The increase in power demand has compelled the power system utilities to use series capacitive compensation in long transmission lines. A problem called sub synchronous resonance (SSR) occurs in long lines because of series compensation. In this paper a flexible a.c. transmission system (FACTS) device is used along with a proposed controller to damp out the sub synchronous oscillations from the system. An IEEE second bench mark model is used for investigating the SSR problem, where a three phase short circuit fault is applied on the compensated transmission line for analysis. A Matlab/Simulink model is used to study the time domain analysis of the system. An improvement in damping is seen with the use of FACTS device i.e. unified power flow controller (UPFC) which is controlled by a fuzzy logic (FL) based proportional integral (PI) controller.