Virginia Electric & Power Co., a pioneer in nuclear energy, today said it was abandoning its North Anna 4 nuclear plant and plans to charge its customers $165 million over the next 10 years to cover the losses.

"That investment was made for the benefits of the customers and we feel the customers should bear it," Vepco President William W. Berry told a press conference. The loss will add about 36 cents to an average residential customer's monthly bill of $60 for the remainder of the decade, he said.

Vepco must win the State Corporation Commission's approval of its plan to charge the $165 million to its customers over a 10-year period. Berry said, however, that the SCC allowed Vepco to pass along to customers losses from the cancellation of two of the company's nuclear plants in Surry three years ago, so it wasn't unreasonable to think the SCC would allow it again to charge the loss to customers in the North Anna 4 case.

Berry, whose company was one of the first utilities in the country to make extensive use of nuclear power, also said that any new Vepco power facility built after completion of a third nuclear unit at North Anna will run on coal.

North Anna 4 is only 10 percent completed and has already cost $215 million. Berry said the project was canceled because capital-intensive nuclear facilities are becoming harder to finance, and added regulations since the accident at Three Mile Island have made the building and use of reactors uncertain. He said that politically, nuclear power is still a hot topic and the public is becoming less fond of it.

Perhaps one of the most compelling reasons for the cancellation of North Anna 4, however, was that it wasn't needed. When the plant was planned 12 years ago, demand for electricity was growing at about 10 percent a year, Berry said. Those projections have been changed to reflect average annual growth of 2 percent annually through 1989.

"The future is going to be the use of both coal and nuclear," Berry said. "You need the balance of the two."

Vepco's nuclear position was already shaky. Of its four completed nuclear generators, only two are in full operation, Surry 2 and North Anna 1. Surry 1 will be out of service until April while a steam generator is replaced and North Anna 2, the first nuclear plant to receive an operating license since the Three Mile Island accident, was expected to begin service at more than 90 percent of its power either late this week or next week.

Surry 3 and Surry 4, which cost $157 million, were canceled in 1977.

About $500 million already has been spent to build North Anna 3, a nuclear unit that will cost $2 billion when completed on schedule in 1989, Berry said. He said the North Anna 3 plant wasn't scrapped because it was closer to completion than North Anna 4 and its generating capacity will be needed. "We already have invested more than $400 million in the unit," Berry said. "We believe it is in our customers' best interests to build North Anna 3 as planned.

"Our commitment to complete North Anna 3 is firm," Berry continued. "However, our construction schedule will not require heavy expenditures in the immediate future. If the economy takes an unexpected turn or if units of similar design now nearing completion encounter licensing difficulties, we will be in a position to reassess our plans any time before 1984."

About $50 million in equipment intended for the North Anna 4 unit will be used in the North Anna 3 unit, Berry said, reducing the canceled unit's loss from $215 million to $165 million, Berry said.

In addition, the company said it will emphasize cutting costs, and it will complete its Bath County Pumped Storage Project, a $1.6 billion facility that looked like another potential loser until the Allegheny Power System last month agreed to share half the cost.

Vepco's decision was made after a $1 million study conducted by four consultants, Berry said.

"We examined the issue from the standpoint of the customer and the investor," Berry said. "The choice we made was best for the stockholders and the customers." CAPTION: Picture 1, William w. BERRY . . . customers should bear losses; Picture 2, Vepco's uncompleted nuclear power plants of North Anna units three and four are shown to the left of the main building.