Hi,
How can I model the "Depth of discharge" or "minimum storage charge" of a storage process in VEDA-TIMES? is there a specific attribute for this characteristic?

Absolute or proportional minimum? For charge or discharge? If proportional, proportional to what?
Absolute bounds for storage discharge can be defined by STGOUT_BND. A minimum discharge flow proportional to the storage level can be easily defined by FLO_SHAR (if it is a timeslice storage). Minimum discharge flow proportional to capacity would be also possible, but would require defining an auxiliary storage flow, and then a UC constraint referring to the aux flow and the capacity.
Absolute bounds for storage charge can be defined by STGIN_BND. A minimum charge flow proportional to the storage level or capacity would be possible by defining an auxiliary storage flow, and then a UC.
EDIT: Or do you mean minimum level for the state of charge?

I do not mean minimum charge and discharge rates, I mean the minimum charge that a storage technology has to have since for some technologies you cannot fully discharge/use all the energy you have stored. Per instance, you can discharge 100% of a flow battery, on the other hand, CAES technology can only be discharge up to ~40% of its storage capacity.

Ok, so it seems you mean the minimum storage level, in proportion to the capacity? If so, you can define NCAP_AF(LO)=<fraction> (assuming the capacity represents the max. amount stored).