Virginia Electric Power Co. yesterday was granted a 3.4 percent electric rate increase for residential customers in Virginia. The increase will add $2.34 a month to the average residential electric bill, effective April 1.

The State Corporation Commission approved the increase in the utility's fuel-factor charge to cover higher costs stemming from a shutdown of one of Vepco's nuclear generating plants. The increase also reflects a legislative change that allows the utility to bill customers under the fuel factor rather than the base electric rate for the cost of electric power purchased from other utilities.

The increase, which also covers commercial customers, was the first in Vepco's fuel factor after three years of declines totaling nearly $10 a customer. The increase comes as Potomac Electric Power Co. is awaiting approval from Maryland officials for a reduction in the fuel factor charged residents in that state.

Pepco asked two weeks ago for approval of a decrease in its fuel factor averaging $3.30 a residential customer a month. In December, it won approval of a $1.17 reduction in the fuel factor. Pepco said it reduced its fuel factor because of declining costs for fuel oil used to power some of its generating plants.

A Vepco spokesman said that declining fuel oil costs have little effect on Vepco because only 4 percent of its generating facilities are oil-fired. The rest are powered by coal or nuclear energy.

The spokesman said a prolonged breakdown at one of the company's nuclear plants had forced it to use an increased amount of coal, raising fuel costs and leading to the fuel-factor increase. In addition, about one-third of the fuel-factor increase is attributable to the change in regulations that switches the billing of the capacity charge, Vepco's cost of buying power from other utilities, he said.

Vepco had asked in January for a $3.73 increase in the monthly fuel-factor cost for a typical residential customer using 1,000 kilowatt-hours of power monthly, but reduced the request a couple of weeks later to $2.53 because of lower oil prices and a new rail-hauling contract for coal. The final figure of $2.34 a residential customer was recommended by the State Corporation Commission staff and accepted by Vepco. State law allows electric companies to recover from customers increases in the cost of fuel used in generating electricity.