Complaints about Npower and Scottish Power doubled in the first quarter of this year after new billing systems caused problems for customers.
Citizens Advice and Citizens Advice Scotland said complaints about Npower rose from 306.8 for every 100,000 customers in the last quarter of last year to 592.4 between January and March - or one complaint for every 168.8 customers.
The charity's latest complaints league table sees Npower "firmly at rock bottom" in sixth place and Scottish Power in fifth place after both introduced new billing systems.
Complaints about Scottish Power increased from 100.5 per 100,000 customers to 197.7 in the first quarter.
Complaints about all suppliers increased, although the rise was only slight for some.
SSE attracted 34.1 complaints per 100,000 customers in the first quarter, followed by British Gas (75.4), E.On (83.6) and EDF (84.5).
Citizens Advice said the rise in complaints to Npower reflected that the supplier had overcome some of the earlier problems with its new billing system, which meant more consumers were now receiving bills.
However, very late bills meant customers had been forced to find hundreds or thousands of pounds to cover the cost, leading to complaints
Last month Ofgem warned Npower to resolve its billing problems by the end of August or halt all telephone sales to new customers.
The regulator said Npower must meet monthly targets to cut the number of accounts affected by late billing or stop all proactive telesales activity.
Ofgem has also opened an investigation into Npower's "prolonged customer service failings", the first under its new Standards of Conduct which state that suppliers must treat consumers fairly.
Citizens Advice chief executive Gillian Guy said: "The knock-on effect of poor billing systems can turn household budgets upside down. Many people do not have the spare cash to cover the cost of a large bill that suddenly lands on their doorstep.
"While we recognise Npower is receiving more complaints because it is starting to get over some of the earlier issues, it needs to do more to stop consumers' problems escalating. Offering repayment plans and discussing ways they can help consumers from the off will nip issues in the bud and remove the need to complain.
"Scottish Power has an opportunity to learn from other suppliers' new billing system failures and address these problems now so more consumers won't have cause for complaint.
"A rise in complaints about all suppliers is concerning. Suppliers won't win the trust of customers back unless they show they understand what consumers need, recognise the financial pressures many people are under and are able to sort out problems quickly. This is something that all suppliers can act on now."
Npower's director of domestic business, Roger Hattam, said: " Since apologising to our customers in December, we have been working hard to fix our billing system issues - which meant we couldn't bill groups of customers. These billing issues led to higher than normal complaint levels, as shown by the figures for January to March.
"We recognise we have more work to do but we're making progress. In June alone we reduced our late bill backlog down to 231,000 customers, received 10% fewer complaints and also cut our complaints backlog by 27%. We're fixing our billing issues and clearing even more of the backlog of late bills. This, in turn, will reduce the numbers of complaints received by Citizens Advice and the Ombudsman."
A Scottish Power spokesman said: "We are disappointed that complaints have increased, and we apologise to any customers who have experienced issues.
"Over the last six months we have been installing a new £200 million account management system, which will mean real improvements to our customer service. However, the transition is difficult and has led to a dip in customer service levels. We have, however, recruited hundreds of additional call handling staff and extended our call centre opening hours to the longest in the industry, as well as expanding our online services.
"We are confident customers will see real service improvements coming through."
A spokeswoman for the Department of Energy and Climate Change said: " It is unacceptable that so many people have needed to complain about their energy suppliers.
"Energy companies need to realise that people will not tolerate poor service and are switching suppliers in unprecedented numbers, particularly to small suppliers whose numbers have nearly trebled since 2010."