Virginia Electric and Power Co. yesterday completed the sale of part of its troubled Bath County Pumped Storage project.

The sale, to Allegheny Power System Inc., will allow Vepco to speed up work on the $1.5 billion power plant, whose construction has been slowed because Vepco does not need the extra capacity.

Allegheny agreed to pay cash for a 20 percent share of the Bath County project and also to buy another 20 percent of the power output.

Allegheny's investment will depend on the final construction cost. Vepco officials estimated the 20 percent share will cost Allegheny about $285 million.

The Bath County project does not produce electricity. It stores water in two lakes now under construction in southwest Virginia.

At night, when Vepco's customers are not using all the electricity the company produces, surplus power will be used to pump water from the larger lake to a smaller one several hundred feet higher in the mountains. When Vepco needs extra power, water will be released from the upper lake to flow down the mountain through a hydroelectric power plant that converts the energy of falling water into electricity.

The Bath County plant is the largest so-called pumped storage facility ever built in the United States. Construction delays and inflation have more than doubled its original estimated cost.

Vepco has delayed completion of the project repeatedly because its customers are conserving energy; demand for Vepco's electricity is growing at a fraction of the rate it was increasing when the plant was started.

The agreement with Allegheny Power System commits that company to taking 40 percent of the plant's output. It also gives Allegheny an option of increasing its share to 50 percent, either by buying a bigger interest or purchasing the power produced.

With a partner in the project, Vepco said it will begin gearing up construction next year. The work force will be increased from the present 700 to about 1,500 next year and to 2,500 for 1983 and 1984.

The first three generating units at Bath County are scheduled to begin operation in late 1985 and three more are to come on line in 1986, giving the plant the capacity to provide 2.1 million kilowatts of electricity.

Allegheny Power System is a group of three utilities -- Potomac Edison Company, Monongahela Power Co. and West Penn Power Co. Allegheny had been planning its own pumped storage plant until Vepco put Bath up for sale at the urging of federal utility regulators.