This study presents the impact of the doubly fed induction generator (DFIG) with power system stabiliser (PSS) on critical low-frequency oscillations (LFOs) caused by the synchronous generators (SGs). These LFOs arise due to uncertainties in a system such as generating/loading conditions, intermittent wind power and may cause instability. To improve the stability, the PSS is added. This study studies the effect of varying wind speed, DFIG locations and its capacity with and without PSS on stability. The system is analysed by replacing SGs with DFIG. The sensitivity analysis is carried out with wind power penetration and voltage gain as sensitivity parameters. This identifies electromechanical modes of oscillations that have positive and negative impacts on the system. The transient and small-signal stability (SSS) investigations are done using non-linear simulation and eigenvalue analysis, respectively. The system uncertainties are modelled using inverse output additive perturbation structure to elude the mathematical difficulty. The location and selection of best local input signals for PSS are evaluated from residue method and time-domain simulation analysis. The effectiveness and robustness of the proposed approaches are verified on IEEE 9-bus test system. The PSS improves the transient stability and SSS of the system.