In this paper we address the problem of optimal sizing of a given number of energy storage systems in a distribution network. These devices represent an effective solution for distribution system operators to prevent over- and undervoltages in distribution feeders. The sizing problem is first formulated in a two-stage stochastic framework in order to cope with uncertainty on future demand and distributed generation. By taking a scenario-based approach, this problem is then approximated in the form of a multi-scenario, multi-period optimal power flow. Since the size of the latter problem becomes rapidly prohibitive as the number of scenarios grows, a novel scenario reduction procedure is proposed. The procedure consists of solving a sequence of problems with scenario sets of increasing size. Tightness of the lower bound generated at each iteration can be checked very efficiently. Typically, a tight solution is obtained for sizes much smaller than that of the original scenario set. The algorithm is tested on the topology of a real Italian distribution network, using historical data of demand and generation to build the scenarios.