System kinetic inertia is declining due to the rapid replacement of synchronous generators (SG) by renewable power generations (RPG). To maintain grid inertia, this paper proposes a generic synthetic inertia (GSI) scheme for RPGs, enabling inertial response by a supercapacitor (SC) bank integrated with a voltage source inverter (VSI) DC link via a DC/DC converter. A GSI control loop is developed for the DC/DC converter controller to vary the SC voltage along with the grid frequency for power exchange following the SG swing equation. The GSI scheme realizes plug-and-play advantage without modifying the RPG original system. Small-signal stability analysis is carried out to optimize the GSI controller parameters. The performance of the GSI scheme is evaluated using a modified IEEE 39-bus test system.