The Virginia Electric and Power Co., citing sluggish growth in the use of electricity, yesterday announced a two-year delay in completion of a huge hydroelectric power project and the expected layoff of 2,000 people in Virginia.

"We realize that this delay will have a serious effect on the economy of the surrounding area," Vepco president William W. Berry said he announced postponement of the partially completed Bath County plant, situated northwest of Hot Springs near the West Virginia border. "Unfortunately, we were not able to find an alternative."

Vepco officials acknowledged that the delay will lead to a $460 million increase in construction costs, bringing the plant's revised price tag to more than $1.7 billion. But Berry said Vepco "cannot bear the cost of the project," as it was previously planned, because of changing economic trends.

The company did not provide any estimate of the impace the postponement will have on rates paid by its customers. A spokesman said the project's delay will help reduce rates in the short term, but will result in steeper increases after the hydroelectric plant goes into operation in 1985.

"Ultimately, the customers will have to pay for the costs of inflation," Berry said at a news conference in Richmond.

Edsel B. Ford, chairman of the Bath County Board of Supervisors, expressed concern about the project's delay in a telephone interview yesterday, warning that it will increase unemployment and cut tax and other revenue for the county government.

"We will have approximately 500 local people out of work," Ford said, noting that about 25 percent of the 2,000 layoffs are expected to affect Bath County residents. "We're talking about 10 percent of the county population." In addition, Ford said, county sales taxes will decline by more than $200,000 a year because of reduced Vepco purchases.

The hydroelectric project has been delayed several times since construction began in 1977 beside Back Creek near the small town of Mountain Grove. As recently as Jan. 4, Vepco announced a one-year postponement, accompanied by 300 layoffs.

Under the newly revised schedule, the 2,100-megawatt plant would go into partial operation in 1985 and full service the following year. Vepco officials attributed the latest postponement to revisions in the utility's forecasts of electric consumption, made public in early March.

Vepco currently estimates that use of electricity will rise a about 3 percent annually. Its previous prediction was for a yearly increase of more than 4 percent. The downturn stems from the continuing impact of inflation and rising energy costs, according to utility officials.

Vepco officials also linked the postponement of the hydroelectric project to high interest rates for borrowed funds and the utility's inability to find another company to share the Bath County plant's costs. Vepco has reported unsuccessful attempts to negotiate a deal with other utilities, including American Electric Power Co. and Allegheny Power System Inc.

The Bath County plant, described as a "pumped storage" system, consists chiefly of two large reservoirs, one several hundred feet higher than the other.

When electricity is in demand, water will be allowed to flow from the upper reservoir to the lower one, powering a turbine to generate electricity. When electric consumption dips, usually at night, the water will be pumped back to the upper reservoir for use in the future.

By postponing completion of the plant, Vepco officials said they will reduce the utility's expenses by about $275 million this year and next. About 670 workers are expected to remain at the Bath County site for maintenance and some minor construction work, the company said.