The White House yesterday acquiesced in -- and the Senate quickly passed -- legislation restricting President Carter's power to impose oil import fees and quotas.

Carter, as proof that he is determined to cut U.S. energy consumption, announced earlier this year that he would use quotas to keep oil imports below 8.2 million barrels a day this year and the 1977 average of 8.5 million barrels a day thereafter.

At the time, administration experts thought such quotas would not bite for several years. But now they are not so sure. Many experts say quotas would drive up prices and be disruptive, especially in import-dependent New England, and the Senate Energy Committee voted 10 to 8 several days ago to let either house of Congress veto any quota.

The face-saving compromise that the White House accepted yesterday would require a veto by both houses. But sponsor J. Bennett Johnston (D-La.) said afterward it still makes imposition of any quotas "very, very unlikely."

The administration accepted the compromise at least partly for lack of the votes to beat it. The compromise was passed, 70 to 23. There has been no House action on the quota question.

The Senate action came as the Commerce Department announced that the U.S. trade deficit increased last month to $2.83 billion, mostly because of increasing imports of oil at steadily rising prices. [Details on Page E1].

In the House, meanwhile, another energy compromise was announced, this one favorable to the administration. It involves the powers of the Energy Mobilization Board that Carter has proposed to cut red tape on large energy projects.

The issue had been the board's power to override state, local and federal laws impeding a project. The compromise would deny it the power to override state and local laws, and let it override federal laws only if both houses of Congress concurred.

In one other development, new deputy Energy Secretary John Sawhill told a House Energy subcommittee that the Carter administration is looking into a variety of further ways to cut gasoline consumption, including possibly proposing new fuel economy requirements for both cars and trucks. He did not elaborate.

The import quota compromise was attached to a bill extending antitrust exemptions for oil companies to participate in an international energy agreement until June 30, 1980. Under that agreement, a shortage caused by an export cutoff would be shared equally among 21 signing nations.

The House has already passed two versions of the extension, one for two months and one for a year and a half. Rep. John Dingell (D-Mich.), House manager of the bill, would not say whether the Senate action was acceptable to him. The last extension expires today, and if the congressional veto mechanism is not acceptable to the House, Dingell may argue that the Senate accept a two-month extension and argue about the quota veto issue later.

Johnston argued that the compromise was a good one. He said U.S. imports are inching close to the Carter target. But if the president stopped imports at that level, as he promised, Johnston said, it could "cause a repeat of the crisis of 1979, with gas lines, shortages and trucker strikes."

At the same time, Johnston said, the White House would not be totally denied its ability to "carry through on its promises. We don't want to take away our credibility in international negotiations."

Sen. Lowell P. Weicker Jr. (R-Conn.) opposed Johnston's amendment. "I don't think the national interest is served by cutting deals. Every time we cut a deal we weaken our ability to withstand the threat of OPEC," the Organization of Petroleum Exporting Countries, he said.

Meanwhile, as House debate opened on two competing committee versions of the legislation to set up an Energy Mobilization Board, the White House finally made clear which version it favors.

The White House told House members at an energy briefing Monday night that it favors a Commerce Committee version of the bill, with an amendment by Rep. James D. Santini (D-Nev.).

Under a competing Interior Committee version, the board could not override any law. But it could go to court to force a decision from a local, state or federal agency.

Majority Leader Jim Wright (D-Tex.) predicted the House would vote for the Dingell-Santini version. The Interior version would set up unnecessary delays that could add five years to the completion of a project, Wright said the White House told House members.

Meanwhile, a House committee on committees opened hearings on proposals to consolidate energy jurisdiction into one committee, partly to forestall the kind of competition for jurisdiction over energy that Interior and Commerce were bringing to the floor.