The Virginia Electric and Power Co. received permission yesterday to boost its Virgina rates by $82 million, about 8 percent, as soon as its new nuclear power plant is deemed "fully reliable," probably within a month.

The State Corporation Commission in Richmond agreed to the utility's request that it be allowed to add the $82 million a year to its electric rates because its North Anna nuclear power plant is now operating. The utility is therefore allowed to charge its, customers for the costs of building it.

Vepco officials said the impact of the increase will be partly offset by a potential fuel savings of about $50 million a year from the use of the new plant, located about 75 miles southwest of Washington. Assuming the savings are realized, Vepco said the increase would cost its customers $32 million a year, or about 3.3 percent more then current prices.

If Vepco's projected fuel savings are realized, the typical summertime electric bill for a centrally air-conditioned home in the Vepco service area will rise this year from about $120 a month to about $124 a month. A typical bill for a home partially cooled by window air conditioners will rise from about $80 a month to about $82.75.

The increase, classified as a "temporary" one by the SCC, is the second largest single increase ever granted the utility. In 1974 the company won another "temporary" increase" of about $100 million. It was made permanent the next year.

The latest increase is subject to review later this year when the SCC opens formal bearings on Vepco's request for an increase totaling $246 million. The total amount includes the $82 million approved yesterday and if approved would boost Vepco rates in Virginia 20 per cent above current rates.

The North Anna nuclear plant began operation last month and its first generating unit is currently running at about 75 per cent capacity, a Vepco spokeman said. Once the SCC declares the unit in "commercial operation," the utility immediately can add the $82 million to electric bills, an SCC announcement said.

W.W. Berry, executive vice president of the utility, said the company expects that to occur later this month or in early June.

While the proposed $246 million increase - the largest such application pending before any state utility agency in the nation - has angered some consumer groups, an SCC official said there was little question that the $82 million request would be approved. Hearings on the other portions of the rate increase request will not begin until July or September, the SCC said.

Berry said the company's need for higher rates than those approved yesterday is "crucial" and expressed disappointment that the SCC would not act more quickly on the remainder of the request.