This study proposes an alternative method to calculate the transient responses of multi-conductor overhead transmission lines based on ABCD representation, recursive convolutions and numerical method for rational approximation in the frequency-dependent curves. In the classical universal line model, the characteristic admittance matrix and propagation matrix are represented by rational functions. In , previous and correct identification of the modal travelling times is required. However, these modal travelling times are estimated numerically, which do not offer good accuracy in some cases. This fact has a considerable effect on the rational representation of itself and consequently on the transient responses. In the alternative method, a previous estimation of the modal travel times is unnecessary because when using the ABCD representation for each propagation mode, a direct relation exists between the currents and tensions of the receiving and sending ends. These relationships are fitted by smooth rational functions, and then, using recursive convolution methods, the authors obtain the explicit equations of the currents and voltages to calculate the transient responses. The results demonstrate that the alternative method is accurate when compared with the frequency-domain solution of the transmission line transformed to the time domain using the numeric Laplace transform and with the Bergeron method.

中文翻译：

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在平衡的架空输电线路中使用递归卷积进行电磁暂态分析的替代方法

本研究提出了一种替代方法来计算基于 A B C D表示，递归卷积和频率相关曲线中有理逼近的数值方法。在经典通用线模型中，特征导纳矩阵 和传播矩阵 用有理函数表示。在 ，需要事先正确识别模态行驶时间。但是，这些模态行进时间是通过数字估算的，在某些情况下无法提供良好的准确性。这个事实对本身，因此在瞬态响应上。在替代方法中，无需事先估算模态行程时间，因为在使用A B C D为了表示每种传播模式，在接收端和发送端的电流和张力之间存在直接关系。这些关系由光滑的有理函数拟合，然后，使用递归卷积方法，作者获得了电流和电压的显式方程，以计算瞬态响应。结果表明，与使用数值Laplace变换和Bergeron方法转换到时域的传输线的频域解相比，该替代方法是准确的。