A future rise in electrical energy demand is expected due to the electrification of the thermal energy supply and the rise in popularity of the Electric Vehicle (EV). This rise in the electrical energy demand results in needed investments in the electrical energy infrastructure to prevent congestion at the transformer due to the higher peak of energy transfer between the microgrid and utility grid. Smart control strategies as EV management and Demand Response (DR) programs are used to lower the peak of electrical energy transfer. In this thesis, the focus is on how the introduction of hydrogen will influence the peak of electrical energy transfer between the microgrid and utility grid to reduce future electrical grid investments. The stochastic processes in the microgrid are forecasted with the best-obtained forecasting models. Using a mixed logic dynamical formulation of the hybrid model of the microgrid, different Model Predictive Control (MPC) control strategies are implemented to solve the multi-objective mixed-integer linear programming problem. Microgrids with different levels of hydrogen penetration are compared. It is concluded that the introduction of hydrogen to a future microgrid will reduce the peak of electrical energy transfer, i.e., reduce future investments in the electrical grid. However, it does result in higher overall economic costs due to the high increase in energy import costs. Furthermore, an increase in the degradation of the EVs due to their more intensive use is concluded when introducing hydrogen to the microgrid. Two stochastic MPC methods, scenario- and tree-based MPC are compared to the nominal controller to see if better performance can be obtained for a hydrogen-based microgrid. Better overall performance of the stochastic MPC strategies is obtained in the winter but could not be realized in the summer. Only tree-based MPC shows a reduction in the peak of electrical energy transfer.