Due to deterioration of fossil fuel and policy directives on greenhouse gas mitigation, wind power generation has been widely developed in recent years. This has raised many issues in terms of power system operation, dynamics, stability and etc. This paper reviews the effect of different kinds of wind turbines on power system stability. Since there are no existing surveys in this area, it provides a comprehensive overview in transient and dynamic stability. The contribution of this survey is to provide a comparison to determine which kinds of wind turbines is better from the system stability point of view. Furthermore, the effects of wind power generation with energy storage systems are reviewed.