With 12 - 0 - 12 V AC Transformer you can get nearly 17 V DC and it is possible to get 15 V DC regulated from 7815 buth this is not a wise approach, a preferable approach could be to use 18-0-18 or higher transformer with a rating little higher than needed.
One important thing in using such regulators is to avoide High capacity across reason being, in the initial charging stages it draws huge surge current derating the performance of regulator (at times resulting in failure). It is important to include a 10 nf as a regular practice in addition to an electrolytic like 5 - 22 uF.
Another thing is what load you are connecting, are you measuring shortcircuit current?
Raoof