Two-dimensional Transmission Line Modeling method: An algorithm considering non-homogeneous media and ionization

Abstract

This work presents a two-dimensional Transmission Line Modeling (TLM-2D) method for modeling non-homogeneous media and non-linearities. The presented method is derived on top of the classical TLM-2D method with reactive and conductive stubs to modify the properties of the medium. Taking advantage of the analogy between electromagnetic and circuits theories, nonlinearities such as soil ionization, can be solved numerically through models formulated to represent electrical conductors, such as grounding systems. Using this analogy, the analysis can be extended more generically to non-homogenous and lossy media. Then, nonlinearity phenomena is included in the classical TLM-2D model through the dynamic variation of circuit parameters. This variation is obtained through the developed analytical based tests. Computational implementation details are also reported. A case study is presented considering a grounding grid mesh in non-homogeneous media submitted to lightning surges. Comparative test results with the state of the art highlight the improved precision of the presented solution.