I. Introduction
Bidirectional public charging stations of plug-in electric-vehicles (PEVs), with particular reference to clusters of rapid charging stations in parking lots, can provide two types of services: grid-to-vehicle (G2V) and vehicle-to-grid (V2G) services. In a G2V scenario, PEVs arrive in the stations to be charged as fast as possible. In a V2G scenario PEVs are parked for a significant long time (e.g., several hours). In this second scenario, the objective for the car owner is to be charged at a cost as low as possible; whilst the owner of the charging station wants to achieve a reasonable profit for the services to the grid. Advantages and drawbacks of different PEVs participation approaches are reviewed in [1]. In [2] experimental tests of the functionalities of PEVs fast charging stations are presented.