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The variability of renewable energy sources (RESs) introduces more frequency fluctuations, and the reserve capacity of generation side needs to be sharply enlarged to maintain frequency stability, which inevitably increases the cost. In this paper, massive inverter air conditioners (IACs) as flexible regulation resources are aggregated to provide capacity support in frequency regulation. This paper establishes the state-space dynamic model and then presents a coordinated optimal control strategy by using model predictive control (MPC). However, the communication delay during the control signal transmission to IACs is one of the main obstacles that degrades the system performance in frequency regulation. To handle this issue, a predictive compensation method (PCM) based on MPC is applied to the control loop of IACs to compensate for the communication delay. Moreover, the robustness of the proposed MPC method with PCM against variations of system delay and parameters in the frequency response process is investigated in comparison to the proportional–integral (PI) controller. The simulation results are conducted to validate the superiority of the proposed method to the PI control method in virtue of the dynamic response and the performance indices, which demonstrates faster response, robustness, fewer fluctuations. • The state-space model of new power system incorporating the IACs is firstly proposed. • Based on this model, advanced control methods can be used for frequency control. • MPC is utilized to control aggregated IACs to obtain an optimal control strategy. • A predictive compensation method is applied to handle the impact of transmission delay. • The proposed method is robust over PI controller in the presence of delay. [ABSTRACT FROM AUTHOR]