To achieve flexible and low-carbon operation of the new power system under the "dual-carbon" goal, an error based active disturbance rejection control (EADRC) strategy was preposed for frequency regulation that simultaneously addresses carbon emission and flexibility. Firstly, to address the requirements for flexible and low-carbon operation, a frequency regulation control framework for the wind-thermal-storage combined system based on the EADRC was established, and the disturbance estimation and compensation characteristics of the EADRC were used to reasonably coordinate the active outputs of the three frequency regulation units, namely, wind, thermal, and storage. Secondly, an enhanced dung-beetle optimization algorithm (EDBO) was developed to achieve accurate optimization of the controller parameters, and a multi-objective optimization function incorporating the frequency regulation performance, carbon emission and state of charge was designed to steer the operation of the combined wind-thermal-storage system to a balance point of flexibility, low carbon and stability. The proposed control scheme effectively integrates the features of fast frequency regulation, accurate disturbance suppression and fast parameter tuning. Finally, experiments were conducted for different types of load disturbance conditions. The simulation results show that the proposed strategy can significantly improve the frequency regulation performance of the combined wind-thermal-storage system under both single load disturbances and continuous unbalanced load disturbances, and realize the flexible and low-carbon operation of the new power system.