Microgrids appear as a key-solution to manage smart grids with high penetration of renewable energy generation and non-linear and unbalanced loads. Their flexibility allows the energy exchange with the utility network in grid-connected mode or the transition to an islanded operation mode from the main grid in case of disturbances or faults. While in grid-connected mode the main grid imposes the frequency and voltage, in the islanded mode the own microgrid must do the load balance between all the connected components to the microgrid and must supervise that the power flow inside the microgrid is done according to the power quality levels that all the devices of the microgrid require. In order to improve the power quality in these kind of applications, a novel control strategy based on Model Predictive Control (MPC) and Fourier analysis is presented in this paper applied to the voltage/frequency control of a Voltage Source Inverter (VSI). At each sample instant, the current demand in the microgrid is predicted through the estimation of the equivalent Thevenin's impedance in the microgrid. This fact allows the inverter controller to select the most appropriate gate-signal combination to maintain the reference frequency and the voltage in the microgrid.