Some help with college project about air battery?

Hello everyone! I'm working on my practical project in college and it's roughly about ''air battery'' (CAES) which is filled with help of solar cell (eventually I need to build small version of it).

My mentor explained it to me roughly as well and I would love some help as I'm not very good at thermodynamics.



First thing that I'm not sure about is processes in model.

They basically go like this:



Compression of air

Cooling compressed air

.

.

Heating an air (later when we want to use it)

Letting some of the air go to maintain same pressure in tank

Expanding an air into turbine



Does all that make sense?



Let me know if you need me to go more in detail.. eventually I will, but this is just to check if my foundation is good or I'm missing something obvious.



Thanks a lot!