Methods and systems are provided to damp oscillations in a synchronous alternating current (AC) grid. Current may be received from the synchronous AC grid through a phase of an n-phase supply line. The current received from the synchronous AC grid is supplied to a phase of the synchronous motor. A sub-harmonic oscillation may be detected in the current received from the synchronous AC grid. The sub-harmonic oscillation may be damped by: shunting a portion of the current away from the phase of the synchronous motor during a first time period in an upper-half of the sub-harmonic oscillation, and/or supplying compensation current from a partial power converter to the phase of the synchronous motor during a second time period in a lower-half of the sub-harmonic oscillation.