With the advancement of energy storage technologies, installing an energy storage system (ESS) in a distribution network has become a new solution to accommodate more and more distributed renewable generations. In this study, the optimal allocation of distributed ESSs is studied to maximise the benefit of the distribution system operator. The ESS allocation problem is divided into two stages: the mixed integer investment problem as the first stage and the optimal operation problems considering daily charging/discharging schedule of ESSs as the second stage. To tackle the uncertainties of distributed generation output and base load, typical days (scenarios) are firstly obtained by the clustering method and thereafter the operation problems include a number of scenarios, each with the corresponding possibility. Then each second stage problem is relaxed to a second-order cone programming model. To efficiently solve the whole problem considering multiple scenarios, the generalised Benders decomposition (GBD) algorithm is adopted, which is further accelerated by relaxing and rebinding integer constraints. Numerical experiments are conducted on a 17-bus test system to demonstrate the effectiveness of the proposed method. Additionally, comparisons between different algorithms are performed to verify the merits of the proposed acceleration method with respect to the original GBD and the branch-and-bound algorithm.