Time-Domain Modeling of Tower-Footing Grounding Systems Based on Impedance Matrix

This paper presents a new method for time-domain modeling of multi-port grounding systems so that it can be implemented in transient analyzer software. To this aim, first, the method of the moment is used for solving the Maxwell equations, which leads to the extraction of the impedance matrix of the grounding system over the frequency range of interest of the lightning surges. In the next step, a logical approximation of the impedance matrix is made using the vector fitting (VF) method. The used VF method leads to the fitting of a set of poles-residues for all the arrays of the impedance matrix of the grounding system. Finally, considering that all the electromagnetic transient solvers perform the simulation based on the admittance matrix, the proper model of the time-domain single-port and multi-port grounding system is implemented by means of state-space equations. The method provides accurate results for the calculation of the lightning-originated overvoltages. The advantage of the proposed model consists of higher accuracy and lower complexity, as it covers all the frequency range of interest and does not need any matrix inversion. Also, it can be implemented directly in a transient analysis solver, e.g., EMTP.