ONCE A MODEL of public management, the Tennessee Valley Authority has fallen into dire trouble. Earlier this year Gov. Gerald Baliles of Virginia, chairman of the Southern States Energy Board, set up an advisory committee to see what needs to be done. Its expert and persuasive report, warning of more trouble ahead, urges fundamental reorganization.

TVA has five nuclear reactors that it ran satisfactorily until about 1980. But then a series of irregularities and glitches began to appear. As they grew more pronounced, in 1985 the TVA -- under pressure from the federal Nuclear Regulatory Commission -- shut the reactors down for extensive renovations. They are still out of commission.

In addition, another reactor is completed but not yet licensed. It awaits the resolution of differences with the NRC about design and construction. Three further reactors are now half to five-sixths completed, but work has been halted. If all were finished, the advisory committee observes, the TVA would have substantially more generating capacity than it needs. The demand for power has been growing less rapidly than it expected.

Altogether the TVA has invested $15 billion in nuclear reactors, none of which is now in operation and some of which may never be used. Hydroelectric power, TVA's original source, is down because of a drought now in its third year. As for coal, the TVA began cutting back on maintenance of coal generators at the beginning of the decade in anticipation of a swing to the reactors. Now it's running into operating trouble in the coal-fired plants as well.

That's why TVA's rates are now rising rapidly. For big customers, industrial and commercial, they are higher than those charged by some of the neighboring utilities.

The advisory committee makes a series of sensible recommendations. Two are crucial. TVA needs to be rebuilt to introduce a kind of accountability that does not now exist. With more or less automatic financing through the federal Treasury, and the ability to set its own rates, it has none of the usual constraints of either a private utility or a government agency. It also needs to abandon a pay cap that holds salaries at one-third or less of the going price for senior managers, ensuring a shortage of talent at the top.

In the past TVA has done great things for the states it serves. Whether it will continue to serve them well is going to depend on the ability of its friends to impose sweeping reforms, starting with its command structure. It's not only the TVA's reactors that need renovation