Power system design is performed using simulation tools which require, among others, a detailed knowledge of cable models. Indeed, cable model is key for power grid studies. Cable modelling introduce difficult technical challenges due to the propagation of electromagnetic waves across long distances, and to the highly frequency dependent physical behaviour.
Calculation of the cable system distributed parameters is performed in the frequency domain. The transients are solved in the time-domain using the known inverse transformation of simple rational functions, the frequency dependent impedance and admittance matrices being fitted by a formula using those functions.
The state of the art model using this method is known as the Wide Band model, readily available in commercial sofwares. The fitting process is indeed an approximation that can lead to inaccuracies and even instabilites due to the created passivity violations. Simulations may diverge when those violations are excited.