An accurate transmission line model must consider the frequency-dependence of the longitudinal parameters. In this context, the lumped parameter model (LPM), despite its well-known limitations, had been largely used to compute transient responses in power systems. To improve its accuracy, the frequency dependence of the longitudinal parameters had been included in the LPM by using fitting techniques and equivalent circuits. However, this representation had been described only for open-circuit tests. In this paper, we present the generic state space model of the frequency dependent LPM. We investigate how the number of line sections and the quality of the fitting affect the performance and accuracy of the frequency-dependent LPM, both in the time domain and in the frequency domain. Results shows that the frequency dependent LPM is accurate when compared to the JMarti line model.