This paper addresses the problem of optimal placement and sizing of distributed energy storage devices in a low voltage network. The objective is to find the configuration which minimizes the total cost of storage devices, which depends both on the number of storage devices and on their size. The optimal power flow framework is adopted for formulating the overall optimization problem. Since the exact problem turns out to be intractable in realistic applications, we adopt a semidefinite programming relaxation for the power flow constraints and different heuristics for circumventing the combinatorial problem of selecting the most appropriate buses where to allocate the storage devices. The overall procedure is tested on a real application involving a portion of an Italian low voltage network.