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Rooftop photovoltaics in Germany generate around 15 TWh of electricity per year, and there is sufficient roof area to increase this many times over. Germany’s transition to renewable electricity requires large increases in rooftop and field-based photovoltaics. However, for household systems, each kWh fed into the grid pays only €0.0653, while households gain a marginal benefit of €0.334 for each kWh of their own electricity they consume. This deters households from installing large rooftop systems, where a large proportion of self-generated electricity is fed into the grid. This study uses cost-benefit analyses based on quarter-hourly electricity data, to estimate economically optimum sized photovoltaic systems, for a typical detached house. It finds that, for a range of battery sizes, optimal systems generate about the same amount as the household consumes, but use only about half of available roof space. Heat …