The penetration of wind power into the power system has been increasing in the recent years. Therefore, a lot of concerns related to the reliable operation of the power system have been addressed. An attractive solution to minimize the limitations faced by the wind power grid integration, and thus to increase the power system stability and the energy quality, is to integrate energy storage devices into wind power plants. This paper gives an overview of the state-of-the-art short-term energy storage devices and presents several applications which can be provided by the energy storage device - wind power plant combined system. Moreover, two methods for estimating the remaining useful lifetime of the energy storage devices are presented.