I would start by checking the rectifier and alternator. A fully charged battery checks 13.2v - you have to exceed battery voltage to charge it. Normally the charging system will supply up to 14.8v - charging systems that check higher at idle than at 2400 to 3400 RPM may have shorted winding's (either shorted together or shorted to ground) or the flywheel can have bad magnets. The problem could also be in the rectifier - it's the easiest to check. Use a multimeter and follow the instructions in the service manual. It could also be the battery. If the battery has a shorted cell, just charge the battery at 1.25 amps (exceeding 2.0 amps can damage the battery) till fully charged - disconnect it from the wiring harness (remove the negative wire) and let it set for a day or two - if the battery has a bad cell, it will not crank the engine when reconnected - it will have gone dead without being used. If the battery goes dead in the vehicle without being used, you may have a "key off draw" that needs to be investigated. Hope this helps.
I just reread your post - it is more than likely you have a shorted diode in your rectifier. A shorted diode will allow AC voltage to get to the battery. ACV will still be limited by the regulator to less than 14.8 volts, but AC will kill the battery - test the rectifier first.