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Electric vehicle (EV) charging and discharging management is an essential component of the smart grids, especially in microgrids due to the high dependence on the local energy sources. In order to provide EV users with freedom to charge and travel, we propose a dynamic scheduling algorithm that does not require EV users to inform their charging time to the control center. The proposed algorithm serves the charging requests from EVs in a best-effort manner while minimizing the energy cost of EV users and guaranteeing the grid related constraint of microgrid. Specifically, we formulate a stochastic optimization problem to minimize the energy cost of charging and discharging for each EV with respect to the same constraints of the proposed algorithm. The simulation results show that the proposed algorithm achieves energy cost better or close to that of the conventional methods without requiring the a-priori …