Due to the popularization of distributed energy resources (DERs), the aggregated prosumer effect excels a general energy storage system characteristic. Virtual energy storage system (VESS) concept is proposed hereby that mimics an actual storage unit and incorporates the same charging (consumer) and discharging (producer) modes. It is possible to provide ancillary services via VESS by exploiting the flexibility and thus much research has been proposed on the optimization of the VESS scheduling. In general, the charging and discharging efficiencies of VESS are different and there can be only one status at a time slot. To achieve the optimal schedule while considering the constraints above, binary terms should be introduced into the optimization problem which end up with a nonconvex problem. In this paper, a complimentary mathematical proof is given for the convexification of this mixed integer linear programming (MILP) problem so that the linear programming (LP) method can be applied instead if the objective function is linear. The proposed proof is validated through a case study and the simulation results show the effectiveness of the proposed method.