Countries are investing in renewable energy such as wind or solar to meet electricity demand and minimize CO2 emissions. Due to the intermittent nature of these energy sources, back-up generating assets or adequate storage is needed to meet peak demand. In this study, we evaluate the extent to which an electricity grid can rely on intermittent renewable energy (wind and solar) if a ‘black box’ battery is used for storage. We examine the potential for 100% generation from wind and solar, as well as scenarios that are consistent with a policy to eliminate coal generation. A constrained optimization model is used that minimizes thermal generating capacity and battery size subject to load and battery constraints. Our application is to the fossil-fuel dependent Alberta electricity system. Our results suggest that it might be difficult and costly to supply the grid with 100% renewable energy. Replacing coal with renewable energy and using natural gas and a battery as back-up would be feasible, but would require a very large battery and result in high costs. Other storage methods should be considered to facilitate increased generation from renewable sources.