Establishing an elastic coupling relationship between the phases of energy storage and renewable energy units through virtual admittance is key to effectively suppressing sub-synchronous oscillations induced by the phase-locked loop (PLL). Drawing on the fixed-point vibration suppression theory from mechanical vibration dynamics, this paper first constructs a two-degree-of-freedom elastic coupling vibration model for grid-following renewable energy units with PLL and grid-forming energy storage. The impedance coupling relationships among renewable energy units, energy storage, and the grid-connected system are analyzed, along with the influence of the short-circuit ratio (SCR) on the sub-synchronous oscillation characteristics induced by the PLL. Next, virtual admittance is introduced to analyze the amplitude-frequency response characteristics of the PLL under the impedance coupling model, adjusting the SCR of the renewable-energy storage (RES) system to optimize the PLL oscillation behavior. Third, leveraging the fixed-point suppression theory, the coupling impedance between renewable energy and storage is optimized based on grid-forming energy storage, proposing a virtual admittance suppression strategy for the RES system. Finally, a grid-connected RES simulation system is built, demonstrating that the sub-synchronous oscillations induced by the PLL in renewable energy units are effectively suppressed after introducing virtual admittance, significantly enhancing the security and stability of the grid-connected system.