The Virginia Electric and Power Co. was granted a $37.1 million rate increase yesterday based on higher fuel costs the firm said it had incurred over the summer while three of its four nuclear power generating plants were shut down.

The increase, the second awarded Vepco, for fuel cost adjustment in the last three months, is expected to add another $5.50 to the monthly bill of customers using 1,000 kilowatt hours of electricity.

In pleading its rate increase case before the State Corporation Commission in Richmond earlier this year, Vepco said its fuel costs had skyrocketed above initial projections.

The utility firm was given permission by the SCC in January to charge its customers $405.6 million in 1979. In May, it asked the SCC for another $63 million but was told in July it could only collect an additional $9.8 million to cover increased fuel costs for the first five months of the year.

Vepco officials said yesterday that without the increase the firm's actual fuel costs for the year would be about $84 million more than it could recover under current billing rates.

The utility company still plans to ask for another increase next year to recover its remaining 1979 fuel costs. This request would be in addition to any increase sought to recover 1980 fuel costs.

"These higher fuel costs have occurred for reasons beyond our control and are equally troublesome for Vepco and our customers," said William W. Berry, the company's executive vice president.

The latest rate increase is expected to take effect by the end of the year following an SCC hearing on Nov. 14.

Berry said Vepco was encouraged that the SCC seemed to recognize the firm's fuel cost problems, and he noted that the regulatory commission had indicated it will allow Vepco to recover its costs for the remainder of the year in 1980.

Although the company made no mention of it yesterday, Vepco's fuel costs problems are likely to worsen as a result of Tuesday's accident at its North Anna Unit I nuclear power plant in which there was a small discharge of radioactive gas.

Vepco has blamed increased fuel costs on the fact that three of its four nuclear power stations have been out of operation for much of the year. Now, its fourth and only remaining operable station has been shut down pending refueling and new plant examinations.

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

Diane Worthington, formerly chairman of the Virginia Consumer Congress, complained that Vepco is making little effort to operate within its projected costs and is spending unnecessarily high amounts on coal.

"The company is really in financial difficulty," she said, "and whether you call it a fuel factor increase or a bailout, it does need the money."

Under an old fuel adjustment system, Vepco was granted increases based on money already spent. But the system was revised this year to require utilities to project their fuel costs for the coming year and to make any readjustment requests at quarterly hearings.