Carnot batteries are critical technologies for increasing the penetration of renewable energy sources because they enable suitable energy storage for long-term periods. The achievement of high efficiencies is an important point that determines the sustainability of the Carnot batteries. In this direction, a novel Rankine Carnot battery with heat upgrading capability based on salt hydrate thermochemical energy storage is proposed herein. The steady thermodynamic and economic models for the basic Carnot battery and recuperators introduced Carnot battery, both with a storage capacity of 10 MW/5h, have been established. The thermo-economic performance of the Carnot battery systems and the effects of several key parameters are quantitatively assessed. Results manifest that the Carnot battery with recuperators behaves better in comprehensive performance thanks to the heat recovery by recuperators. The power-to-power efficiency, exergy efficiency, and levelized cost of storage for the basic Carnot battery and recuperators introduced Carnot battery systems are 48.48 %, 38.48 %, 0.2502 $/kWh and 64.1 %, 48.94 %, 0.1922 $/kWh, respectively. The maximum exergy destruction occurs in the heat exchanger for the Carnot battery systems and the throttle's exergy destruction is diminished by 70 % in the recuperators introduced Carnot battery. The compressor and turbine account for the largest cost ratios, i.e., 26.5 % and 24.8 % in the basic Carnot battery and 28.2 % and 27.2 % in the recuperators introduced Carnot battery; while the cost proportion of throttle in both systems is nearly ignorable (0.3 %). Elevating heat source temperature and the reactant's hydration temperature and descending ambient temperature contribute to the improvement of power-to-power efficiency and levelized cost of storage. The isentropic efficiencies of compressor and turbine, especially the latter, have a great impact on the thermo-economic performances. As the daily charging time expands to 7 h, the levelized cost of storage of the recuperators introduced Carnot battery reduces to 0.1434 $/kWh. Replacing the reactive salt of potassium carbonate sesquihydrate (K2CO3·1.5H2O) with magnesium sulfate tetrahydrate (MgSO4·4H2O) brings a lower levelized cost of storage of 0.18 $/kWh. The findings of this study demonstrate great potential for the exploitation of this thermochemical energy storage-based Carnot battery for large-scale electricity storage.