This research studies the stability of a grid-connected battery energy storage system (BESS) with a voltage source converter (VSC) and a filter. The VSC is a grid supporting controlled converter, which is enhanced with a primary and secondary frequency/voltage droop controllers, to enable grid connected and islanded mode operation without changing the controller structure. The linearized small signal model of the entire system is derived considering the inner current controller, the outer power loop, the primary and secondary frequency/voltage controllers, the LCL filter, and the phase-locked loop (PLL). The eigen values of the linearized system are obtained using state space modeling. To analyze the effects of certain parameters on the system stability, different case studies are performed.