播时会发生衰减和变形,其原因主要是在雷电暂态情况下线路的电晕效应和线路参数的频变效应。本文分别针对这两个方面展开了研究和讨论。
当输电线路上承受的雷电过电压幅值超过电晕起始电压时,电晕开始发生。为减小误差,本文将发生电晕时输电线路的空间电场分成两部分之和,一部分是没有空间电荷时产生的标称场(拉普拉斯场):另一部分是引入空间电荷所产生的空间电荷场。在求解方程时,用模拟电荷法求解标称场,而用有限元法求解空间电荷场。其中在运用有限元法求解空间电荷场的过程中,首先利用给定的电荷密度初始值计算空间电场,再利用计算得到的合成电场反向计算空间电荷密度,通过逐步迭代计算得到雷击点处发生电晕时的Q-V曲线以及每一时刻输电线路对地的动态电容。对于线路上其它点的电晕过程的考虑,本文采用查表的思路,当该点处的电压达到某一幅值时,即查寻雷击点处的Q-V曲线,得到对应的电晕电荷和动态电容值进行计算。
在考虑参数频变时,输电线路径向参数的频率相关性可用一系列并联的电阻和电感的组合来描述。文中通过计算分析证明了该模型不仅能在很大的频率范围内较精确地表征输电线路的频率相关性,而且不必进行频域和时域的相互变换,节省了计算时间,更重要的是可以很方便地与电晕模型进行衔接。利用收敛速度更快的Newton-type迭代法计算了各RL模块的参数值。若在计算过程中同时考虑线路参数频变特性和电晕效应,则可将频变参数线路模型中描述线路的每一个π型单元的对地电容修改为电晕发生后的动态电容即可。
为了使本文所建立的输电线路暂态特性的分析模型更完整,文中用倾斜导体模型取代了现有的计算杆塔波阻抗时普遍采用的竖直导体模型,能够更好地反映杆塔的实际结构特征,进而建立了较为精确的输电线路杆塔的多波阻抗分析模型。该模型结合绝缘子闪络模型可分析杆塔遭受雷击,由于其电位的升高,引起绝缘子闪络,进而使线路上产生雷电过电压波的整个过程。对于所建立的暂态电路,采用暂态等值计算电路的方法,将电阻、电感以及电容组成的复杂网络转化为仅包含电阻及电流源并联的形式,利用节点电压法求解输电线路上每一点的电压波形。
根据所建立的模型和计算方法,文中计算了双指数雷电波、衰减振荡波和快速脉冲作用下的电晕效应,对其Q-V曲线各分支阶段的物理过程进行了阐述,并在此基础上分析了衰减振荡波作用下的次回环曲线的特性。文中设计了模拟实验,验证了本文所提出的计算方法的有效性。此外,本文分别对仅考虑冲击电晕效应、仅考虑线路参数频变效应以及同时考虑电晕和参数频变效应两方面影响的输电线路暂态特性进行了分析和比较。计算结果也显示电晕效应对于输电线路雷电过电压波形的衰减和畸变作用要大于参数频变效应,但是同时考虑这两方面影响更符合实际情况。文中还比较了不同因素对雷电过电压波的影响,如波头时间短的雷电波以及波尾时间短的雷电波在沿线路传播时其衰减和畸变作用更明显。文中运用matlab程序编写了输电线路过电压分析计算软件,文中的计算方法和结果可为实际线路的雷电防护和绝缘设计提供很好的参考依据。
The basic purpose of lightning protection of transmission line is to reduce lightning accident times and decrease the losses caused by lightning. The overvoltage protection and insulation coordination of transmission lines depend in great degree on the magnitude and waveform of the overvoltage. The insulation level of transmission line and the insulation coordination of different divices such as insulator, transformer and breaker, must endure the possible overvoltage. So doing research on lightning overvoltage of transmission line is propitious to the design of the insulaton coordination of transmission line and electrical devices and to the ecomic optimization of the system.
Attenuation and distortion may occur on lighitning overvoltage when travling along the line and the main causations are corona effect and frequency dependent effect of transmission line in lighting transient situations. The two aspects are studied in this paper.
When the voltage on line exceeds corona inception voltage, corona occurs. In order to reduce calculation errors, the electric field is devided into two parts, one is the nominal field with no charge and the other is the field by space charge. When solving the equation, simulation charge method is used to solve the nominal field and finite element method to the space charge field. When solving the space charge field, the given initial value of charge density is applied to calculate the space electric field, and the calculated total field is then used to calculate the space charge density reversely. The Q-V curve and the dynamic capacitance of the line at corona can be obtained by iterative calculation. For the corona effects of other points on the line, the thinking of lookup is used in this paper, that is, when the voltage on some point reaches a certain value, the corona charge and dynamic capacitance are obtained by lookuping the Q-V curve on the lightning stroke point.
When considering the frequency dependent parameters of the line, its radial parameters are described by series and parallel of resistance and inductance. The calculation results verify that the model not only can describe the frequency dependent characteristics of the line in a large range of frequency, but also need not to do transformation between frequency domain and time domain which can save the calcualtiong time and the more important is that it can be connected to the corona model convinently. The paramenters of each RL module are evalued by Newton-type iteration method whose convergence rate is more rapid. If it is needed to consider the frequency dependent characteristics and the corona effects of the line synchronously, the capacitance in the frequency dependent model is changed to the dynamic capacitance.
In order to make the models established in this paper more complete, the general vertical conductor model to express the tower is replaced by the inclined conductor tower model, and the more accurate multiwave impedance tower model is proposed to analyze the lightning transients of transmission tower. The tower model combined with the insulator flash model can be used to analyze the total process that when the tower is stroked by lightning, the voltages on it are rised, and then the insulator flashes and lightning overvoltages are produced on the line. For the transient circuit model, the method of transient equivalent calculation circuit is applied, which converts the complex network composed of resistances, inductances and capacitances into the circuit made up of only parallel resistances and current sources. Node voltage method is used to solve the voltage on each point of the line.
According to models and calculation methods proposed in this paper, the corona effect under double exponential lightning waveform, damped oscillation waveform and fast surge are calculated, the physical process of each branch on the Q-V curve is described, and on the basis the characteristics of minor loop curve under damped oscillatory waves are also analyzed. A simulation experiment is made to verify the effectivemess of the model proposed in this paper. In addition, the situations of only considering impulse corona effect, only considering frequency dependent effect of line parameters and considering corona effects and frequency dependent characteristics synchronously are analyzed and compared with each other. The calculation results indicate that the attenuation and distortion of corona effects on transmission line are larger than those by frequency dependent effects, but it is more conforming to reality considering the two aspects synchronously. The influences of different aspects on lighting overvoltage are also compared in this paper, for example, it is more obvious for the attenuation and distortion functions of lighitning waveform with short wave fronts and wavetails on the travelling waves. Software for analyzing lightning overvoltages on transmission line is programmed by matlab, and the calculation method and results proposed in this paper can provide guidelines for the lightining protection and insulation design of practice lines.
引文
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