In recent years, the number of air conditioner users has increased rapidly, becoming a major component of the peak load in a power system. As a typically flexible load, air conditioners can participate in demand response and provide efficient adjustable capacity to the grid because of their thermal inertia. In contrast to the studies on fixed-frequency air conditioners, this paper constructs a physical model of inverter air conditioners based on their load characteristics and evaluates their flexibility potential from two perspectives, including total power after control and maximum control time. From the trading volume of inverter air conditioner aggregators in the day-ahead market for demand response, an optimal load control strategy for inverter air conditioners based on bi-level group rotation control is proposed. The strategy is aimed at minimizing the deviation between the power reduction of the inverter air conditioner cluster and the trading volume, while minimizing the change of user comfort. Simulation results show that the strategy proposed in this paper can not only extend the maximum control time through rotation control, but also is user-friendly, such that it is of guiding significance for the inverter air conditioner cluster participating in the demand response of the power grid. This work is supported by the High-tech R & D Program of China (863 Program) (No. 2015AA050401) and the National Natural Science Foundation of China (No. 51577029).