Energy Secretary Ed Davey said he wants to bring Ofgem in line with other regulators such as Ofcom and the Financial Services Authority, who can ensure compensation goes to customers.
Currently energy suppliers voluntarily give cash to consumers following errors - but there is no obligation - while Ofgem has been able to fine companies, but that money has gone to the Government.
The redress could include pound-for-pound compensation, goodwill payments or public apologies.
More top news
British actress Emma Watson called for more feminists in society and called upon men to promote gender equality in a speech at the weekend.
Twitter falls out of favour and Instagram makes ground in the 2014 CoolBrands UK survey.
At a reception tonight at the Labour Party conference, our correspondent Emily Morgan believes she saw a glimpse of formidable Team Miliband