This paper presents a mixed-integer second-order cone programing (MISOCP) model to solve the optimal operation problem of radial distribution networks (DNs) with energy storage. The control variables are the active and reactive generated power of dispatchable distributed generators (DGs), the number of switchable capacitor bank units in operation, the tap position of the voltage regulators and on-load tap-changers, and the operation state of the energy storage devices. The objective is to minimize the total cost of energy purchased from the distribution substation and the dispatchable DGs. The steady-state operation of the DN is modeled using linear and second-order cone programing. The use of an MISOCP model guarantees convergence to optimality using existing optimization software. A mixed-integer linear programing (MILP) formulation for the original model is also presented in order to show the accuracy of the proposed MISOCP model. An 11-node test system and a 42-node real system were used to demonstrate the effectiveness of the proposed MISOCP and MILP models.