All the early Ducati's up to the 996 Biposto had the two-phase alternator and a 30 amp fuse, a big green thing with a clear plastic housing, next to the battery.
If it melts down, your alternator has either come loose and is eating the stator wiring, or the two yellow or the red connectors are dirty, or the regulator has gone on holiday.
All the bikes with the Nippon Denso 3-phase alternator had a 40 amp fuse, a big yellow/brownish colored one, in a sealed black fuse holder in the same place, next to the starter solenoid and battery. Same scenario if that goes "Sputnik !" and starts blowing.
It usually fritzes when there's a problem with the charge circuit, so it shouldn't be too hard to troubleshoot.