By combining the advantages of different energy storage technologies, the hybrid energy storage system (HESS) can satisfy the multiple requirements of prosumer systems. However, the required capacity of the HESS is larger than that of the single-battery energy storage system (ESS). This paper investigates the energy exchange within the HESS caused by the phase shift of the low-pass filter controller and its relevant impact on the HESS. The results show that unnecessary energy exchange results in an oversized capacity and increased energy loss. In addition, the increase in the time constant of the low-pass filter controller leads to a larger phase shift, further contributing to the increases in the total capacity and energy loss. Furthermore, this paper compares the single-battery ESS, the battery-supercapacitor HESS, and the battery-flywheel HESS implemented in a household-prosumer system along with a renewable energy source (RES). The comparison of the ESS combinations demonstrates the differences between their power flows, the required capacities of their individual energy storage devices (ESDs), their energy losses, their battery lifetimes, and their project costs. The results indicate that techno-economic analysis should be performed carefully to select the appropriate ESS solution for specific household-prosumer systems.