A nuclear industry advocacy group has launched a $30 million advertising, polling and lobbying campaign to promote the safety of nuclear power, but environmental groups say private utility customers will be billed for the cost.

"There's a lot of fear of nuclear power out there that is not rationally justified," said Harold B. Finger, president of the Committee for Energy Awareness, funded largely by utility companies having nuclear facilities.

According to the committee's internal planning documents, obtained by The Washington Post, the publicity drive will include "training and placement of independent energy experts on local radio and television talk shows in priority regions . . . letters to the editor by energy experts . . . constant contact with networks and other major broadcast media to encourge positive nuclear coverage and to balance charges by critics."

These activities, under way in nationwide test markets, are designed to "establish the credibility of CEA as more than a propaganda organization," the documents say.

Finger said many member utilities will pass the cost of the media campaign to customers through higher rates. He said several state utility commissions would regard this as "a legitimate business expense."

More than 30 states have adopted restrictions that could prevent utilities from charging customers for political or promotional advertising, depending on how such messages are defined. CEA board member Robert Scherer, chairman of Georgia Power Co., has said utilities are prepared to fight utility commissions that oppose these expenses.

Janet Bearden, speaking for the Safe Energy Communication Council, a coalition of environmental groups, said the committee is "a front group" playing down the risks of nuclear energy. To make an unsuspecting public foot the bill for their propaganda is outrageous," she said.

Virginia Electric & Power Co. plans to include its $600,000 CEA contribution in charges to customers this year. "We believe it's a legitimate expense," a spokesman said.

The nuclear industry generally regards the Reagan administration as a strong supporter of nuclear power, and CEA plans "to establish high-level lines of communication with the administration and executive agencies involved with nuclear power," according to the internal documents.

The committee plans to "place op-ed columns and other bylined articles by nuclear supporters outside the industry" and to "commission three position papers on specific issues . . . to be conducted by credible experts outside the industry in concert with a CEA program manager."

Finger said he is not sure whether the position papers will mention CEA's sponsorship.