Virginia Electric and Power Co. yesterday won the approval of Pennsylvania regulators to sell a 20 percent stake in its half-built $1.6 billion Bath County pumped storage project to Allegheny Power System.

The sale will help hold down electric rates for Vepco customers by saving them the cost of completing the job, Vepco said, but it could not estimate the impact on rates.

Vepco plans "to resume full-scale construction of the project," which had been slowed because Vepco could not afford to pay construction bills, said President William Berry.

In the next three months, Vepco intends to hire 800 workers for the project. The unemployment rate in Bath County is more than 17 percent.

Permission for Allegheny Power to buy into the project was granted by the Pennsylvania Utility Commission, which had previously questioned the need for West Penn Power Co., an Allegheny subsidiary, to participate in the construction.

Pennsylvania officials dropped their objections to West Penn's participation after Virginia Gov. Charles Robb met with Pennsylvania Gov. Richard Thornburg to urge approval of the pact, Robb's office said yesterday.

Utility regulators in Virginia, West Virginia, Ohio and Maryland and the Federal Energy Regulatory Commission had earlier approved the deal. The Securities and Exchange Commission is the only regulatory agency whose approval is needed, and SEC clearance is expected shortly, Vepco officials said.

The Bath County project will be used to store electricity for use at times when demand for power is greatest, particularly on hot summer days. The sprawling project consists of two lakes, one several hundred feet above the other.

When power is needed, water will be released from the upper lake to flow through a hydroelectric generating plant into the lower lake. At night, when Vepco has surplus power from other plants, that electricity will be used to reverse the process.

Allegheny Power will pay Vepco $190 million for a 20 percent stake in Vepco's investment so far, and also will pay 20 percent of the cost of completing the project. Three Allegheny subsidiaries have agreed to buy an additional 20 percent of the plant's output and the company has an option to increase its investment to 50 percent of the total.

The $190 million cash payment "will substantially reduce Vepco's external financing requirements for 1982," Berry said.