In (1), ER(t) is the energy still required to complete the charging process at the time instant t, TR(t) is the time which is still available before the user leaves the system, PAVMAX is the maximum available power from the grid, KUMAX and KFMAX are the maximum values admissible for KU and KF, respectively, and ˛1,˛2 and ˛3 are weighting coefficients. The priority function (1) is formulated to take into account both the user satisfaction and the
utility profit by means of GS and GP, respectively. In particular,˛1 = 0.5 and ˛2 = ˛3 = 0.25 are fixed in order to balance the requirements in terms of degree of user satisfaction and utility profit,and to have G = 1 when the user is characterized by the maximum tariff and penalty (i.e. KU = KUMAX and KF = KFMAX), and the power required to complete the charging process is equal to the maximum available power (i.e. ER(t)/TR(t) = PAVMAX). Obviously, although the user priority function exceeds 1 when ER(t)/TR(t) > PAVMAX, the maximum power which can be allocated to the user is limited to PAVMAX