In response to ongoing worldwide theme of sustainable development, more and more fossil energy based conventional synchronous generators are being replaced by renewable energy sources for the electricity production in modern power systems. However, some low inertia issues will be brought into future power systems, which will not be conducive to system frequency stability. This paper aims at improving frequency stability in low inertia power systems by using synthetic inertia from DFIG based wind turbines. All simulation work involved in this paper is performed on the software platform MATLAB/SIMULINK. The test model is chosen to be a power system connected by an integrated DFIG based wind farm. After modification and validation the chosen test model will be applied to simulate the GB equivalent large system model. It can be eventually verified that the impacts of synthetic inertia from wind turbines will become more significant on system frequency stability in terms of both ROCOF and frequency nadir when more wind farms are being integrated into future low inertia GB power system.