Power systems in the world are undergoing a major transformation due to the displacement of conventional synchronous generators (SGs) and increasing penetration of non-synchronous renewable energy sources (NS-RES) in the electricity grids. A computationally efficient analytical tool incorporating FFR services to determine the frequency performance of a low synchronous inertia power system is a major contribution of this thesis. First, we study the impact of high penetration of NS-RES on the frequency stability of the electricity grids. Second, we study the impact of reduced synchronous inertia on the power system stability of the electricity grid. Third, we study the frequency stability of a low inertia power system by means of the time domain simulations. We considered the impact of different grid topologies on the frequency performance of the system because frequency dynamics are also affected by grid topology in a power system. Furthermore, we developed a wind-based FFR service and used that service to improve the frequency stability of a low inertia power system. Finally, we developed a computationally efficient analytical tool incorporating FFR services to improve the frequency stability of a low inertia power system by avoiding computationally expensive simulations. The tool identifies the locations in a low inertia power system that are highly sensitive to the disturbance by computing rate of change of frequency (RoCoF) sensitivities with respect to synchronous inertia for the placement of FFR services in those locations. Hence in this thesis, we have presented both simulation-based and system-theoretic approaches to improve the frequency stability of the FGs by using FFR services that will help policymakers to determine and improve the frequency performance of a low inertia power system.