Abstract: Establishing the elastic connection between energy storage and wind turbine through virtual stiffness is the key to effectively suppress sub-synchronous oscillation induced by phase-locked loop. Based on the mechanical vibration mechanics, this paper first establishes the phase elastic coupling relationship between the phase locked of wind turbine and the virtual synchronous machine of energy storage, and defines the virtual phase-locked stiffness. Next, the virtual phase-locked stiffness is introduced to establish a two-degree- of-freedom motion model of the wind-storage elastic system, and the amplitude-frequency response characteristics of the fan phase are analyzed. Based on the fixed point theory, the virtual phase-locked stiffness and damping are optimized. Then, a virtual phase-locked stiffness control strategy is proposed, which is embedded in the energy storage virtual synchronous machine control system, and the control structure of the wind-storage elastic coupling control system is constructed with the virtual inertia and damping links. Finally, a wind- storage high-permeability grid-connected simulation system is built to verify that after adding virtual phase-locked stiffness, the sub-synchronous oscillation induced by the fan phase- locked loop can be effectively suppressed and the stability of the system can be significantly improved.