This paper presents a novel finite control set Model Predictive Control (MPC) approach, for grid connected converters. The advantage of using MPC for this application lies in the fact that it does not require cascaded control loops, PWM modulators or PLLs. However, the supply impedance is generally unknown causing remarkable errors in the MPC control action, in the case its value is not negligible compared to the converter inductance. This paper presents a novel idea for estimating the supply inductance, based on the difference between the grid voltage magnitudes at two consecutive sampling instants. The grid voltage magnitudes are calculated on the basis of the supply current and converter voltage directly within the MPC algorithm, in order to achieve a fast estimation and integration between the controller and estimator. The proposed method is verified via simulation tests on a three-phase two level active front-end.