This paper presents a method to enhance the stability of grid connected wind farm composed of fixed speed wind turbine generator system (WTGS) using a combination of small size series dynamic breaking resistor (SDBR) and static synchronous compensator (STATCOM). SDBR and STATCOM have the active and reactive power control abilities, respectively, and a combination of these units pave the way to stabilize well the fixed speed wind farm. In this study, centralized control scheme of using SDBR and STATCOM in together is focused, which can be easily integrated with wind farm. Different types of symmetrical and unsymmetrical faults are considered to evaluate the transient performance of the proposed control scheme, applicable to grid connected wind farm. The effect of multi-mass drive train of fixed speed WTGS in fault analysis along with its importance in determining the size of SDBR to augment the transient stability of wind farm is investigated. Extensive simulation analyses are performed to determine the approximate sizes of both SDBR and STATCOM units. Dynamic analysis is performed using real wind speed data. A salient feature of this work is that the effectiveness of the proposed system to minimize the blade-shaft torsional oscillation of fixed speed WTGS is also analyzed. Simulation results show that a combination of small size SDBR and STATCOM is an effective means to stabilize the wind farm composed of fixed speed WTGS.