The extended describing function (EDF) is a well-known method for modelling resonant converters due to its high accuracy. However, it requires complex mathematical formulation effort. This paper presents a simplified non-linear mathematical model of series-series (SS) compensated inductive power transfer (IPT) system, considering zero-voltage switching in the inverter. This simplified mathematical model permits the user to derive the small-signal model using the EDF method, with less computational effort, while maintaining the accuracy of an actual physical model. The derived model has been verified using a frequency sweep method in PLECS. The small-signal model has been used to design the voltage loop controller for a SS compensated IPT system. The designed controller was implemented on a 3.6 kW experimental setup, to test its robustness.