高压直流单极离子流场的有限元迭代计算

Finite Element Iterative Computation of High Voltage Direct Current Unipolar Ionized Field

采用有限元方法对HVDC单极离子流场进行迭代求解,在采取一定近似条件的情况下,将描述高压直流线路周围场分布的三阶非线性偏微分方程分解为对泊松方程和电流连续性方程的分别求解。在给定空间电荷密度初值后,不断迭代求解并根据每一步结果对空间电荷密度修正直至收敛。讨论了计算中需要考虑的若干问题,舍弃了Deutsch假设,并用更符合实际的导体表面场强经验公式代替Kaptzov假设,提出一种空间电荷密度更新公式。最后用具有解析解的同轴圆筒电极问题对该算法进行了验证,并与相关HVDC模型实验数据进行比较,得到了较满意的结果。该方法可适用于HVDC单极离子流场的计算分析。

Unipolar ionized field around high voltage direct current（HVDC） was solved iteratively with finite element method. Under certain approximate conditions, computation of the third-order nonlinear partial differential equation discribing the field was separated into iterative calculation of both Poisson and current continuity equations. After providing an initial value of charge density throughout the interested region, results can be obtained by updating charge density after each iterative solution until convergence. Several problems related to the computation were discussed, Deutsch assumption was waived and Kaptzov assumption was replaced by： an empirical formula; an update formula for charge density was presented. Both known analytical and experimental results were compared with those obtained by the method, and satisfactory agreement was obtained. The method presented is applicable for the analysis of HVDC unipolar ionized field.