Data published by the "big six" gas and electricity suppliers shows that the vast majority of concerns were resolved by the end of the next working day.
EDF had the most complaints per 100,000 customers, while Scottish Power had the fewest.
The former said it had improved its service over the last six months.
"We recognise that last year our customer service levels were not up to the high standard we expect and our customers deserve," an EDF spokeswoman said, predicting that things would continue to get better.
"Our new systems are delivering clear benefits to our customers through clearer, more accurate bills and the introduction of better online services."
However, with 8,072 complaints per 100,000 customers, EDF had more than double the complaints level of Npower which was next in the complaints league at 4,001.