Comparing Lumped and Distributed Parameters Models in Transmission Lines during Transient Conditions

Abstract

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 pi-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 pi-circuit and submitted to diverse conditions of energization.