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This paper presents the development of an analytical formulation for estimating the potential on the soil surface, caused by electric current calculated on a grounding conductor. The formulation has a great significance in its use in conjunction with 1-D numerical methods, which are not able to determine such potentials directly. The proposed study focuses on lightning surges considering the frequency dependence of the soil properties. First, the subject is introduced emphasizing important aspects related to the analysis and representation of grounding systems against lightning. Afterward, the proposed analytical formulation is introduced with a focus on the computational implementation of the transmission line modeling method in 1-D. Simulations were carried out considering a typical horizontal electrode used as grounding in the power electric system. The formulation was validated by comparing the results with the solution based on the electromagnetic model (CDEGS Software), which is considered the most stringent for the solution of full Maxwell equations due to their minimum approaches. The results demonstrate that the generalized formulation presents good accuracy, contributing to an improved representation of grounding systems based on numerical techniques in 1-D. [ABSTRACT FROM AUTHOR]

This paper presents an extended methodology based on the transmission line modeling method (TLM) aiming at a soil ionization representation for the simulation of grounding systems. This natural phenomenon can be represented by considering the variation of the conductive components present in the TLM circuit. The proposed analytical formulation is introduced with a focus on the computational implementation of the TLM method in one dimension. The method is not subject to divergent solutions, being numerically stable and the methodology can be incorporated into a general algorithm irrespective of the soil properties or characteristics of the grounding electrode and lightning surge. [ABSTRACT FROM AUTHOR]