More than 1,200 members of the American Nuclear Society were told at the opening of their winter meeting yesterday of plans for a $30 million public relations campaign to counter the widespread impression that atomic energy represents a "faded dream."

"Even though we are in a partial nuclear moratorium in the United States, every one of us believes that a second nuclear era is on the way," said Dr. Alvin M. Weinberg, director of the Institute of Energy Analysis at Oak Ridge.

But the speakers' recitation of statistics showing that "nuclear power is the fastest growing energy source in this country" failed to fully counter the "harsh reality" of yesterday's announcement by Virginia Electric and Power Co. that it was canceling construction of yet another atomic power plant.

Vepco's decision to abandon North Anna Unit 3 and write off $540 million already invested comes only two weeks after Duke Power Co. canceled Cherokee Units 2 and 3, bringing to 16 the number of nuclear power plants canceled this year and to 38 the number canceled since 1980.

No utilities have announced plans to build new atomic power stations in this country since 1978.

Nevertheless, Weinberg and other speakers following him yesterday expressed confidence that "ultimately, common sense will prevail," and the nation will again turn to nuclear power to meet what they forecast would be a doubling of electricity demand by the end of the century.

"There is no reason to be defensive about nuclear power," Robert Scherer, chairman of Georgia Power Co., told the conference. "It is not the technology that has faded but the country's vision of it."

To the suggestion that $30 million is a lot of money to spend on a public relations campaign that will be waged primarily through television advertising, Scherer responded: "Coca-Cola spends $100 million a year to prove 'Coke is it.' We can spend $30 million to $40 million to prove nuclear power is essential to our well-being."

But for all the expressions of confidence in nuclear energy, many of those attending the American Nuclear Society meeting made it clear they were troubled and disappointed by the Reagan administration's failure to move more rapidly to implement reforms that would make it easier to construct and license atomic power stations.

Lewis J. Perl, senior vice president of National Economic Research Associates, told the annual conference of the Atomic Industrial Forum yesterday the continued rapid escalation of construction costs "could erode or reverse" the cost advantage atomic energy has long held over other ways of producing electricity.

Even Scherer, whose company has four atomic power plants, appeared to reflect uncertainty over the nuclear future when a questioner from the audience asked if given today's conditions he would recommend construction of a nuclear power station to his board of directors.

Because electricity demand largely as a result of the recession is not growing, Scherer said, "we're suffering from the luxury of not having to make the decision [whether to build more nuclear plants] immediately.

"But within the next five years," he said, "those questions will have to be faced and answered."