Hi. A320/321 can fly for 17 mins on batteries alone; 22 mins if you pull certain circuit breakers, or was it 22/29 mins? (Can't remember how long the A330 can fly for on just batteries.)
They have a ram air turbine (RAT) which will deploy if AC bus 1 and 2 fail. This pressurises the Blue hydraulics, which can run an emergency generator. (I can't remember the A330 specifics, but it is similar.)
Each engine has a small alternator which powers its FADEC above something like 12% N2, so in theory, the engines - once running - can run with no external electrical power? I am not 100% sure about this and am just back after an "oh god o'clock" early today, so I have no energy to look all this up now.