This sounds exactly like the behavior of my car just before they changed the OBC.
My case of OBC failure is unique. No other car has reported the same erratic behavior as mine. It fails sometimes. It works sometimes. The commonality is that at the start my car seems to draw a much lower current than is actually available. It then reverts to the real value or fails.
I suggest you check for error codes using the OBD. I had the Error Code - P1CF5.