The increasing wind power penetration in electrical power systems results in a reduction of operative conventional power plants. These plants include synchronous generators directly connected to the grid. Facing a change in grid frequency, these generators inherently respond by varying their stored kinetic energy and their output power, which contributes to grid stability. Such a response is known as inertial response. Wind turbines (WTs) are mostly based on Doubly-Fed Induction Generator (DFIG) or Permanent Magnet Synchronous Generator (PMSG) machines. Their power electronics interface decouples the electromechanical behaviour of the generator from the power grid, making their inertial response null or insignificant. Therefore, in order not to weaken the frequency response of the power system, WTs must be able to react to frequency variations by changing their output power, i.e., emulating an inertial response. Common techniques for inertia emulation in WTs rely on pitch control and stored kinetic energy variation. This contribution proposes a strategy (applicable for both DFIG and PMSG) which uses the energy stored in a supercapacitor connected to the back-to-back converter DC link to emulate the inertial response. Its performance is compared by simulation with aforementioned common techniques, showing ability to remove certain limitations. This work has been supported by Siemens Gamesa Renewable Energy, by the Spanish State Research Agency (AEI/ 10.13039/501100011033) under grants PID2019-111262RB-I00 and PID2019-110956RB-I00, and by the Public University of Navarra under project ReBMS PJUPNA1904