As far as I can see, the power sounder is a fairly dumb device that raises an alarm if the main alarm goes off OR if the battery is disconnected. It has no control over the indicator lights so if the sounder goes off without the indicators it's an indication that the sounder itself has got the hump, not that the main alarm has triggered. This is probably due to a flat battery or a fault in the power sounder. There is no intelligence in the power sounder so there's nothing to program if the battery goes flat. If the bar battery has been allowed to go flat, the power sounder will have gone flat as well, and it's likely that its' batteries haven't recovered and need replacing.
If the main alarm triggers, it flashes the indicators and sends a signal to the power sounder to activate. It also enables power to the main sounder, which is a horn-like device MUCH louder then the power sounder. As a matter of fact, the main sounder and the power sounder are connected to the same line from the alarm / central locking module so they should be triggered together in an alarm condition.
So, I'd suspect that the power sounder is faulty as it has been going off on its' own without the main alarm activating.
I'd also suspect a problem with the main sounder as this should operate when the alarm activates the indicators. It may have been disconnected or it may be faulty.
For future reference, if you turn on the ignition before unplugging the power sounder it shouldn't go off (power sounder is disbled for 15 seconds after power from the ignition feed is disconnected).
It might be worth reconnecting the power sounder to see if it is triggered with the alarm. Have a look for the main sounder while you're there and see if there are any obvious problems with it.
Kevin