Using state-space techniques to represent frequency dependent single-phase lines directly in time domain

This paper proposes to use a state-space technique to represent a frequency dependent line for simulating electromagnetic transients directly in time domain. The distributed nature of the line is represented by a multiple pi section network made up of the lumped parameters and the frequency dependence of the per unit longitudinal parameters is matched by using a rational function. The rational function is represented by its equivalent circuit with passive elements. This passive circuit is then inserted in each pi circuit of the cascade that represents the line. Because the system is very sparse, it is possible to use a sparsity technique to store only nonzero elements of this matrix for saving space and running time. The model was used to simulate the energization process of a 10 km length single-phase line.