This paper proposes an energy storage-based method using adaptive quasi-resonant control to suppress the propagation of power oscillations in ultra-high voltage transmission lines induced by random excitation in new energy sources. First, an equivalent model of the power system, including the energy storage system (ESS), is established to analyze the mechanism of how the output power of the ESS affects the propagation of power oscillations to the external grid via the ultra-high voltage transmission line under random excitation. Secondly, an adaptive quasi-resonant controller is employed to track the generalized forced oscillation signal and adjust the active power command of the ESS. Based on the transfer function of power propagation in the system, the suppression mechanism of adaptive quasi-resonant control on the propagation of power oscillations is analyzed and compared with traditional resonant control. Simulation results validate the accuracy of the analysis, demonstrating that adaptive quasi-resonant control can effectively block the propagation of generalized forced oscillations when the control direction aligns with the propagation direction. Conversely, it cannot completely suppress the oscillations but significantly reduces their amplitude.