Large-scale power grid entry of electric vehicles will have a significant impact on the power grid. Aiming at the charging and discharging problem of large-scale electric vehicles with dynamic response characteristics, two models of global optimal scheduling and local optimal scheduling are proposed. Based on the real-time price model of electric vehicle response, convex objective functions with battery loss cost, continuous differentiability and linear constraints are established respectively. The global optimal model needs the information of load and electric vehicle to solve the scheduling scheme with the minimum global total cost. Local optimal scheduling model is used to group electric vehicles to minimize the total cost of electric vehicles in sliding windows in a distributed way. The interior point method is used to solve the two models. The results show that the local optimal scheduling scheme can be extended to large-scale electric vehicle group and has elasticity to the dynamic arrival characteristics of electric vehicles. Compared with the complex solution information of the global optimal scheduling model, the local optimal scheduling scheme has higher practicability and similar solution results. This work is supported by National Natural Science Foundation of China (No. 51777027) and Science and Technology Project of the Headquarters of State Grid Corporation of China (No. YD7116013).