This paper deals with Smart Grids including renewable generation plants and plug-in vehicle fleets managed by aggregators and connected to the grid through power electronic devices. A new multi-objective optimization model is proposed in order to obtain the optimal operation of the Smart Grids. The proposed model originates from the need of accomplishing numerous and sometime conflicting objectives in the Smart Grid operation and allows to perform several services, aimed at contemporaneously meeting needs internal to the SG and external to it. Among the possible optimization methods to solve the multi-objective model, two different approaches were used in this paper based on objective sum criterion and weighted sum criterion, respectively. The objective sum criterion does not require any articulation of preferences and seems particularly suitable when low CPU time is required. The weighted sum criterion could lead to better quality of decisions since it evaluates the relative importance of each objective. Numerical simulations applying the analyzed methods for the optimal operation of a low voltage test Smart Grid were performed and discussed.