A high share of renewables in the energy sector introduces volatility and forecast uncertainty on the generation side of the electricity system. These uncertainties are mitigated using storage systems. An example of such storage systems are residential photovoltaic battery systems that operate in an increasingly complex economic and regulatory environment. This thesis investigates model predictive control of such systems. Therein, external and historic data is used to model forecast uncertainty of household load as well as photovoltaic generation. This leads to stochastic optimal control problems which are solved using stochastic dynamic programming. With this approach, the nonlinear and discrete dynamics of the controlled system can be modeled without significant increase in computational requirements. The control scheme was applied to two cases in simulation and field test. In both cases the stochastic modelling yielded better performance than a comparable state of the art control scheme.