For the response requirements in the electromagnetic timescale of power systems, based on the voltage wave (VW) propagation characteristics, a local control method was proposed in this paper. By establishing a uniform continuum the VW propagation model, the dynamic propagation mechanism of the VW and the distinction between the VW and the electromechanical wave (EW) were revealed. The results demonstrate that the VW model exhibits rapid fault disturbance identification capability in power systems with wind farms. Therefore, a power compensation control strategy was proposed in this paper, enabling the DFIGs to detect system faults more rapidly and adjust active power output to mitigate rotor speed oscillations of the synchronous generator. RTDS-based simulation verifications show that the proposed method reduces the rotor speed oscillation amplitude of synchronous generators by 28% during faults. It effectively reduced the rotor speed variations of synchronous generators during fault conditions and reduces mechanical wear on the rotor caused by speed fluctuations during faults inception and recovery.