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Microgrids have been widely applied to improve the energy quality parameters of a distribution system locally, in addition to ensuring the operation of the system in an isolated manner. The Model Predictive Control (MPC) is a great solution to guarantee the operation of the system considering forecasting models and also physical restrictions of the system, which ensure the optimal operation of the Microgrid. However, the construction of a control scheme following the objectives established in order to meet the connected and isolated operation of a Microgrid is still a challenge. This paper proposes the development of an MPC control scheme that assures optimal system operation in connected and islanded mode, improving power quality indexes, ensuring network requirements, and extending battery life cycle. The proposed control operation in the connected mode can attend to the needs of the Microgrid, reducing the impacts of peak demand and the intermittent variations in renewable generation, where a linear objective function is developed for this purpose. In the islanded mode, grid requirements are guaranteed through load shedding, considering improvements in continuity indicators. Forecasting models are implemented considering the MPC approach and a detailed network model is developed. Simulation results highlight the effectiveness of the proposed control strategy.