This paper presents real-time control strategies for peak shaving and voltage control provided by a Battery Energy Storage System in a low voltage grid. Two performance indices, one for peak shaving and one for voltage control, are proposed to quantify the results. The strategies are compared with a benchmark which is calculated as an ex post optimization that solves the control problem together with the sizing problem. First, a rule-based strategy for peak shaving is presented which only injects active power. Afterwards, the strategy is extended with voltage control through reactive power injection. In the latter case, an optimization problem is solved at each time step to decide at which rate active and reactive power should be injected. (4 pages)