Modern high voltage direct current (HVDC) power cables consist of nonlinear electric field and temperature depending insulation materials, eg, polyethylene (PE) or mass‐impregnated paper (MI). Within the insulation material, slowly time varying electric fields are the result of accumulated space charges. Due to the long operation time of power cables, the stationary charge distribution and the resulting additional field stresses inside the insulation material need to be taken into account, to ensure a stable operation of the cable system. The long accumulation time of charges in comparison to fast charge dynamics usually requires extended computation times within transient electro‐quasistatic simulation models. An alternative approach to calculate the final steady‐state charge distribution arises from the simultaneous solution of both, the stationary current and the electrostatic potential problem, which are nonlinearly coupled by Ohm's law. Each of the two potential equations are discretized using the finite difference method. Utilizing a nonlinear fixed point iteration for the electric potential, the steady‐state solution of the charge distribution is computed until convergence is obtained. During this pseudo time stepping process, oscillations may occur that yield incorrect results of the charge distribution. These oscillations are eliminated utilizing underrelaxation strategies. Numerical tests on a cylindrical and a plane parallel problem, using both approaches for the calculation of the steady‐state charge distribution, show a faster computation with the nonlinear fixed point iteration, reducing the computation time by at least one order of magnitude.

中文翻译：

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快速计算高压电力电缆中的稳态电荷分布

现代高压直流（HVDC）电力电缆由非线性电场和温度相关的绝缘材料组成，例如，聚乙烯（PE）或质量浸渍纸（MI）。在绝缘材料中，缓慢变化的电场是空间电荷累积的结果。由于电力电缆的工作时间较长，因此必须考虑固定电荷分布以及绝缘材料内部产生的附加场应力，以确保电缆系统的稳定运行。与快速充电动力学相比，较长的电荷累积时间通常需要在瞬态准静态仿真模型中延长计算时间。计算最终稳态电荷分布的另一种方法是同时解决这两种问题，静态电流和静电势问题，它们通过欧姆定律非线性耦合。使用势差法离散化两个势方程中的每一个。利用非线性定点迭代法计算电位分布的稳态解，直到获得收敛。在此伪时间步进过程中，可能会发生振荡，从而产生不正确的电荷分配结果。利用欠松弛策略可以消除这些振荡。对圆柱和平面平行问题的数值测试，使用两种方法计算稳态电荷分布，都显示出利用非线性定点迭代的更快计算速度，将计算时间减少了至少一个数量级。