Energy storage is a potential alternative to conventional network reinforcement of the low voltage (LV) distribution network to ensure the grid’s infrastructure remains within its operating constraints. This paper presents a study on the control of such storage devices, owned by distribution network operators. A deterministic model predictive control (MPC) controller and a stochastic receding horizon controller (SRHC) are presented, where the objective is to achieve the greatest peak reduction in demand, for a given storage device specification, taking into account the high level of uncertainty in the prediction of LV demand. The algorithms presented in this paper are compared to a standard set-point controller and bench marked against a control algorithm with a perfect forecast. A specific case study, using storage on the LV network, is presented, and the results of each algorithm are compared. A comprehensive analysis is then carried out simulating a large number of LV networks of varying numbers of households. The results show that the performance of each algorithm is dependent on the number of aggregated households. However, on a typical aggregation, the novel SRHC algorithm presented in this paper is shown to outperform each of the comparable storage control techniques.