Considering the effects of climate change around the world, the transition from fossil fuels to renewable energy sources is currently demanded. Development is therefore required in a number of areas like storage, transmission, and the conversion of power. This paper presents a comprehensive literature review and thermodynamic modeling of hydrogen energy storage system designed for renewable energy integration. The designed system combines two renewable energy sources—hydropower and solar photovoltaics—with advanced energy storage technologies, in an effort to address the intermittent nature of renewable power generation. A proton-exchange membrane (PEM) electrolyzer is included in the model for the production of high pure efficient hydrogen from the renewable energy sources and emits only oxygen as a byproduct without any carbon emissions. Furthermore, the present study discussed the implementation of magnesium–nickel alloy (Mg2Ni) for solid-state hydrogen storage and a PCM named RT44HC; it improves the metal hydride's performance by being incorporated with it. The stored hydrogen is then utilized by a proton-exchange membrane (PEM) fuel cell to generate electricity when required. The literature review also explores the thermodynamic modeling of individual components involved in hybrid energy storage systems. The energy efficiency comes out to be 52.71%, and the exergy efficiency turns out to be 53.34%. The sustainability index comes out to be 2.14.