Inclusion of the frequency effect in the lumped parameters transmission line model: State space formulation

The objective of this paper is to include the frequency dependence of the longitudinal parameters in the lumped parameters line model. The distributed nature of the transmission line was approximated by a cascade of π circuits and the frequency effect was approximated by a rational function which was synthesized by an equivalent circuit. Then, the equivalent circuit was inserted in each π circuit of the cascade. After that, the currents and voltages along the line were described in the form of state equations. This way, it was possible to obtain a formation rule of the state matrices lumped parameters model taking into account the frequency dependence. To confirm the validation of the state matrices obtained, the lumped parameters representation of frequency-dependent lines was used to represent a single-phase line and a three-phase line. The simulations were carried out using state space techniques and an electromagnetic transient program (EMTP) (in this case, the cascade was inserted in the EMTP). It is observed that the simulation results obtained with state space representation are in agreement with those results obtained with EMTP.