The data revealed that the number of complaints against the energy supplier has increased from 197.7 per 100,000 customers between January and March this year, to 256 per 100,000 in April to June.
This is a substantial increase on the 46.2 complaints per 100,000 customers the supplier recorded for the period of June to September 2013.
Scottish Power said the increase had partly been caused by “our people adapting to our new £200m customer system”.
A Scottish Power spokesperson said: “The transition has been challenging we will also continue to have the longest call centre opening hours in the industry, and we are committed to restoring our customer service levels to the highest possible standards.”
Despite the growth in the number of complaints against Scottish Power, Npower remained the most complained about of the major energy suppliers with the latest figures showing 647.9 complaints per 100,000 customers, although this was down from 664.8 per 100,000 customers between January and March.
Npower has consistently been at the bottom of the complaints table for the past two years following the implementation of its new billing system, and it was warned by Ofgem in June that it needs to either reduce late bills and customer complaints by August or stop selling contracts on the phone until the problems were resolved.
Last month, Npower met the first target set by the regulator, and was allowed to continue with its telephone sales procedures.
When British Gas introduced its new billing system in 2006, it also saw the number of complaints it received almost triple to 250 per 100,000 customers by the end of that year.
At the other end of the table, SSE has remained the least complained about supplier, with 33.7 complaints per 100,000 between April and June 2014.
Eon (79.2 per 100,000) came second, ahead of British Gas (81.4 per 100,000) and EDF Energy (82.7 per 100,000).
Citizens Advice chief executive Gillian Guy said energy firms should “pro-actively identify and help affected customers”.
“Whilst there is a real need for energy firms to overhaul poor billing systems, this should be managed so that customers’ problems are not left to get worse,” she said.