The rapid growth of renewable energy, accompanied by intermittent and instability, has brought great challenges to energy storage technology. Rankine-based Carnot batteries are considered a promising solution to electricity storage in view of their high energy density at a low temperature. Determining the suitable Rankine-based Carnot battery configuration for its development and application requires accurate prediction and comprehensive comparison of the system performance under different conditions. In this paper, three Rankine-based Carnot Battery systems were constructed using a heat pump-organic Rankine cycle. Mathematical models of the aforementioned systems were built to assess and compare their performance from a thermodynamic standpoint. The results showed that the basic heat pump-organic Rankine cycle and reversible heat pump-organic Rankine cycle are better in energy and exergy aspects, where power-to-power-efficiency and exergy efficiency are higher by about 21.4% and 18.7% than that of reversible heat pump-organic Rankine cycle using a dual-function machine, respectively. Compared with basic heat pump-organic Rankine cycle and reversible heat pump-organic Rankine cycle, the levelized cost of storage of reversible heat pump-organic Rankine cycle using a dual-function machine is lower by about 12.3% and 5.4%, respectively. Taking the three criteria together, it seems that the reversible heat pump-organic Rankine cycle is better thermo-economically. The sensitivity analysis revealed that the heat source temperature has a greater impact on the reversible heat pump-organic Rankine cycle using a dual-function machine, and its absolute value of the sensitivity coefficient is 3.