Integrating photovoltaic (PV) produced electricity into the electric power system is proving to be a growing challenge due to its fluctuating nature. The combination of more rigid regulation for feed-in of PV production and steadily rising electricity prices means that battery systems are becoming more attractive to private households as a way of upping their self-consumption. At the same time, batteries make the household's electricity purchasing strategy more complex. For these reasons, control concepts are required for PV + battery systems that ensure grid-friendly operation as well as considering the household's primary objectives. This paper presents a forecast-based modelling approach for the operation of a battery in combination with a grid-connected PV system. PV production and electricity demand are forecasted on an hourly time-resolution using artificial neural networks (ANN). The battery charging and discharging is optimized to maximize self-consumption, and additionally a variable feed-in tariff is considered to incentivize a grid-friendly operation. The developed model was applied for a household with 3300 kWh electricity consumption equipped with a 5 kWp PV system and a 5 kWh battery. For this case, we show that the model enables a grid-friendly operation of the battery as well as an intensified usage. However, the inevitable forecasting errors lead" to overall lower economic benefits for the consumer in comparison with a simple strategy that only maximizes self-consumption. Considering the inaccuracy of forecasting, we conclude that if a grid-friendly integration of PV + battery systems is to be promoted in the future, households should be provided with better forecasting data or offered other incentives to compensate their lost benefits.