Turbine generator shaft torsional oscillations is an interdisciplinary problem since it involves mechanical and electrical engineering. Torsional oscillations occur in the mechanical systems for electrical reasons. There is a great incentive to mitigate the shaft torsional oscillations especially when unrestricted high speed reclosure (HSR) is utilized on the overhead transmission lines emanating from a power plant.Torsional oscillation damping compromises between the use of HSR and preserving shaft fatigue life of the involved turbine generator. In this paper a novel dynamic braking resistor model is utilized for the purpose of damping torsional oscillations. The novel model is the rectifier controlled braking resistor (RCBR). It is connected at the generator terminals and controlled by fuzzy logic controller to damp the turbine generator shaft torsional oscillations after unsuccessful reclosure. Comparative simulation study between the unsuccessful reclosure with and without RCBR proves the effectiveness of the scheme for damping torsional oscillations.