Virgina Electric and Power Co., which last week requested a 5.8 percent rate increase, asked the State Corporation Commission yesterday for another 9 percent increase to cover the rising cost of fuel.

The company's latest request, to raise rates during the last six months of this year, is designed to raise an additional $62 million over that period. Vepco, which serves 1 million customers in the state, including most Northern Virginia homes, stores and factories, said the bill of the average residential customer would rise by $4.43 a month.

The proposed increase marks the third time in a year that Vepco has sought or reveived more money from its customers. If the company receives both requested increases, consumers will be paying at least 30 percent more for electricity in August, compared to $51.29 a year ago.

Company spokesmen said yesterday, however, that typical homeowners in Northern Virginia are more likely to use at least 1,500 kilowatt hours each month. Those with all-electric homes - including central air conditioning and electric heat - could use as much as 3,000 they said.

Although he gave no statistics, Vepco Executive Vice President William W. Berry blamed most of yesterday's proposed increase on forced shutdowns of the company's two Surry nuclear last March to determine whether their cooling pipes could withstand a major earthquake. No date has been set for their reopening.

Without the two reactors, Berry said the company had been forced to rely on costlier coal and oil-generated power. He said the price of oil had increased from $12 to $15 a barrel this year, and he noted that strict new federal environmental standards, to take effect this August, could force the company to use more low-sulfur oilt at prices of up to $19 a barrel.

Taylor Cousins, research director for the Virginia Consumers Congress, said his group would oppose yesterday's request at SSC fuel factor hearings, which begin June 19. Cousins blamed bad management decisions, which he said led Vepco to rely too heavily on poorly designed nuclear reactors, for the company's financial woes.

"It's high time the company began looking linternally at how decisions are being made, and stop asking the SCC to put the burden of mistakes on the backs of consumers," said Cousins.

Until this year, Vepco could have passed on the cost of fuel to customers without an SCC hearing by increasing a monthly fuel adjustment clause. But the 1978 Virginia General Assembly outlawed the clause and ordered electric utilities to make annual forecasts of coal, oil, and nuclear fuel costs subject to quarterly review by the commission. The law took effect in January.

At that time, the company forecast a fuel factor for 1979 of .219 cents per kilowatt hour, or $2.19 for a 1,000 kilowatt-hour bill. Vepco officials predicted that after the North Anna II nuclear reactor opened this summer, the fuel factor would fall to .005 cents.

Events have proven the forecast too optimistic. The Surry units were among five ordered shut by the NRC last March. And a recently announced three-month NRC moratorium on operating licenses for new reactors means the second North Anna unit will not be on line by July 31, the date Vepco originally planned on.

With the Surry plants out of operation, the company has been forced to rely increasingly on ghigher-priced power purchased from neighboring utilities.

Vepco officials said yesterday they anticipated the company would be able to generate enough electricity during the summer months when demand is highest. But they warned that the company's reserve margin would be smaller than usual, and that Vepco may be forced to rely even more heavily on power from neighboring utilities.

The SCC granted Vepco an 8 percent temporary increase of $82 million last June. It included that amount in a $148 million or 17 percent permanent increase that it awarded the company in March.

Last week, Vepco filed again for a rate increase of about 5.8 percent designed to raise another $64 million annually. It said $18 million was need to bring its rate of return on electric facilities up to the 9.6 percent rate authorized by the SCC. The remaining $46 million will go to cover start-up costs for North Anna II when the new reactor finally opens. CAPTION: Picture, WILLIAM W. BERRY . . . cites higher oil prices