Virginia homeowners' average electric bills will go up by $6.59 a month starting New Year's Day as a result of a fuel factor increase granted yesterday to the Virginia Electric & Power Company.

According to the utility, the average monthly bill for 1,000 kilowatt hours of electricity will rise by 11.8 percent from the present $55.89 to next year's $62.48.

The bill would be about 40 percent greater than the $45.21 charged by the utility last January.

The increased, approved by the State Corporation Commission, is designed to permit the utility to recover the added costs of fuel expected to be used in generating electricity in the coming year.

Vepco, which was awarded two fuel cost rate increases within three months earlier this year, has blamed the heightened costs in part on the fact that three nuclear power stations have been out of operation for much of the year.

Vepco officials have estimated that for every month a single nuclear power plant is out of operation, the utility spends an extra $10 million in fuel costs because it must purchase more expensive coal and oil for its conventional power plants.

Vepco had asked the SCC for $152 million to cover higher 1980 fuel costs. The commission authorized an increase of $117 million.

A Vepco spokesman said last night she understood that the regulatory body anticipated a greater use of coal-burning generators than was foreseen in the company's own estimates. Use of coal to generate electricity is cheaper than the use of oil, although both are more expensive than the nuclear energy.

Before yesterday's increase the company had received fuel cost increases in July and September. Part of yesterday's increase to to help pay for fuel costs not covered by those increases, in addition, the company received a general rate increase in March.

The increases affect about 1.1 million Vepco customers in Virginia. Those of the 1.1 million with electric heating would pay larger bills than average.

In Addition to problems with the company's nuclear plants, the utility's executives have attributed the steep increases in Vepco's fuel costs to the skyrocketing rise in oil prices.

A statement issued yesterday by the utility said Vepco is pleased that the SCC action has recognized "the impact of the most recent OPEC oil price increase."

Of Vepco's three licensed nuclear reactors, Unit 2 in Surry, about 130 miles south of Washington, was closed in February for replacement of damaged steam generators. The Nuclear Regulatory Commission ordered Surry One shut down in March because of uncertainty about its ability to withstand a severe earthquake. After returning to operation, Surry One shut down again when a motor burned out.

Fuel is being reloaded in the licensed unit, Unit 1 at North Anna in Louisa County, about 40 miles southwest of Washington, according to a Vepco spokeswoman. She said the NRC also is calling for further checks of a pipe support.

According to the spokesman, the utility expects both Surry One and North Anna One to return to service in about two weeks, and anticipates that Surry Two will start up again in the spring. A fourth reactor, North Anna Two, has not yet been licensed.

The system of predicting fuel costs for the coming year is required under a revised regulatory system established in 1978 by the General Assembly. Adjustments may be made later.