With the aim of increasing the self-consumption rate of grid-connected Photovoltaic (PV) home systems, two main options can be implemented: the inclusion of an energy storage system, in particular a battery bank, and the adoption of a Demand Side Management (DSM) strategy. However, both the reshaping of the load consumption curve with the displacement of deferrable loads and the optimal management of the battery bank require estimation of the daily PV generation profile. The assessment of the on-site energy production can be carried out based on weather forecast data. However, the latter are characterized by uncertainty, which may affect the achievable self-consumption rate. This work investigates the influence of weather forecast errors on the performance of home PV systems equipped with a battery bank and characterized by a certain share of deferrable loads. Two different weather forecast services are considered, referring to the annual meteorological conditions occurring in Rome, and energy consumption data for 150 different households are analysed. The self-consumption rate is maximized by solving a suitable optimization problem, while different combinations of relative battery capacity, PV-to-load ratio and share of deferrable loads are considered. Two different approaches—deterministic and stochastic—are adopted and compared with an ideal approach where the PV generation profile is perfectly forecasted. The results show that the adoption of the deterministic approach leads to a reduction in the achievable self-consumption rate in the range of 0.5–4.5% compared to the ideal approach. The adoption of a stochastic approach further reduces the deviations from the ideal case, especially in the case of consumption profiles with a high share of deferrable loads. Finally, a preliminary economic analysis proves that the use of a battery bank is not yet a cost-effective solution and a price reduction of the current battery prices is therefore required.