Empirical Sensitivity Analysis of the State Matrices of a Transmission Line

The objective of this work is to employ an empirical approach to simplify the state matrices that represent a transmission line, describing the equivalent $\pi$ circuit directly in the time domain through state-space equations. The formation rules of these matrices are addressed in an overview manner, with emphasis on the matrices related to the sensitivity study, enabling the empirical removal of terms that do not significantly impact the system response. This results in a simplified matrix with straightforward computational implementation. For validation purposes, a simplified model was compared to a model based on formation rules validated in previous studies, both simulated in MATLAB and in the time domain, considering energizations with step inputs. The results demonstrate the feasibility of the proposed simplification, highlighting its applicability in electromagnetic transient studies and its computational cost efficiency without compromising system accuracy. It is important to note that the models analyzed in this work are simple and characterized by a low number of poles and branches.