This work aims to analyze the feasibility of utilizing hybrid storage systems to enable the operation of high-power payloads during eclipse periods. The main objective of the study is to reach possible configurations with the same performance as traditional designs, but with reduced mass and/or volume, or to maintain the mass and volume while increasing the peak power capabilities. The proposed solution involves the use of supercapacitors and high-energy lithium-ion cells, with the former serving to meet peak loads and the latter supplying the mean power needs. Additionally, a simple architecture for the electrical power system is proposed, and the sizing equations for the supercapacitors and lithium-ion cells are derived from the governing power and energy balance equations. The results allow well-founded decision-making process on the suitability of the hybrid configuration based on the peak power demand and its duration, as well as the mean power demand during eclipse operations.