An increase in distributed small-scale generation and storage in residential prosumer households requires an understanding of how the household-controlled operation of these distributed technologies differ from a system-optimal utilization. This paper aims at investigating how residential photovoltaic (PV)-battery systems are operated, given different assumed incentives, and whether or not a prosumer induced operational pattern differs from what is desirable from a total electricity system point of view. The work combines a household optimization model that minimizes the annual household electricity bill for two price zones in southern Sweden with a dispatch model for the northern European electricity supply system. The results show significant differences in the charging and discharging patterns of residential batteries. A household annual electricity cost minimization gives many hours in which only a fraction of the battery capacity is used for charging and discharging, mainly driven by incentives to maximize self-consumption of PV-generated electricity. In contrast, in a total electricity system operational cost minimization larger fractions of the available battery capacity are utilized within single hours. In the total system optimization case, the batteries are charged and discharged less frequently and the energy turnover in the batteries is only half that of the household optimization case. For all the cases studied, the hourly electricity price provides only a limited incentive for households to operate their batteries in a system-optimal manner.