Thanks dutch

I Will try that.

My water pump seems pretty new (3y)

The pulley was a bit too stiff when I take it out.

May be it has worn out the bearings (?)

That pulley should spin without any tension IMO. Is that Ac I see in the background hooked up during testing?

Edited June 15Jun 15 by Yarb

I finally found what was the issue…
I had a bad electric connection that was creating shortcuts in the alternator
It results that it was the connection of the oil sensor that was incorrectly connected (wrong pin connected)