CHS (cascaded heat storage) plays a significant role in the improvement of thermal efficiency and the utilization of multi-graded thermal energies. This work presents thermodynamic modeling of the CHS for direct thermal utilization purpose with the lumped parameter method employed for the PCMs. The optimization of temperatures of HTF (heat transfer fluid) and multistage PCMs (phase change materials) is performed based on the entransy theory. Analytical solutions for optimal temperatures of HTF and PCMs are obtained with heat optimization for fixed entransy dissipation and entransy optimization for fixed heat. The existence conditions of the two optimizations are put forward with corresponding critical stage numbers proposed. The results show that CHS can extend applicable temperature scope for multi-graded thermal energies. Heat transfer enhancement is essential for multistage heat storage. The uniform distribution of parameter C in each stage is beneficial for thermal efficiency improvement. The present thermodynamic optimization and solutions can guide the selection of PCMs, and establish a benchmark for similar research in CHS. (C) 2015 Elsevier Ltd. All rights reserved.