Choose a battery for variable speed application
Check out the Simulink Battery Block. Even if you don't have Simulink or this library, the docs here are pretty helpful.

The block diagram (from the mathworks site) shows a primitive battery model update is to simply add an internal resistance, and track capacity (Ah) by integrating instantaneous current.



The docs also have details on much better battery models that include the charge/discharge curves for different battery chemistries. There is even an example to show how to get simulation parameters from battery datasheets.