For future energy supply systems the effects and benefits of battery storage systems in households with photovoltaic (PV) generators and the effects on distribution and transmission grids need to be identified and analyzed. The development of grid relieving management strategies for the storage system in due consideration of self-consumption is a necessary step forward in order to analyze the potential of private home battery storage systems to reduce stress on the power supply system. A MATLAB-based model of a lithium-ion storage system has been developed. The model is applicable for a wide range of PV generator sizes, different battery storage systems and diverse management strategies. In order to identify the potential of grid relieving forecast strategies, without discharging the storage into the grid, a management strategy based on persistence forecasts of solar radiation and household load demand has been implemented and analyzed. To minimize forecast uncertainties a proportional plus integral controller has been developed. The persistence forecast management strategy is applicable in real-life PV-battery-systems and due to the simple forecast it is easy to equip existing systems with such a management system with only low effort. As a result it will be shown that a storage system management based on forecasts has a significantly higher potential to relieve the grid than a system that only maximizes self-consumption as it is usually used nowadays. Besides, such a management strategy is able to unload the grid more than a static power reduction to 70% of the nominal power rating according to the current German Renewable Energy Sources Act (EEG). At the same time, the self-consumption can be retained at nearly the same level as by using a management strategy to purely maximize the self-consumption. Even less energy is wasted then with the feed-in limitation.