为了高效稳定求解特高压直流输电线路离子流场问题, 本文提出了一种基于梯度流电荷密度更新策略的上流有限元快速算法。首先, 根据梯度流思想, 建立导线表面最大场强偏离起晕场强的能量泛函, 并沿其负梯度方向更新导线表面电荷密度, 推导了一种新型的导线表面电荷密度更新公式。其次, 通过同轴圆柱电极模型, 单极200kV输电线路模型, 双极±800kV输电线路模型, 以及三维含建筑物的双极直流输电线路模型, 验证算法的有效性。最后将新提出算法与经典算法和牛顿-拉夫逊法进行对比, 验证算法的高效性。研究结果表明: 新提出算法计算结果与相关文献中的计算数据或实验数据相吻合, 验证了算法的有效性。在不同电荷密度初值情形下, 新算法相较于其他两种算法对初值不敏感, 迭代步数控制在20步以内, 具有良好的收敛性与计算效率。该研究为复杂环境下特高压直流线路离子流场的数值模拟提供了有效手段。

In order to solve the ion flow field problem of UHVDC transmission lines efficiently and stably, this paper proposes an upstream finite element fast algorithm based on gradient flow charge density update strategy. This paper proposes a fast upstream finite element algorithm based on gradient flow charge density update strategy. Firstly, by introducing the gradient flow concept, an energy functional for the deviation of maximum electric field on conductor surfaces from corona onset field is established, and a new conductor surface charge density update formula is derived by updating along the negative gradient direction. Secondly, the algorithm' s effectiveness is verified using coaxial cylindrical electrode model, monopolar 200kV transmission line model, and bipolar ±800kV transmission line model, and a three-dimensional bipolar transmission line model incorporating buildings. Finally, comparative studies with classical algorithms and Newton-Raphson method validate its efficiency. Results show that the proposed algorithm agrees well with the computational and experimental data reported in the relevant literature, demonstrating its effectiveness. Compared with other methods, it demonstrates insensitivity to initial charge densities, ensures iterative convergence within 20 steps, and exhibits excellent convergence and computational efficiency. This study provides an effective approach for numerical simulation of UHVDC ion flow fields in complex environments.