An increasing number of distribution generations (DGs) are being integrated in distribution network (DN), which may cause voltage deviation (VD) and network loss. By considering the distributed energy storage system (DESS) as an effective solution, this paper proposes an optimal scheduling model, the objectives include main network electricity purchasing cost, network loss cost, and voltage deviation penalty combined with the power four-quadrant output control strategy of the battery energy storage system (BESS). Besides, interval robust optimization (RO) model is applied to deal with the uncertainties of wind power output and load demand. The second-order cone relaxation (SOC) technique is used to convexify the power flow equations in the optimization model. Consequently, the original optimal scheduling model is converted to a second-order cone programming (SOCP) problem. It solves the problem which is difficult to consider the voltage in DN. Meanwhile, Big-M method is used to deal with the nonlinear terms with absolute value in the objective function. Therefore, the entire DES optimal scheduling model of the DN is transformed into a mixed integer second-order cone programming problem (MISOCP); and a mature CPLEX solver is invoked to solve the optimal scheduling model. Finally, comparative studies based on IEEE 33 are performed to validate the effectiveness of the proposed methods.