Amidst China's pursuit of carbon peaking and neutrality targets, there is a pressing need to establish a novel power system that primarily relies on renewable energy sources (RES). To tackle the challenges this transition poses to the existing power grid, it is imperative to fortify the power system's frequency modulation capabilities, which in turn calls for the exploration of diverse energy storage solutions. This research introduces, simulates, and evaluates an innovative charge-discharge control methodology designed to augment the frequency modulation capabilities of the thermal power unit (TPU) through the integration of the compressed air energy storage (CAES) system. Firstly, by considering the dynamic characteristics and operational mechanism, fundamental transfer function models for TPU and the CAES system are established; based these models, the frequency modulation model of a two-area power grid incorporating TPU and CAES is presented. Subsequently, a power adaptive allocation strategy is formulated with nonlinear signal decomposition techniques, enabling adaptive power distribution between TPUs and CAES. Furthermore, a control strategy utilizing model predictive control (MPC) is proposed, taking into account the state of charge (SOC) of CAES, to refine the energy charge and discharge process. The effectiveness is tested under two scenarios: step disturbance and continuous disturbance. Compared to TPU-only frequency modulation, the presented strategy achieves remarkable outcomes: a 21.9 % reduction in maximum frequency deviation following step disturbances, a 52.2 % decrease in steady-state frequency deviation, and a 37.5 % mitigation of TPU output power fluctuations under continuous disturbances. The results underscore the significant potential of the proposed strategy in alleviating the frequency modulation burden on TPUs, thereby contributing to their secure and stable operation within the evolving power system landscape.