This paper presents the design of an energy management strategy based on a low complexity Fuzzy Logic Control (FLC) for grid power profile smoothing of a residential grid-connected microgrid including Renewable Energy Sources (RES) and battery Energy Storage System (ESS). The proposed energy management strategy uses generation and demand forecasting to anticipate the future behavior of the microgrid. Accordingly to the microgrid power forecast error and the Battery State-of-Charge (SOC) the proposed strategy performs the suitable control of the grid power. A simulation comparison with previous energy management strategies highlights the advantages of the proposed work minimizing fluctuations and power peaks in the power profile exchanged with the grid while keeping the energy stored in the battery between secure limits. Finally, the experimental validation in a real residential microgrid implemented at Public University of Navarre (UPNa, Spain) demonstrates the proper operation of the proposed strategy achieving a smooth grid power profile and a battery SOC center close to the 75% of the rated battery capacity.