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电力线路雷电感应过电压的时域积分方程法分析

Time Domain Integral Equation Method for the Lightning Induced Over-Voltages in Power Lines

【作者】 刘晨

【导师】 赵志斌;

【作者基本信息】 华北电力大学 , 电磁场与微波技术, 2011, 硕士

【摘要】 占雷击率90%的感应雷是造成低压输电线路雷害故障次数和线路跳闸率明显增加,高压输电线路绝缘老化的重要原因。并且感应雷电波沿线路的传播分布会严重影响电能质量及二次设备的正常运行。架空输电线路的雷电感应过电压计算是电力线路绝缘设计、采取防雷保护措施的基础计算。本文首先采用时域近似公式计算方法计算了雷击在空间某点处感应的水平电场:对雷击模型做了基本假设与建模,推导了梯形波在空间某点处感应产生的水平电场的两个分量,叠加得到水平电场,任意电流波形在空间某点感应产生的水平电场用梯形波进行拟合得到。推导过程中考虑了土壤电导率对水平电场的影响,还分析了影响雷电流周围水平电场的因素。建立雷电水平电场与单根细线导体耦合的时域积分方程,计算得到的雷击在空间某点处感应的水平电场值,可作为入射场的值代入推导得到的时域积分方程中。建立的时域积分方程应用矩量法的思想进行空间和时间离散,得到的线性方程组应用时间步进算法进行求解。在此过程中,本文讨论了基函数权函数选取的原则,及改善时间步进算法后时稳定性的一些方法。讨论了大地影响及带负载情况下对方程的改造方法,最后采用上述方法对单根及三相架空输电线路带负载情况下的感应过电压进行了一些算例计算,结果显示,与相关文献的结果吻合的很好,证明了方法的可行性。另外,针对工作的不足提出了下一步工作重点与展望。

【Abstract】 Most of low-pressure transmission line’s fault and trip and high-pressure transmission line’s insulation aging are caused by lightning induced over voltages, which is 90% of the total lightning. Induction lightning over voltages along the lines will seriously affect the power quality and the normal operation of secondary equipment. The calculation of lightning induced over voltage in overhead transmission lines is the basis of power line insulation and lightning protection design.Firstly, this paper use an approximate formula method to calculate the horizontal electric field at a point in space. A basic lightning model is built, and according to the modeling assumption, the two components(one due to the return stroke charge and the other due to the return stroke current) generated by a trapezium wave are derived. Superimpose the two components derived the horizontal electric field. Any arbitrary current waveform can be represented by the superposition of a set of trapeziums so we can get the electric induced by any arbitrary current waveform. In the process, we considered the soil conductivity’s influence, and also analysis the factors that impact the electric field.Then, this paper establish the time domain integral equations of horizontal electric field coupled with a single thin wire. The horizontal electric field can be seen as the incident field in the time domain integral equations. Apply moment method to this equation in space and time discretization. Use time stepping algorithm to solve the obtained linear equations. In this process, the article have discussed the principle to chose the basic functions and weighting functions, and improved the stability of time stepping algorithm.The impact of the earth and lines under load have been discussed. At last, some calculation samples are presented. The results agree well with relevant literatures, the feasibility of the method is demonstrated. In addition, the lack of job and the aspect are presented.

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