Energy storage systems are pivotal in efficiently integrating renewables into the grid for achieving a net-zero energy system. Hydrogen is increasingly recognized as a viable alternative to electric batteries for long-term and high-capacity storage. This paper presents the dynamic performance of an integrated Power-to-Power system, employing a dual approach. This involves the implementation of a hybrid storage solution that utilizes both physisorption and chemisorption, coupled with the modeling of the thermal management system. This study builds upon prior research focused on hydrogen storage at room temperature and medium-high pressure. The extension involves expanding the hydrogen storage system model to operate at lower temperatures and pressures, aiming to increase the hydrogen storage capacity and operating conditions.