Sparse matrices for transient simulations with computing memory reduction

Abstract

Modified numerical integration methods and modelling have been analysed for application to simulations of electromagnetic transient phenomena in transmission lines. Both objectives are considered: minimize numerical errors caused by Gibbs’ oscillations and decrease the computational memory necessary for the mentioned simulations. For this, transmission lines have represented by cascades of π circuits. Based on this representation, modifications in numerical integration methods applied to the mentioned simulations can be introduced easily and the comparisons can be carried out quickly. In case of minimization of numerical errors, two approaches have checked. One of these options is related to the way how the numerical integration method is applied. The numerical integration has applied using 2-order matrices. These matrices are related to each π circuit applied to represent transmission lines. The other option is related to the damping resistance application. It has made by introducing damping resistances in the longitudinal structure of the π circuits. Sparse matrices have applied for decreasing the computational memory used during the simulations, because this matrix has a great quantity of null elements when the cascade of π circuits are represented by only one matrix with great order. Comparisons have carried out considering the non-modified numerical methods and the three modified methods suggested in this paper.