Grid-forming inverters (GFI) are important elements in modern AC microgrids, operating as high-bandwidth controllable voltage sources. Finite-Control-Set Model-Predictive Control (FCS-MPC) has demonstrated to be an effective alternative to conventional linear voltage controllers due to advantages such as fast dynamic response and intuitive design. However, the dependence on an accurate mathematical model of the plant is a drawback that limits the performance of FCS-MPC when facing model uncertainty or time-varying parameters in the controlled system. To overcome this problem, Model-Free Predictive Control (MF-PC) strategies have been developed using ARX time-series models for prediction, with parameters estimated online from available data mesurements. This paper proposes a variant of the MF-PC method with ARX predictor that fully eliminates the dependence on physical parameters and reduces the number of required measured variables and parameters to be estimated. The realtime feasibility of the proposed MF- PC is verified by Hardware-In-the-Loop (HIL) experiments.