There is a growing awareness of the need to reduce carbon emissions from the operation of mobile networks. The massive deployment of ultra-dense 5G and IoT networks will significantly increase energy demand and put the electricity grid under stress while also driving up operational costs. In this paper, we model the energy performance of an off-grid sustainable green cellular base station site which consists of a solar power system, Battery Energy Storage (BESS) and Hydrogen Energy Storage (HESS) system, and various types of macrocells, microcells, picocells, or femtocells, with broadband optical or microwave transmission systems, and other electrical and electronic systems (air conditioner, power converters, and controllers. We propose diffusion-based models of the charging and discharging processes of the energy storage systems, and obtain the probability of charging them to their full capacities during the day and completely discharging them at the end of each day. We also investigate the impact of design parameters such as the mean charging rate and the mean discharging rate on the probability densities of charging BESS and HESS to their full capacities during the day and of completely discharging them before the end of each night period.