This paper presents a multi phase induction system modeling for a metal disc heating. This architecture leads to a reduced element system, without any coupling tranformers, phase loop, mobile screens or mobile magnetic cores. The model is based on simplified equivalent models but takes into account data extracted from finite element software concerning the transfer between the coil currents and the piece to be heated. It is implemented in a versatile power electronic software, PSim. An optimization procedure calculates the optimal supply currents in the inverters in order to obtain a desired heating of the work piece. The simulated and experimental results are compared in open-loop and closed loop. The paper ends with a first simple current control method which sets RMS-values of inductor currents in continuous and digital conditions.