Purpose

This paper aims to present a new approach to the numerical solution of skin effect integral equations in cylindrical conductors. An approximate, but very simple and accurate method for calculating the current density distribution, skin-effect resistance and inductance, in pulse regime of cylindrical conductor, having a circular or rectangular cross-section, is considered. The differential evolution method is applied for minimization of error functional. Because of its application in the practice, the lightning impulse is observed. Direct and inverse fast Fourier transform is applied.

Design/methodology/approach

This method contributes to increasing of correctness and much faster convergence. As the electromagnetic field components depend on the current density derivation, the proposed method gives a very accurate solution not only for current density distribution and resistance but also for field components and for internal inductance coefficients. Distribution of current and electromagnetic field in bus-bars can be successfully determined if the proximity effect is included together with the skin effect in calculations.

Findings

The study shows the strong influence of direct lightning strikes on the distribution of electrical current in cables used in lightning protection systems. The current impulse causes an increase in the current density at all points of the cross-section of the conductor, and in particular the skin effect on the external periphery. Based on the data calculated by using the proposed method, it is possible to calculate the minimum dimensions of the conductors to prevent system failures.

Research limitations/implications

There are a number of approximations of lightning strike impulse in the literature. This is a limiting factor that affects the reliability and agreement between measured data with calculated values.

Originality/value

In contrast with other methods, the current density function is approximated by finite functional series, which automatically satisfy wave equation and existing boundary conditions. It is necessary to minimize the functional. This approach leads to a very accurate solution, even in the case when only two terms in current approximation are adopted.

中文翻译：

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圆柱导体脉冲趋肤效应计算的改进方法

目的

本文旨在为圆柱导体趋肤效应积分方程的数值求解提供一种新方法。考虑了一种近似但非常简单且精确的方法，该方法用于计算具有圆形或矩形横截面的圆柱形导体的脉冲状态下的电流密度分布，集肤效应电阻和电感。差分演化方法被用于使误差函数最小化。由于其在实践中的应用，可以观察到雷电冲击。应用直接和逆快速傅立叶变换。

设计/方法/方法

这种方法有助于提高正确性和更快的收敛速度。由于电磁场分量取决于电流密度导数，因此所提出的方法不仅为电流密度分布和电阻提供了一种非常准确的解决方案，而且为磁场分量和内部电感系数提供了一种非常准确的解决方案。如果在计算中包括邻近效应和集肤效应，则可以成功确定母线中电流和电磁场的分布。

发现

研究表明，雷击直接影响雷电保护系统电缆中电流的分布。电流脉冲在导体的横截面的所有点上引起电流密度的增加，尤其是在外周边上的趋肤效应。根据使用建议方法计算出的数据，可以计算出导体的最小尺寸，以防止系统故障。

研究局限/意义

文献中有许多雷电冲击的近似值。这是一个限制因素，会影响测量数据与计算值之间的可靠性和一致性。

创意/价值

与其他方法相比，电流密度函数由有限函数级数逼近，该函数自动满足波动方程和现有边界条件。有必要使功能最小化。即使仅采用电流近似中的两个项，这种方法也可以得出非常准确的解决方案。