Energy customers have missed out on an estimated £5.1 million in compensation over the last three years, according to Citizens Advice.
The payments for poor customer service, such as power cuts due to bad weather which take a long time to rectify, should have been made by network providers - the companies which run the energy infrastructure rather than suppliers, the advisory service said.
But it found that "very few" domestic and small business customers claim the payments, due to a mixture of not realising they qualified for compensation, forgetting to claim, or not applying within the three-month time limit.
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Energy network operators are required to meet 39 guaranteed standards of service set by regulator Ofgem, including how they respond to emergencies, their complaints procedures, and the speed of reconnection after bad weather.
In the case of one of the standards, 99% of compensation due for not meeting it went unclaimed, Citizens Advice found.
One electricity customer with a one-year-old baby complained to the organisation following numerous power cuts over a two-week period. Despite repeated calls to the network company, the family was never contacted or sent promised information about how to make a complaint.
In another example, a gas customer whose supply was cut off for 10 days by a contractor carrying out roadworks was continually referred back to the contractor by the network supplier and was not offered any temporary heating or cooking facilities.
Citizens Advice is calling on Ofgem to tighten its current regulations and introduce automatic compensation across all standards.
It said network companies need to work harder to make customers more aware of the compensation they are entitled to.
Citizens Advice chief executive Gillian Guy said: "This money should be in customers' pockets. We want Ofgem to get tougher with the energy network companies so that customers automatically receive all the compensation they're entitled to.
"Guaranteed standards should mean guaranteed compensation. At the very least there should be a system of financial penalties for those energy firms who still don't proactively pay people what they're due."
Energy Networks Association chief executive David Smith said: "The network companies take their responsibilities to their customers incredibly seriously. In many cases, their response has gone further than the regulations require by making millions of pounds in additional, voluntary payments.
"They take many steps to ensure all customers due payments are identified and where payments cannot be made directly to those affected, the companies do not keep this money, it is shared with all consumers through lower bills."