Fairfax County, which is rapidly running out of space to dump its garbage, won permission from the state Senate today to build a multimillion dollar trash-burning facility that would also generate electricity.

The measure, approved 33 to 4 by the Senate, has been opposed strongly by the influential trash haulers lobby, which argued that local government will now have monopoly control over the lucrative garbage business.

The facility would replace a landfill as the county's primary means of garbage disposal.

The House has already approved the bill, which will now go to Gov. Charles S. Robb for his signature.

Fairfax legislators fought off a fierce attack on the Senate floor from legislators who said the county shouldn't be allowed to build and maintain such a massive plant without voter approval.

Fairfax officials have estimated that the facility would cost at least $225 million.

"We all know what estimates are when you get in a project this size," said Sen. J. Granger MacFarlane (D-Roanoke). "We should give the residents the opportunity to have their local officials come forward and document what the true costs would be."

"I feel like county officials have the pulse of the public at heart," shot back Sen. Joseph V. Gartlan Jr. (D-Fairfax). "If we want to do it to ourselves, we should be allowed to do just that . . . . I would hope once and for all that this meddling would stop."

County officials plan to sell the electricity generated by the plant to Virginia Electric & Power Co., and say they need the state law to control the flow of garbage in the county so the plant gets enough trash to burn.

The General Assembly gave Arlington and Alexandria permission last year to build a similar facility jointly, but turned down a last-minute effort by Fairfax officials to add their county to the legislation.

Although the Fairfax bill, sponsored this year by Del. Kenneth R. Plum (D-Fairfax), met strong opposition from some legislators, it confronted less resistance than did the similar Arlington-Alexandria proposal.

"We're getting people to agree to the whole concept," said Plum. "I predict that in the next two years Prince William and Manassas and others will be asking for the same thing."

Fairfax County supervisors and other officials have met with legislators several times during the last year to try to build support for the proposal. Local officials said legislative approval of the trash-burning plant was crucial because the rapidly growing suburban jurisdiction soon will be producing far more garbage than county facilities can accommodate.

County officials said they needed the legislation partly to protect the county against possible antitrust action because they would be setting fees.

The proposal has raised serious questions about how such a massive facility would be maintained and what role the county would play in its operation. The bill provides for the County Board of Supervisors to set the fees haulers would be charged to dump trash at the facility. Fairfax officials say they would contract with a private operator to run the plant.

"It's an issue of government intrusion into the private sector," said David A. Pointon, a lobbyist for the Virginia Waste Industries Association, which represents trash haulers. "Flow control is an issue that threatens the livelihood of our industry."

Fairfax officials say they would most likely build the facility near the county's existing landfill on the southern end of the county near Lorton Reformatory.