The advanced control technique Model predictive control (MPC) is gaining popularity in power electronics for converters with distributed energy resources. It combines closedloop control and minimizes errors and control effort. As a model-based control technique, MPC's performance can degrade due to plant disturbances, such as parametric errors or large perturbations in grid voltage or load current. Our research used an MPC with modulation on a converter connected to the grid with an inductive filter for integrating renewable energy sources. The margin of robust stability (RS), derived from the singular Value Decomposition (SVD), provides a theoretical investigation of the robustness of the MPC controller tuning in dependency on the cost function weight factors and the time horizons. In the experiments conducted on a 2 kW workbench, it was confirmed that the proposed controller is stable and robust in nominal and under severe parametric uncertainty conditions, addressing the power quality criteria defined in IEEE Std. 519-2014. The experimental results show that the proposed MPC controller tuning outperforms the classical PI current controller in nominal conditions and is more robust to uncertainty in the passive filter of the grid-connected converter.