The energy transition towards renewables must be accelerated to achieve climate targets. To do so, renewable power plants, such as wind power plants (WPPs) must replace conventional power plants (CPPs). Transmission System Operators require this replacement to be made without weakening the frequency response of power systems, so it must be ensured that WPPs match the response of CPPs to grid frequency variations. CPPs consist of grid-tied synchronous generators that inherently react to frequency variations by modifying their stored kinetic energy and their output power, thereby contributing to grid stability. Such response is known as inertial response. By contrast, wind turbines (WTs) are mostly based on either doubly-fed induction generators (DFIG) or permanent magnet synchronous generators (PMSG). Their power electronics interface decouples the electromechanical behavior of the generator from the power grid, leading to a negligible inertial response. Therefore, in order to replace CPPs with WPPs, WTs must be able to react to frequency variations by changing their output power, i.e., emulating an inertial response. Currently implemented inertia emulation strategies in WTs rely on pitch control and stored kinetic energy variation. This paper proposes an alternative strategy, using the energy stored in a supercapacitor directly connected to the back-to-back converter DC link to emulate inertia. Its performance is validated by means of simulation for both DFIG and PMSG. Compared to state-of-the-art techniques, it allows a more accurate emulation of grid-tied synchronous generators, favoring the replacement of these generators by WTs. This work was supported in part by Siemens Gamesa Renewable Energy, in part by the Spanish State Research Agency, AEI/10.13039/501100011033 under Grants PID2019- 111262RB-I00 and PID2019-110956RB-I00, and in part by the Government of Navarre under Grant 0011-1411-2022-000049 through EnVeNA Project.