The JET enhancement project PCU (Plasma Control Upgrade) aimed at increasing the capabilities of the plasma Vertical Stabilization (VS) system. One of the activities of this project was devoted to the development of simple but sufficiently accurate models of the VS system so as to address the main design choices, use the simulation tools as reliable test-beds, and provide an adequate support to the engineering design and commissioning of the new Enhanced Radial Field Amplifier (ERFA). This paper illustrates some of the main achievements of the modelling activity, which gave rise to a closed loop model of the VS system, including plasma, PF coils and passive structures. In particular the paper deals with the selection of the set of turns to be used in the control coils and with the estimation of the eddy current effects on the VS system. The latter analysis addressed an upgrade of the converter units of ERFA, which was successfully implemented during its commissioning on plasma in August 2009.