In the mobility sector Electric Vehicles represent one of the main opportunities to ensure strong reduction of local pollution. However, their higher costs compared to gas-fuelled cars are still a barrier for their large diffusions. One possible solutions to increase EVs penetration is their use as storage within households equipped with Renewable Energy Sources enabling a flexible energy management, for instance by the Vehicle-to-Grid and/or Vehicle-to-Home scheme. The aim of this paper is to investigate possible management of the EV battery through an optimization approach capable to minimize the electricity supply costs for an Italian residential end-user with PV, considering battery constraints, such as driving habits. A statistical approach of driver behavior is integrated within the optimization approach to define some possible daily driving patterns. The optimization takes into consideration mobility needs, prices for selling and purchasing electricity and hourly electrical, heating and cooling load profiles of the household. On the basis of these constraints the optimizer identifies when PV overproduction can be either used to charge batteries or to partially cover the load demand of the household. Finally, economic and energy evaluations are performed under Monte Carlo simulations to highlight reliability of potential benefits for the household case study. (C) 2019 Elsevier Ltd. All rights reserved.