Large-scale renewable energy consumption and low carbon development of power systems have a higher need to reduce carbon emissions in the peak frequency modulation of thermal power units. To improve the economical efficiency of the system and the low carbon of the thermal motor peak adjustment, this paper proposes a hierarchical optimal scheduling method of the thermal storage considering the thermal power unit's heat storage transformation and optimal solar energy abandonment. Considering the reverse peak adjustment characteristics of wind, an optimal energy-discarding constraint model is established, and an upper model is constructed to minimize the net load variance of the power grid. The net load curve is "peak-clipping". To expand the peak-shaving depth of thermal power units, a carbon transaction cost model is established considering the transformation of heat storage units. From this, the lower layer model is established with the goal of minimizing the total system cost and carbon transaction cost. A collaborative optimization of system economy and low carbon is realized while the net load curve is "peak-cutting and valley filling" twice. The rationality and validity of the proposed model are verified by an example. This work is supported by the National Natural Science Foundation of China (No. 51765042, No. 61773051, and No. 61963026).