With the increasing number of electric vehicles (EVs), their uncoordinated charging poses a great challenge to the safe operation of the power grid. In addition, traditional individual-EV scheduling models may be difficult to solve due to the increasing number of constraints. Therefore, this paper proposes a cluster-based EV scheduling model. Firstly, electric vehicle clusters (EVCs) are formed based on the charging and discharging preferences of EV users and the expected time for EVs to leave. Secondly, the EVC energy and power boundary aggregation method based on the Minkowski addition algorithm is proposed. Finally, for the sake of reducing user charging cost and distribution network energy loss, and smoothing the daily load curve, an EVC scheduling model for EV participation in grid auxiliary services is proposed. The optimization model includes the reactive-power compensation of EV charging piles. The simulation results show that the proposed EVC scheduling model can greatly reduce the solution time compared to traditional individual-EV scheduling model. The model has high potential to be applied to large-scale EV scheduling. The reactive-power compensation provided by EV charging piles improves the voltage quality of the grid and enables more EVs to be connected to the grid.