基于分形理论雷电先导建模与仿真毕设论文终极版.doc

基于分形理论的雷电先导建模与仿真 摘要 雷电是一种自然放电现象，它是由雷云(带电的云层)对地面建筑物及大地的自然放电引起的。雷电放电的随机性以及雷电先导在其产生和发展过程中易受周围环境影响的特点导致雷电活动对电力系统产生巨大危害。由于雷电放电的随机性，需要用统计学的方法来进行防雷性能的评估。为此采用分形模型模拟了先导的发展过程，在二维和三维中描述雷电放电通道的分支和扭曲。通过比较自然界中雷电放电和仿真结果的分形维数，可以找到最接近实际的分形系数。与传统的电气几何模型、改进电气几何模型以及先导发展模型对比，分形模型不仅能够给出逼真的先导通道图形，而且能够从统计学意义上对一些不合理的侧面绕击现象作出解释。 本课题基于对雷电发展过程准静态场的假设，采用有限差分法作为电场计算的方法，将偏微分方程的问题化为线性方程组问题，并用迭代法进行线性方程的数值解。结合以上计算出的空间电场，采用分形方法完成了二维和三维雷电先导放电通道的建模与仿真，并实现了雷电先导发展过程及相应的空间电势图形静态和动态显示。在此基础上，本课题还讨论了避雷针(线)对闪电轨迹的影响。 关键词：分形模型；三维建模；雷电先导；有限差分法；MATLAB Modeling and Simulation of Lightning Leader based on the Fractal Theory Abstract Lightning is a natural discharge phenomenon, which is caused by thundercloud’s (electrically charged clouds) natural discharge to ground-level structures and earth. Lightning causes great damage to power system due to the stochastic nature of lightning discharges and the vulnerability of lightning leaders to various environments in the process of inception and propagation. As a result of the randomness of lightning discharge, it’s necessary to introduce statistical methods into the evaluation of lightning performance of transmission lines. Consequently, we introduced the fractal model to simulate the developing process of the lightning leader, reproducing branches and tortuosity of lightning channels in both 2-D and 3-D simulations. By comparing the fractal dimensions of natural lightning discharges and simulation results on various discharge settings, we discovered a fractal coefficient which can deliver a credible model of lightning strikes. Compared with traditional electromagnetic model, improving electromagnetic model, as well as leader progression model, the fractal model is not only able to give a realistic pilot channel graphics, but also able to give a explain to some unreasonable shielding failure phenomenon in the statistically significance. This topic is based on the assumption of quasi-static field in lightning development process, using the finite difference method to c