To celebrate the centennial of the birth of Georges Braque, the eminent French artist whose work comprises one of its largest and more glorious "units" of paintings, the Phillips Collection yesterday announced a major traveling exhibition, "Braque: The Late Paintings," that will open here next fall.

The Braque exhibition, comprised mainly of loans from European collections, is yet another signal that the 61-year-old Phillips Collection, the nation's first museum devoted principally to modern art and the city's most beloved art institution, is transforming itself from a relaxed, family-run gallery of great pictures into an active, fully professional public museum.

Frank Hodsoll, chairman of the National Endowment for the Arts, was present at yesterday's ceremony to confirm the endowment's backing of the Braque exhibition to the tune of a $105,000 matching grant, one of the "seven or eight" largest exhibitions grants dispensed by the arts agency in fiscal 1982.

In accepting Hodsoll's letter of support, director Laughlin Phillips stressed that it represents "the sort of timely, catalytic help that small, non-government museums such as the Phillips Collection must have for their major efforts and that at least in my opinion only an agency of government is in the position to provide."

This is indeed a dramatic turnaround for the institution established in his 21st Street home by Duncan Phillips, Laughlin Phillips' father, and opened to the public in 1921. Duncan Phillips, heir to part of the Jones & Laughlin steel fortune, was the prototypical patrician connoisseur who ran his museum pretty much the way he saw fit.

It was a magnificent way, while it lasted. Phillips amassed one of the world's truly distinctive collections of, as he said, "modern art and its sources," and at the time of his death at age 80 in 1966 he had reason to believe that the $3 million endowment he had provided would safely see the institution through any conceivable crisis.

But when Laughlin Phillips assumed fulltime directorship in 1979 the museum's future was seriously clouded. The old building was--and still is--in dire need of repair. Many of its more than 2,000 works were--and still are--in desperate need of the conservator's expensive touch. Perhaps most alarming of all, the museum was--and still is--operating at a deficit of about $150,000 per year.

As Phillips said at the time, "the question of money" became the number-one priority, and for the first time the family institution turned to outside sources for help. One of these sources was the federal government. Though arts endowment programs to aid museums existed throughout the 1970s the Phillips, in its sleepy way, had largely ignored them.

As the grant for the Braque exhibition demonstrates, this situation has been reversed. In the past two years the Phillips has pursued endowment grants aggressively and as a result has received $300,000 to support major and minor exhibitions, a systematic program of conservation and restoration, and an overdue research project that will result in the first scholarly catalogue of the collection.

The other untapped source of support, of course, is donations from the private sector, and to this end Laughlin Phillips formed an organization, Friends of the Phillips Collection, studded with prestigious names. The main goal of this group has been to spearhead a three-year, $5-million capital fund drive to beef up the endowment by some $3 million and to pay for badly needed interior repair of the old building, which needs new offices, plumbing, wiring and, most importantly, a climate control system to preserve the art.

Phillips reported yesterday that in little more than a year $1.4 million had been raised toward this goal. He also reported encouraging results from the collection's most daring fund-raising enterprise to date--the touring exhibition, "Impressionism and the Modern Vision: Master Paintings from the Phillips Collection," that opens on Sunday at the Minneapolis Institute of Arts.

Supported by a $330,000 grant from BATUS Inc., a Louisville-based subsidiary of Britain's third-largest corporation, this show of 75 of the collection's very best paintings has exceeded expectations in its stops at San Francisco and Dallas. By the time it completes its expanded, six-city tour (stops in Atlanta and Oklahoma City remain, and a deal for an appearance in Tokyo is being negotiated), Phillips said, the show will bring in more than $1 million from exhibition fees and sales of catalogues, posters and post cards. Even so, Phillips confided, government support is an important part of the strategy: the museum has applied to the endowment for a $600,000 challenge grant (matched on a 3-to-1 basis) to spur private contributions.

Laughlin Phillips pointed out yesterday the ironical fact that despite its continuing deficits the collection has embarked upon an ambitious, truly national program of exhibitions. In addition to that, the institution actually has increased its operating budget. "We have to raise salaries," he said. "No one here makes more than $20,000 a year, and I don't take any salary at all. But we have to prepare for the time when I step down." If the capital fund drive succeeds, he said, "it will all work out."

The Braque exhibition, a major undertaking organized by assistant curator Robert C. Cafritz, Laughlin Phillips' stepson, will consist of 45 paintings by the master from his late period, from 1940 to 1963, the year he died. Three of the paintings in the show are in the Phillips Collection; 33 others will be loaned from private and public collections in Europe, nine of them from the Centre Georges Pompidou in Paris. The show will open at the Phillips in October and make two-month stops at museums in San Francisco, Minneapolis and Houston.

As Cafritz emphasized, the show concentrates on a relatively unknown period in the career of the great painter who, with Picasso, invented Cubism before developing his own subdued, poetical voice. It is an entirely fitting enterprise for the Phillips to take on--Braque was one of Duncan Phillips' favorite painters--and it is a sign of the vigor with which the old institution is facing its new hard times.