Abstarct: One of the challenges facing any electrical system that deals with unwanted transients such as lightning is the ground network and its modeling. In most models, the ground grid is considered as a simple resistance at all frequencies. In this treatise, we have presented a new method for extracting the exact circuit model of the earth system that can be implemented in transient state analysis software, which first extracts the frequency response of the earth grid by accurately solving Maxwell's equations with the help of the moment method. do. Then, with the vector fitting technique, and with the least approximation, we approximate the obtained frequency response as a fractional function consisting of zero and pole. Then by making appropriate changes, we change the obtained fractional function so that the obtained system is causal. In the end, with the help of the circuit synthesis discussion, we extract the RLC equivalent circuit of the earth grid from the obtained fractional function. And we achieved a newer orbital model with more optimal and accurate values. The proposed modeling has been implemented in a 765 kV network and the performance of the proposed ground system has been compared with previous methods including the model baxsed on soil ionization and the conventional mode, i.e. the use of simple linear resistance, and the results have been investigated. The advantage of the proposed model includes higher accuracy in simulating the effect of lightning overvoltage on the network and results close to reality in the studied frequency range. The results show that in the case of using the proposed model, which is a more accurate model, the return discharge current we have in the tower is greater too.