Why does my laptop suddenly shut down?

I’ve experienced this problem a couple weeks ago, but not with the same frequency.
I’ve just set up things to suit my necessities, and “BAM” it’s started to shut down all of a sudden. No warning, Nothing. Blank.
It’s happened three time today, the first with less time in between shut downs.
I tried disconnecting a couple of my HD, just out of suspicion, even though I doubt they may be the cause.

The laptop’s three years old, it’s an acer, so… nothing more needs to be added.

I’d worked with the power cable plugged in and the battery detached in these last few days.
I don’t think this is the cause either.
All sort of help is welcome, folks.
I’m learning computer science rather quickly, but I’m still a novice.