Just before President Carter returned to Washington at the end of a visit last week to the Tennessee Valley Authority, he turned to new TVA chairman S. David Freeman and said: "Don't worry, Dave, I'm going to send you two good people."

The "two good people" will fill the two vacancies on the three-member board of directors of TVA, the largest public power organization and by far the most powerful supplier of energy anywhere in the United States. The names of more than a dozen candidates for the TVA jobs have been sent to the White House by labor and business interests and by the governors, senators and members of Congress of the seven Southern states served by TVA.

'Don't ever forget that TVA country is the base of President Carter's political power," said one longtime political observer of TVA. "These two appointments are two of the most important he'll make all year long."

The candidates include Ralph Nader's sister Claire, who worked for 11 years at Tennessee's Oak Ridge National Laboratory; Ned McWhirter, the speaker of the Tennessee legislature, and Richard Herod, associate counsel of the Senate Committee on Environment and Public Works, who has the support of Sen. Howard H. Baker Jr. (R-Tenn.).

Business is backing Richard Freeman, a vice president of Chicago and Northwestern Railroad, who is not related to the TVA chairman. Labor is behind Herbert Sanger, TVA's general counsel. The Congressional Black Caucus has nominated Memphis accountant Frank Banks.

Two other women have been pushed for the TVA posts - Patricia Gish, who's in charge of state housing in eastern Kentucky, the Agnes Byrd, a Maryville, Tenn., lawyer.

The distributors of TVA electricity have chosen Norman Clapp, a former administrator of the Rural Electrification Administration. The universities advising TVA want John Gibbons on the board. He's a professor at the University of Tennessee who served in Washington as an aide to former federal energy administrator John F. Sawhill.

Whichever two are chosen will get their jobs after which one White House aide insists has been the most intensive talent search since Carter's Cabinet was put together. One thing is clear: Carter has had a personal hand in the search, at least in part because he is aware of the importance of TVA to the South's livelihood.

"There are no front-runners for these two jobs," said one source close to the administration. "Everybody's got a chance."

Apparently, some have better chances than others. The White House says it has finished personal interviews with the candidates but that not every candidate was interviewed.

Baker's candidate, Herod, was one of the first interviewed by White House personnel director James Gammill. Black candidate Banks was interviewed, as was Gish, possibly the leading women's candidate. Reports leaking from Capitol Hill last week said that Claire Nader, who works for the Commission for Advancement of Public Interest Groups, was interviewed, but the White House and Nader deny it.

Sources say the White House will trim the list of candidates this week to as few as five. Those names will go to White House aide Timothy Kraft for further scrutiny. From Kraft the list will go either to Carter aide Hamilton Jordan or directly to the president for final selection.

Interest groups are already lobbying against candidates as well as for them.

Tennessee is lobbying against Kentucky, Alabama against Mississippi, labor against business and business against labor. Few candidates have as many interest groups against them as does Nader, who was described privately last week as an ally of her brother and a political friend of the Palestine Liberation Organization.

Friends say Nader was an early supporter of Palestinian causes, in part because of her Lebanese heritage. They say she has never supported the extreme wings of the PLO.

"This is a chance to get the TVA doing what it was supposed to do," Nader said, admitting she would like to have the job. "It's at a turning point right now. It should be used to pioneer for the nation, to set standards for what's technically possible in energy, to find out if solar energy is workable, to get the communities involved in energy decisions. It is a chance right now to get TVA to live up to its mission."