About 200 homes lost electricity for about an hour after the accident near Eastington, Gloucestershire, Western Power said.
Heaven Crawley, who was piloting the private flight, said poor light meant she had not seen the overhead cable suspended above a field.
No-one was hurt in the crash, at 20:15 BST on Wednesday.
"We were very lucky, we weren't that far from the ground," Ms Crawley said.
The balloon had taken off from Aston Down, near Cirencester, and was trying to find a suitable place to land on the outskirts of Stroud.
"We spotted this field and the lines on the way in but unfortunately because the sun was low, we saw the first dark line of the telephone but not the power lines behind it," said Ms Crawley.
As she tried to land, she said, the bottom part of the balloon envelope struck the 6m (20ft) high cable.
"Obviously if anything electric had hit the metal poles or the basket that has the gas in it, than potentially you're looking at a different scenario," she said.
"But as it was we broke the cables and landed with very little damage."
Two people on board a hot-air balloon had a "lucky escape" when they crashed into an 11,000 volt power line.