Every FADEC control engine have a PMA, permanet magnet generator driven by corresponding engine gear box.
Long time did not work on 320, correct me is I'm wrong, but the logic is more or less:
At plane power up, FADEC will be powered by a/c system for a short time, then auto switched off since on ground FADEC, which is cooled by engine air flow, may overheats. Maintenance/Crew my bypass this by a dedicated FADEC test sw, for instance, to know is EGT is low enough for next flight or in other airbys, to check oil qty indication.
When eng is started, Fuel sw on, FADEC is again powered by a/c buses, at n2 =7% (repeat out of memory), PMA have enough rpm to generate power to FADEC removing a/c power bus from it. Should PMA fail, a/c power takes place till engine shut down, where you are AOG with a related mssg.