The National Symphony Orchestra has raised $1,021,000 so far toward the $3 million in matching funds required to meet a $1 million challenge grant awarded by the National Endowment for the Arts. The orchestra has until Dec. 1, 1979 to raise the rest. It was incorrectly reported in Wednesday's editions that the full $3 million had already been raised.

The National Endowment for the Arts announced $30 million in grants for arts institutions around the country yesterday - including three in Washington.

Local recipients are Arena Stage, which received $300,000: Ford's Theater, which got $200,000: and the Media Software division of the Booker T. Washington Foundation, $500,000.

Also, two New York-based companies with regular seasons at the Kennedy Center were given substantial sums: American Ballet Theater, $1 million, and the New York City Opera, $700,000.

The sums fall into the special category of challenge grants: one-time only donations that must be matched three times over with money from foundations, corporations and private sources before they become available.

They are meant to stabilize the financial bases of cultural institutions, many of which are chronically deficit-ridden, and to allow for expansion in some cases.

This was the second year in the challenge grant program, and competition was intense. Three-hundred-fity-three groups, seeking $103 million, applied for the $30 million that had been appropriated.

Last year's biggest winner, the Metropolitan Opera, applied again, ignoring the provision against repeats. But no institution received a large a sum as the Met received last year, $1.5 million, which is the largest amount allowed to an individual institution by law.

Three institutions were granted $1 million - the Ballet Theater, the Chicago Symphony Orchestra and New York's Guggenheim Museum.

"The Endowment awarded more large grants last year, and assisted fewer institutions. The National Council on the Arts decided this year to assist a greater number of organizations and to widen the geographic spread. As a result, there is an increase of 43 grants for fiscal 1979 over the previous year and the grantees are located in nine additional states. The medium range for the grants changed from $350,000 last year to $187,500 this year."

The grantees have until July 1, 1981, to raise their matching funds. But if last year is any example, some will meet their goal well before that date. The National symphony, for instance, has already fully matched its $1 million grant with $3 million more.

This was done in less than a year despite the special problem of raising matching money in Washington - the relative shortage of corporations from which to obtain support.

Thomas C. Fichandler, Arena's executive director, said yesterday. "That's why we went after only a bit more than a third of what the Guthrie Theater in Minneapolis did. If you can't convince the Endowment you can match the sum, you don't get anything at all.And Minneapolis has immense corporate wealth that we just can't equal."

Arena's money will be used to set up an endowment to protect the theater from deficits and for limited expansion. "I don't know exactly how we'll divide it," Fichandler said. "Maybe we'll enlarge the acting company. And also I'd like to hire a deputy to me. If I were hit by a truck tomorrow, there'd be nobody here trained to step into my shoes."

The grant to Ford's Theater also will be used to bolster a cash reserve and for increased "audience development" and for upgrading "fund-raising and promotion."

A number of this year's recipients were turned down last year, some because of distribution requirements and some because they could not demonstrate the ability to raise the matching money.

A highly publicized example of both problems was American Ballet Theater, whose principal rival, the New York City Ballet, received $1 million on the first round.

Because of its chronic financial problems, losing on the first round was a particularly hard blow to ABT. And its board went into high gear to insure that this year's money would come through.

Pepsico Chairman Donald Kendall took over the board and led the effort to pull the theater's finances together fast.

"There was a real question of whether we could survive or not," Kendall said last spring, "$250,000 in unpaid bills were more than 90 days overdue and the company could not meet its payroll."

But by this spring the fund-raising efforts of Kendall and others had met with such success that the company was worth the investment.

ABT lost no time in advising its subscribers of the good news. One Montgomery County balletomane returned home from the office yesterday to find a Mailgram which began: "Today the National Endowment for the Arts gave American Ballet Theater a $1 million challenge grant. To receive the cash now, we must raise $1 million in new or increased gifts as soon as possible." The Mailgram suggested that an immediate gift of $70 "would help."

Salvaging and stablizing famous institutions like ABT, however, is not the only purpose of challenge grants.

In the case of the Media Software division of the Booker T. Washington what is essentially a pilot project will be expanded into a nationwide network of about 30 cable TV outlets within the next 3 years, according to its acting director, Liesel Flashenberg.

The program produces and distributes cable television and radio programs, particularly directed at minorities, in cities that have cable networks. Though based here, it has no outlet here because Washington lacks a comprehensive cable system.

Founded in 1976, the organization now has projects in Knoxville, Tenn., Austin, Tex, and Frankfort, Ky.

Among the recipients of other large grants were the Boston Symphony, the Carnegie Hall Society, the Seattle Art Museum, the San Francisco Symphony, the San Francisco Opera, the museums of fine arts in Boston, Houston and San Francisco, the Minnesota Orchestra, and consortiums of cultural institutions in Cincinnati and Arizona.