In this paper an alysis of the stability enhancement and improved damping of power swings in a multi-machine power system by means of thyristor-controlled braking resistor installed in the network has been presented. The control law has been derived using direct Lyapunov method and non-linear multi-machine system model. It is optimal in the sense that it causes the quickest dissipation of the power system energy released by a disturbance. Simple implementation of this control using only locally available signal has been also demonstrated. A computer simulation of a multi-machine power system model has verified the effectiveness of the proposed algorithm-In this paper an analysis of the stability enhancement and improved damping of power swings in a multi-machine power system by means of thyristor-controlled braking resistor installed in the network has been presented. The control law has been derived using direct Lyapunov method and non-linear multi-machine system model. It is optimal in the sense that it causes the quickest dissipation of the power system energy released by a disturbance. Simple implementation of this control using only locally available signal has been also demonstrated. A computer simulation of a multi-machine power system model has verified the effectiveness of the proposed algorithm