The most energy-hungry parts of mobile networks are the base station sites, which consume around $60-80\%$ of their total energy. One of the approaches for relieving this energy pressure on the electricity grid infrastructure and reducing the Operational Expenditures (OPEX) is to power base stations with renewable energy. However, the design of a green mobile network requires the dimensioning of the energy harvesting and storage systems through the estimation of the network's energy demand. Therefore, this paper develops a diffusion-based modelling framework for solar-powered green off-grid base station sites. We apply this framework to evaluate the energy performance of homogeneous and hybrid energy storage systems supplied by harvested solar energy. We present the complete analysis, with numerical examples, to study the relationship between the design parameters and the energy performance metrics. The numerical computations demonstrate how the proposed framework can be applied to evaluate homogeneous and unconventional hybrid energy storage systems.