A supplementary excitation damping controller（SEDC） is designed on the IEEE SSR first benchmark model and the IEEE ST1A type excitation system. By using test signal method， the sub-synchronous electrical damping characteristics of a generator and the impacts of the designed SEDC on the generator's electrical damping are analyzed. The results show that when the generator speed deviation is used to modulate the outputs of the excitation system only by phase shifting and amplifying， enough positive damping can be achieved to suppress sub-synchronous resonances. Furthermore， when bandpass filters tuned to each torsional frequency are added in the SEDC， the electrical damping at all possible torsional frequencies are increased.