As the global energy consumption is rising dramatically, wind energy is a prominent one among the renewable energy sources. The penetration of wind energy into grid is increasing day by day. In order to carry huge amount of wind power during the grid integration of large scale wind farms, high transmission line capability is demanded. In order to improve the power carrying capability of the transmission line and to improve the stability of the system, series compensation is the best practical solution. Series compensation can result in Sub-Synchronous Resonance (SSR) oscillations in the electrical system which will lead to damages in the system such as shaft failure. In this paper, a novel idea of using the Real Time Recurrent Learning (RTRL) based adaptive neuro controller is proposed for damping SSR oscillations in grid connected windfarms. The controller is trained in real time without a reference model. The effectiveness of the proposed controller is tested under varying series compensation, wind speeds and grid impedance conditions and it has been proved that the proposed controller performs far better than any other linear controllers.