Air conditioners (ACs) have been widely considered as one of the most important reserve resources for power systems. However, few attentions have been given to inverter ACs (IACs), which account for a larger share nowadays and show more suitable characteristics than regular ACs to provide reserve. Moreover, interconnected power systems are becoming increasingly large and complex, which puts forward higher request on the reserve resources for the system's reliability and safety. Dealing with the above-mentioned challenges, this paper proposes a novel frequency regulation model of multi-area power systems considering large-scale IACs providing regulation service. In order to decrease the impact on customers' comfort, the action number constraint (ANC) and action time constraint (ATC) of IACs can be set by each customer. On this basis, the scheduling model of IACs considering ANC and ATC is proposed in multiple time scales, in which the total regulation capacity of IACs can be allocated among days in the month and areas in the multi-area power systems. Besides, the control parameters of IACs can also be optimized by the proposed optimization model for minimizing the area control error of the power system. The effectiveness of the model and method are verified in the numerical studies.