batteries - Relation between C-rate and power of a battery

I'm a non-engineer, but I need to understand the function of a battery. I hope you can help me!

For example, I have two bulk storages.

1. 
   

   5MW (power) 5 MWh (capacity)

   
   


2. 
   
   

   5MW/10 MWh

   
   

So the definition of the c-rate is: A C-rate is a measure of the rate at which a battery is discharged relative to its maximum capacity. A 1C rate means that the discharge current will discharge the entire battery in 1 hour.

So for the second storage, a 1C shouldn't be possible? Because it is not possible to discharge the whole capacity in one hour because of the power? I'm a little bit confused.

Answer

You're right (provided that the 5 MW spec is the upper limit of the power).

In the first case you have an exactly 1C-rated storage, whereas in the second case it's 0.5C. Note that putting two 1C-rated storages in parallel will still provide 1C maximum discharge rate.