Virginia Electric & Power Co. asked the State Corporation Commission yesterday for permission to increase average monthly residential bills by $3.73--or slightly more than 5 percent.

The utility asked for an increase in its fuel charge, a charge that dropped during the 1980s as the company shifted from expensive oil-fired generation. Yesterday's request was the first increase sought in more than three years, utility officials noted.

The increase would raise rates in winter 5.5 percent to $71.23 for 1,000 kilowatt-hours and would raise rates in summer by 5.2 percent to $75.87 for 1,000 kilowatt-hours.

Vepco said the increase is needed because the share of electricity supplied from nuclear units in 1982-1983 was lower than anticipated. The lower share reflected extended periods when the company's North Anna Unit 1 was out of service. The unit is expected to return to service April 1.

Another factor was inclusion in the fuel charge of capacity charges related to electricity purchased from other utilities.

In a related development, the Potomac Electric Power Co. asked yesterday for a 6.4 percent reduction in the fuel rate for its Virginia customers. The reduction would affect approximately 3,000 Pepco customers in Arlington.

Pepco said the reduction would mean a savings of about 50 cents per month for the average Virginia residential customer who uses 291 kilowatt hours. Pepco said the reduction resulted from the continuing substitution of coal for oil to produce power and savings from power purchased from coal-based utilities in the Midwest.