Engineers for Virginia Electric & Power Co. discovered this month they made a mistake in designing back-up pumps for two nuclear power plants under construction along the North Anna River in Louisa County.

The mistake, discovered during what was described as a routine check, was another in a series which have plagued the project since its beginning in 1971. A Vepco spokesman said the latest finding is likely to delay completion of the power stations. One was due to start operating this summer, the other, by early next year.

After being notified of the problem last week, the federal Nuclear Regulatory Commission, ordered Vepco to submit a written report within 30 days. The agency was preparing to grant the utility a license to operate the plants, based on reassurances given last month by its Advisory Committee on Reactor Safeguards that the nuclear systems are safe. But a commission spokesman said yesterday the latest development is serious enough to withhold a license for the time being.

"The company is analyzing the situation to determine an appropriate resolution," said W.L. Proffitt, a Vepco vice president.

Under examination are the recirculating spray pumps for North units 1 and 2. According to a Vepco spokesman, these pumps are located at the base of the buildings which will hold the radioactive nuclear cores. The cores generate an enormous amount of heat, some of which is to be absorbed by a liquid coolant circulating in the system.

If coolant is lost, those pumps are supposed to flood the basin of the containment building and spray water into the building from its top. This safety system is one of a number of what a Vepco statement called "reducement" cooling systems around the power station. "There is a remote possibility that you would ever need it in the first place," the spokesman added.

He said the pumps were designed incorrectly as the result of "an assumption made by its architect-engineer which was not adequately conservative." The spokesman declined to elaborate.

The architect-engineer, Boston-based Stone & Webster, said only that the defect was discovered in a final audit of the pump system conducted by a computer. Asked why the mistake had not been discovered earlier, a spokesman said, "We are continually re-evaluating our designs in terms of the latest analytical methods."

When completed, the first two North Anna stations are expected to supply about 43 per cent of Vepco's electricity. Construction so far has whoe cost of the project, which includes a total of four nuclear-powered units, now is projected to be $2.5 billion.

Virginia's State Corporation Commission announced this week it had hired a California consulting firm, Theodore Barry & Associates, to investigate charges made by former Vepco auditor, Nathaniel W. Hatch, that Vepco has wasted about $63 million in construction.

In a statement issued earlier this month, Proffitt denied Vepco was guilty of mismanagement. "In the final analysis, we believe our construction performance should be judged on the basis of how the cost fo our facilities compares with similar facilities constructed in the same time, frame, under the same regulations," he said.