This paper presents a new model of voltage source converter (VSC) based battery energy storage systems (BESSs) that interface with power grids. A VSC-based BESS is made up of a series connection of a VSC, its connecting transformer, and a BF-SS. The VSC allows a BF-SS to generate both active and reactive powers in all four quadrants. The proposed model captures the coupling between active power, reactive power, and the voltage of a BESS. In addition, the proposed model explicitly describes the relationship between the control configuration of pulsewidth modulation (PWM) VSC and the power output of the BESS. Therefore, the proposed model possesses unparalleled control capabilities in the operational parameters of both the ac and dc sides of the converter. By incorporating such a model into the active-reactive optimal power flow (A-R-OPF) formulation, we can not only optimize the active and reactive power output of the BESS in power systems, but also understand how the optimal powers are generated by setting the operational parameters of both the BESS and PWM-VSC. To solve the A-R-OPF problem with the proposed model, we propose a sequence of strong relaxations to transform the problem into a mixed-integer second-order cone programming problem. Such a formulation is amendable for efficient solutions using off-the-shelf solvers. Case studies on the IEEE benchmark systems show that more than 17.73% of power losses in transmission lines and more than 0.961% of interface losses can be reduced by using the proposed model in comparison to the traditional BESS model.