Wind energy is attracting more attention from researchers and even utilities due to its benefits as a clean and abundant source of energy. In this paper a comprehensive and intensive study of a wind farm connected to the grid has been proposed. The aim of this paper is to investigate the system stability of a wind farm connected to medium voltage grid in different operating conditions and to investigate the behavior of the system when using a Static Var Compensator (SVC) and Static Synchronous Compensator (STATCOM). A wind farm of 12 MW consisting of four wind turbines connected to medium voltage grid has been proposed. Wind turbines, transmission systems, transformers and grid models as well as SVC and STATCOM models are all developed in SimPowerSystems library in MATLAB / SIMULINK. It was observed from the simulation results that STATCOM and SVC support the system voltage and reactive power in case of healthy conditions. However, it was noticed that they considerably improve the system stability during and especially after severe disturbances.