In the context of the low-carbon energy transition, the importance of energy storage devices in integrated energy systems has become increasingly significant. This paper establishes a bi-level dynamic optimization model to investigate the impact of different energy storage devices on system design and operation. It optimizes the design and operation of integrated energy systems coupled with different energy storage devices using a genetic algorithm nested with a Gurobi solver. The results show that, compared to the integrated energy system without energy storage devices, the cold and thermal energy storage devices can reduce the operation cost, primary energy consumption, carbon dioxide emission, and total cost of the integrated energy system, of which the primary energy saving rate and carbon dioxide emission reduction rate can be up to 6.01% and 9.08%, respectively. The electrical energy storage device can further reduce the system's operation cost and total cost, which can be reduced by up to 9.03% and 2.98%, respectively. It is evident that coupled energy storage devices can significantly improve the operational performance of integrated energy systems.