Energy regulator Ofgem has ordered 11 of the UK's biggest suppliers to improve how they deal with complaints.
The regulator said it had "compliance cases" open against four companies over customer dissatisfaction with how they handled complaints.
It has also asked another seven to improve their procedures.
However, the chief executive of industry body Energy UK said suppliers' overall performance in dealing with consumers' problems was improving.
Lawrence Slade pointed to Ofgem's own figures which showed that the number of complaints received by suppliers had nearly halved since 2014.
However, when the regulator last carried out its complaint handling survey in 2016 only two firms were singled out for their performance.
Following its latest survey, Ofgem has opened compliance cases into First Utility, Ovo Energy and Utilita over their poor handling of customers' grievances.
It has also expanded a customer service compliance case against ScottishPower to include how they handled complaints.
During the compliance process Ofgem works with the energy suppliers to achieve improvements. If that does not work the regulator could then open an enforcement case, which could result in the supplier having to pay a fine.
Ofgem has also required all the other domestic suppliers included in its survey - British Gas, Npower, Utility Warehouse, SSE, EDF Energy, E.On and Co-operative Energy - to come up with plans to improve how they deal with complaints.
Dermot Nolan, chief executive of Ofgem, said: "Although the level of satisfaction about complaint handling has increased over the past two years, it is still unacceptably low.
Ofgem's customer complaints survey is carried out every two years. This year it found that of more than 3,000 domestic customers who had complained about their energy companies, 32% were satisfied with how their complaint was dealt with, up from 27% in 2016.
But 57% of respondents said they were dissatisfied.
The main causes of their dissatisfaction were the time taken to resolve the issue, not being kept up to date on the progress of the complaint, and suppliers not giving complainants a clear idea of how long the issue will take to be resolved.
Gillian Guy, chief executive at Citizens Advice, said it was "simply not good enough" that only a third of customers were happy with how their complaints had been handled.
"Resolving issues in a timely manner and keeping customers informed about their complaints are just the basics. Suppliers need to also make sure that anyone who complains has access to independent advice," she added.
Matthew Vickers, chief executive at the Energy Ombudsman, said the remit of the Ofgem survey should be widened beyond large and medium-sized suppliers.
"More than 40% of complaints that come to us are about smaller suppliers, so including customers of these companies would give a more complete picture of the energy sector's performance on complaint handling," he said.
Energy UK's Lawrence Slade said his organisation was working with the industry and Ofgem to see if the rules governing the complaints handling process could be improved.
"Also, given that the majority of complaints arise from billing issues, the continuing roll-out of smart meters, which ensure accurate and up-to-date bills, will help reduce this number further still," he added.