## 1 Introduction  
The diffusion of electric vehicles (EVs) is likely to experience a sharp increase, as predicted by several studies and scenario evaluations of transport and energy stakeholders. In particular, power system operators are guided by several policies aimed at reducing the environmental impact of transport [1]. A remarkable support to EV diffusion is given by technological improvements. The newest battery technologies ensure pocket-size units and the ability to provide a longer duration of travel and for wider distances to be covered. For charging stations, the interchangeability has been improved thanks to connector standardization [2], while the realization of more powerful plug systems helps reduce waiting times. Although EV intelligence controls the charging process to preserve battery life, the electric grid operator is rather interested in controlling the EV charge in order to reduce the counter-effects caused by massive requests at limited intervals and concentrated in specific locations. Thus, the concept of smart charging has gained significant ground [3, 4], and the communication ability between EVs and the power system has remarkably improved. In this sense, for EV smart charge to have effects on the power system, the figure of the EV aggregator is introduced [5]. In order to improve the positive interactions with the power system, the integration of EV charging stations with distributed generation (DG) facilities based on renewables is a field of interest for industry and research [6]. In fact, the combined operation with DG can ensure renewable energy supply to EVs, reducing grid power purchases. Moreover, the addition of energy storage devices can improve the exploitation of local sources by EVs, even in the absence of temporal synchronization [7]. Thiscoordinated control of different sources is one of the most promising uses for the development of smart microgrids for EV needs. Furthermore, since photovoltaic systems, batteries for EVs, and local storage are based on direct current (DC), they can easily constitute DC microgrids [8; 9]. DC microgrids represent an interesting development of the power industry, since they ensure high controllability and cause less problems with respect to alternating-current power system integration (e.g., inertia and frequency, reactive power), although the development of DC systems with increasing sizes and voltage levels is still challenging. Moreover, EV connection to DC microgrids opens the field to efficient vehicle-to-grid (V2G) applications, enabling EV bidirectional energy exchanges analogous to storage devices when parked. One of the functions of a DC microgrid controller is the operational programming, which is called upon to elaborate, with suitable advance notice (generally on daily basis), the optimal power setpoints of all controllable devices, according to inputs (renewable source and load forecast, EV usage for mobility, economic parameters) and taking into account device technical limitations. After this stage, the real time operation control is aimed at verifying the correct DC microgrid function that is able to sustain possible the variation of inputs or other unplanned events (e.g., unintentional islanding) [10; 11]. In the framework of day-ahead operation programming of microgrids, including EVs, different approaches are found in the literature. In some works, EV charging duration and intensity are considered as known inputs in programming procedures. In particular, in one previous study [12] a stochastic generation of plug-in hybrid EV usage is exploited in an optimal management model solved with the modified symbiotic organism search (MSOS) algorithm and compared with the genetic algorithm (GA) on two test systems. Another study [13] includes charging station features in the determination of EV charging scenarios in mixed-integer linear programming (MILP) microgrid optimization.