Energy storage system plays an important role in modern power systems for mitigating the variation and intermittency of renewable energy sources. The Lithium-ion battery is currently the most widely used solution for energy storage system. However, its high cost is considered as one of the major barriers hampering the integration of renewable energy and the adoption of electric vehicles. Reusing electric vehicle batteries seems a promising solution to the aforementioned problem. Based on a dynamic degradation model of Lithium-ion batteries, this paper first compares the profits that second-life and fresh batteries can bring to the wind farm. Model predictive control is adopted to solve an hourly optimal wind scheduling problem and maximize the profit of wind farm owner. The optimal size of battery is determined and then the comparison of second-life and fresh batteries is conducted taking the battery degradation, the profit of the wind farm owner, and various remaining capacities of battery into account. Two case studies in USA and Denmark are conducted and the analysis shows that given the current prices of wind energy and Lithium-ion batteries, reusing batteries is not worthwhile for the studied wind farms, but it may outperform fresh batteries in the future if the wind energy price decreases much faster than the battery price.