The distributor is badly named, it is in fact your 'Weapon/Engine/System Capacitor', so when you fire when its empty you overload the weapon part of the 'capacitor' and it gets toasty. You can see this in EDSY on how long it takes to deplete the reserve power, depending on the priority. You can increase this by using High Capacity , Weapon Focused and also cluster capacitors as an experimental. For example beam lasers can drain it in a few seconds - like 4 seconds before you start toasting the distributor, with Weapon focused Cluster capacitors this can increase to double digits.