Over mean current

21:33 May 27, 2020 

This phrase in isolation is too cryptic and too ambiguous to be certain of anything. If you have ANY further surrounding context, we need that!
If you don't, then you need to give us as many a pssoible of the other fault conditions, so we can try and work it out by elimination.
The problem is, a battery normally supplies current — hence the notion of exceeding some average current consumption doesn't really make technical sense; unless one is talking not about a fault in the battery itself, but rather, an external fault that may harm the battery. That is a totally different kettle of fish!
The likelihood of the battery providing too much current is small, and in any case, relatively unlikely to be considered a 'fault'.
Without more context, we can only guess that 'over' = 'dépassement' and 'mean current' = 'courant moyen' — without any certanty as to how those fit together.