The federal agency that regulates natural gas prices has agreed to permit five big gas companies -- including one that supplies the Washington area -- to charge their customers for the cost of building a $1 billion plant to make gas from coal.

The decision by the Federal Energy Regulatory Commission begins to clear the way for construction of the nation's first commercial coal gasification plant and could set a precedent for financing other synthetic fuels projects.

FERC overruled a June decision by one of its administrative law judges, who said the cost of the plant should be paid by all taxpayers rather than by the customers of the companies involved in the project.

The federal agency, however, has yet to decide exactly how the cost of the project will be passed on to consumers. The decision is expected to be made at a FERC meeting Nov. 14.

The plant to turn coal into a substitute for natural gas would be built at Beulah, N.D. It has been planned by American Natural Resources Co., which leads a consortium of five gas producers.

Among the companies involved in the project is Columbia Gas System Inc., the principal gas supplier to Washington Gas Light Co.

The Beulah plant would make gas from lignite, or brown coal, using the Liurgi process developed in Germany.

Although the process for extracting gas from coal has been well developed, the plant would be the biggest ever built in this country and is considered both a technological and financial risk.

Gas made from coal is expected to cost several times as much as ordinary natural gas.

Questions about how the risk of building the plant would be shared and who would pay for the costly gas have help up the project.

In June a FERC administrative law judge ruled that "whatever benefits are to be derived from this project will be shared by the entire country, not merely some ratepayers."

Department of Energy officials, including former Energy secretary James Schlesinger, urged FERC to overturn that ruling, contending it could block important parts of the administration's synthetic fuels program.

In a ruling handed down Monday, FERC accepted the principal of passing the costs of such a project on to consumers and gave its general backing to the Dakota plant.

FERC's staff has recommended that the cost of the synthetic gas be "rolled in" to prices paid by consumers. Since the synthetic fuel would make up a relatively small portion of the gas used by customers of the five companies, the impact on gas bills probably would be small.

The other critical issue to be addressed by the federal regulators is what happens if the plant is a failure. The companies want permission to charge their customers for the plant, even if it never produces any gas. FERC's staff opposes that, contendit would would give the companies no incentives to make the plant a success.

If, as expected, FERC answers the financial questions next month, construction could begin in the spring of 1980. The plant would be completed in four years.