A method for increasing the contact area of a grounding system with the earth is the installation of counterpoise wires. Counterpoise wires improve the reliability of overhead power transmission lines. They are conductors buried in the ground parallel to or at an angle to the line conductors. This paper presents an electrokinetic model refinement via a perturbation finite-element method to calculate the grounding resistance of counterpoise wires. The perturbation method is herein developed for refining the electric field distribution in soil starting from simplified models, based on electric field distributions from 2-D models, that evolve towards a 3-D accurate model. The analysis of the distribution of the electric field and of the electric potential around the tower footing allows accurately determining the tower footing resistance. The comparisons between the grounding resistance simulated and calculated analytically of a counterpoise wire are presented.