Grid-connected low voltage photovoltaic power plants cover most of the power capacity installed in Italy. They offer an important contribution to the power demand of the utilities connected but, due to the nature of the solar resource, the night-time consumption can be satisfied only withdrawing the energy by the national grid, at the price of the energy distributor. Thanks to the improvement of storage technologies, the installation of a system of battery looks like a promising solution by giving the possibility to increase auto-consumption dramatically. In this paper, a model-based approach to analyze and discuss the performance and the economic feasibility of grid-connected domestic photovoltaic power plants with a storage system is presented. Using as input to the model the historical series (2008–2017) of the main ambient variables, the proposed model, based on Stochastic Hybrid Fault Tree Automaton, allowed us to simulate and compare two alternative technical solutions characterized by different environmental conditions, in the north and in the south of Italy. The performances of these systems were compared and an economic analysis, addressing the convenience of the storage systems was carried out, considering the characteristic useful-life time, 20 years, of a photovoltaic power plant. To this end the Net Present Value and the payback time were evaluated, considering the main characteristics of the Italian market scenario.