The solutions of differential equations of transmission line are generally difficult to obtain due to the convolution integral present. Considering this, there are models proposed for the study of electromagnetic transients in transmission line. In this paper a single-phase transmission line is represented by two models. The first model represents the transmission line by its distributed parameters and its differential equations in the time domain are transformed into algebraic equations in the frequency domain. This model is named ULM. Once the solutions were obtained in the frequency domain, using the ILT implemented numerically, the solutions are obtained in the time domain. The second model uses lumped circuits parameters and it considers the transmission line represented by π-circuits connected in cascade. This model has the advantage of being developed directly in the time domain, but there is a need to apply numerical integration methods to solve the equations. A fact observed in the responses using this models is the spurious oscillations. In this paper are shown spurious oscillations presents in simulations and using FT to analyze the spectral content of this oscillations for a single-phase transmission line considering different conditions as its length, represented by different quantities of π-circuit and submitted to diverse conditions of energization.

This article investigates the influence of four causal frequency-dependent (FD) soil models and their impact on the responses of a multiphase overhead transmission line (OHTL) with ground wires, generated by a lightning strike. The FD models proposed by Longmire-Smith (LS), Messier (M), Portela (P) and Alípio-Visacro (AV) are considered. The ground-return impedance and admittance matrices are computed with the Nagakawa approach for both frequency-constant and FD soil models. The frequency-domain modal voltages and time-domain transient voltages are assessed in this work. Modal decomposition technique is used to study the attenuation constant, propagation velocity and voltages for each propagation mode. Simulations are carried out in a frequency range of 100 Hz to 10 MHz, for OHTLs with lengths of 1 and 10 km, on soils of 700 and 4000 $\Omega$·m. Simulation results demonstrated that the Portela (P) model has resulted in more significant variation in the ground-return impedance and admittance, constant attenuation and propagation velocity in which a pronounced variation, especially at the high frequencies, is seen. On the other hand, Longmire-Smith (LS) and Messier (M) have produced similar results in both frequency and time domains. Additionally, the Alípio-Visacro (AV) model has produced intermediate responses, being the model recommended by CIGRÈ WG C4.33. Time-domain induced voltage waveforms obtained with the Portela (P) model has shown pronounced differences, especially at the peak values, for the high-resistive soil. This study demonstrates the importance of considering the FD soil models to assess the transient responses adequately, especially when OHTLs are on high-resistive soils.