The use of energy in the world today is increasing with increase in population. The cost and availability of energy significantly impacts our quality of life, the health of national economies and the stability of our environment. The rapid depletion of fossil fuel resources on a worldwide basis has necessitated an urgent search for alternative energy sources to cater to the present day demands. In recent years there has been a significant global commitment to develop clean and alternative sources of energy such as solar and wind. Wind energy technology has been the fastest growing energy source because it is fairly distributed around the world and readily available for use. However, more penetration of wind energy into existing power networks has some impacts on the stability of the power system. Therefore, this paper studies and analyzes the stability of a power system with increasing wind penetration. The paper presents some analyses of a power system and the dynamic behavior which identify the issues that limit the large-scale integration of wind generators in a power system.