A Spice-Compatible Macromodel for Field Coupling to Underground Transmission Lines Based on the Analog Behavioral Modeling

This article presents a time-domain macromodeling algorithm for buried transmission lines subject to coupling of an incident field and terminated with linear and nonlinear loads. Different from overhead lines, the determination of the transient ground admittance is of great importance due to the complexity of the analytical expressions and the necessity of assuring a good approximation over a wide frequency range. The proposed macromodel adopts the analog behavioral modeling (ABM) library of Spice solvers to model frequency-dependent transmission line parameters directly, and calculate convolution in time domain, making it simple and convenient to treat time-domain field-to-line coupling equations without the need of time and spatial discretization and curve fitting used in other time-domain numerical algorithms. Besides, the model complexity is not limited by the line length. Hence, the proposed algorithm can significantly simplify the modeling process and improve simulation efficiency, especially for long multiconductor transmission lines. Furthermore, an effective and simplified expression for self and mutual ground impedance and admittance of underground lines is proposed in this article. With the proposed expression, the time-consuming numerical integration can be avoided, leading to a saving of 98% of the computational time. Finally, several validation examples of field coupling to buried power cables terminated with linear and nonlinear devices are investigated. The comparison of calculated waveshapes and CPU times shows the accuracy and efficiency of the proposed method.