This paper deals with the load shifting problem in a household equipped with smart appliances and an energy storage unit with conversion losses. The problem is faced by establishing an event driven Model Predictive Control framework aiming to meet the real life dynamics of a household and to keep low the impact of the control system on the total electric energy consumption. The proposed approach allows the consumer to minimize the daily energy cost in scenarios characterized by Time of Use tariffs and Demand Side Management, by dynamically evaluating the best time to run of the appliances and the optimal evolution of the battery level of charge. A proper set of realistic simulations validates the proposed approach, showing the relevance of the energy storage unit in the domestic load shifting architecture.