To address the system operability challenges due to the continuous reduction of system inertia by increasing penetration of renewable power generation, this paper proposes a new synthetic inertia control (SIC) strategy for doubly fed induction generator (DFIG)-based wind turbine generators. The proposed SIC scheme enables individual DFIG generators to contribute an effective inertial response which helps to stabilise the rate of change of frequency and minimize the maximum frequency deviations in particular under severe disturbance conditions. To achieve the proposed SIC, lithium-ion supercapacitors are required in the dc link of the DFIG power electronic conversion system to increase extra energy storage capability. The DFIG's dc voltage operates at various levels following the derived SIC algorithms for energy exchange with the connected ac grid, and the conventional control system for DFIG is modified to implement the algorithms. The functions and system benefits of SIC scheme are verified using a DFIG model connected to a power system and compared with the simulations of conventional DFIG control scheme. Practical issues such as size, cost, weight, connection configuration, and charging/discharging rate of lithium-ion capacitors for the SIC are discussed and relevant recommendations are presented.