A dynamic mechanically-switched damping (DMSD) system is described which utilizes one or more mechanical switches and appropriate controls to switch series or shunt reactive impedances (14) in order to provide power oscillation damping in power systems. The DMSD system provides a controller (16) which can be configured based on the number of mechanical switches in the DMSD system, the type of reactive impedances interfaced to the power system by each switch and the magnitude of each of the reactive impedance. The DMSD system monitors parameters of the power system (17, 18) and the controller generates a modulation signal based on the monitored parameters. The modulation signal is processed to identify a reactive impedance of the available DMSD system reactive impedances required to damp power oscillations. Appropriate switches (32) are selected for supplying the required reactive impedance. A switching control signal is generated and output to each of the selected switches to synchronously open or close the switch at a predetermined instant.