Carterton, Brize Norton and Minster Lovell were all hit by a power cut on December 22.
A fault on a high-voltage network shut off electricity supplies at 4.20am, affecting 2,200 customers.
Power was restored for 1,000 customers within three minutes. Remaining customers had their supplies restored by 8am.
Julian Reeves, Southern Electric spokesman, said: "Even a three-minute break in supply can be a major inconvenience, so we would like to apologise to our customers."
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