Energy firm Ovo had been fined £2.4m after the regulator found it had not been dealing with customer complaints correctly.
Ofgem said that 1,395 Ovo customers were hit by problems, including long delays in dealing with complaints, in some cases up to 18 months.
Those affected will get about £271 on average in compensation, while Ovo will also pay £2m to the Energy Industry Voluntary Redress Scheme, which provides money to charities helping vulnerable customers.
Ofgem said affected customers would be contacted directly by Ovo, and do not need to take any action.
The energy regulator said that following its intervention, Ovo had given more resources to complaint handling, and improved its complaints management system.
“Energy is an essential service. When things go wrong, it can cause consumers a lot of distress, ” said Jacqui Gehrmann, deputy director of retail compliance at Ofgem.
“In this case Ovo failed to adequately protect and respond to their customers when it was needed most. This is not acceptable.
“Consumers deserve a clear and timely response when they make a complaint, and that’s why we stepped in quickly when we identified that Ovo’s performance was falling below acceptable standards.”
In a statement, Ovo said: “We recognise that a particular group of our customers in 2023 waited longer than we’d like for a resolution and were overdue a response from us, so we’ve sent them a letter of apology and compensation to help.”