In the course of cutting the budget, the Reagan administration has unobtrusively rewritten the energy policy that prevailed during the last four years.

In the budget to be revealed next week, President Reagan will ask Congress to increase dramatically the federal subsidies for nuclear energy that the Carter administration tried to limit. At the same time, Reagan will propose reductions in most of the other energy programs started since the 1973 oil embargo.

No other federal department has suffered as deep a budget cut, proportionally, as the Department of Energy, administration sources say.

These cuts tread hard on such once-dominant energy interests as the coal caucus, led by Senate Minority Leader Robert C. Byrd (D-W.Va.), and on the synfuels group, led by House Majority Leader Jim Wright (D-Tex.), who helped make that programs the heart of the Carter energy policy.

They strike at the antinuclear lobby and the advocates of solar power and other alternative energy sources. They undercut companies that have been lining up for synthetic fuel subsidies. They severely reduce the federal programs intended to help the poor cope with soaring fuel costs.

Behind these moves is the Reagan administration's philosophical determination to get the government "out of the energy business," Reagan aides say. With recent increases in oil prices, heavy federal subsidies are no longer needed to support competing energy technologies, they say.

The exception is nuclear. While former president Carter cut the federal nuclear budget by 50 percent in his term, Reagan is proposing to pour funds back in, partly to support experimental technologies, partly in recognition of the new centers of political power created by Reagan's election victory.

The Clinch River, Tenn., breeder reactor, which Carter tried unsuccessfully to kill, will reportedly receive $254 million for the 1982 fiscal year in Reagan's March 10 budget, enough to begin construction. This is a victory for Senate Majority Leader Howard H. Baker Jr. (R-Tenn.).

Other basic research in breeder reactor technology will be increased nearly 40 percent, to $500 million in fiscal 1982, sources said, a victory for the Senate Energy Committee's Republican chairman, Sen. James McClure of Idaho, whose state is a center for nuclear research.

And the most determined nuclear booster of all, Energy Secretary James B. Edwards, has won a partial victory in securing funds for the controversial Waste Isolation Pilot Plant in New Mexico, which he hopes to use as the entering wedge in breaking the stalemate over disposal of high-level nuclear wastes.

WIPP, designed for deep burial of low-level radioactive waste, could become a disposal site for the highly radioactive wastes that no one seemingly wants next door, in Edwards' view. Carter would have spent $2 million in fiscal 1982 on WIPP; Edwards wanted $80 million as a down payment on the $500-million-plus project, and reportedly will get about $40 million.

Edwards' victories have come at the expense of David A. Stockman and his staff at the Office of Management and Budget, administration sources say.

As a Michigan congressman, Stockman strenuously opposed the Clinch River project. In a 1977 statement recently unearthed by Sen. Edward M. Kennedy (D-Mass.), Stockman said that financing Clinch River would lock the government into wasteful energy subsidies.

"Today it is the nuclear breeder lobby looking for a large, uneconomic subsidy. Tomorrow it will be the solar power gang, then the windmill freaks, and so on in a never-ending stream of outstretched palms," Stockman said then.

One battle that Stockman apparently won, however, blocked Edwards' bid to have the federal government purchase the Barnwell, S.C., nuclear fuel reprocessing plant owned by Allied Chemical and a Gulf Oil Co. subsidiary, for the DOE's use.

Stockman also has slammed the door on the palms of the synfuel industry.

The solvent refined coal projects in Newman, Ky., and Morgantown, W.Va., two $1.4 billion demonstration plants to turn coal into a liquid fuel for utilities and industries, would lose promised federal subsidies under the Reagan's budget.

Reagan will ask Congress to cut off funding in the current fiscal 1981 budget for the Kentucky plant and three other demonstration projects, and delay funding for the Morgantown plant, the pride of former congressman Harley O. Staggers (D-W.Va.), once a kingpin of the coal caucus.

These cuts will save $3.63 billion in construction and operating costs between now and fiscal 1985, the administration says.

Support for synfuels development will come solely from the federally chartered Synthetic Fuels Corp. under Reagan's plan, and the new directors he will appoint will rely on loan guarantees rather than cash support, minimizing the budget impact.

Other changes demonstrate the administration's hard line against subsidies outside the nuclear area.

The budget for geothermal energy development, supporting projects that tap energy from underground steam and hot-rock regions, will be halved, from $48 million, industry sources say.

The solar energy budget reportedly will be cut from $564 million in the current fiscal year to about $200 million in Reagan's 1982 fiscal year budget.

Grants to help low-income families weatherize homes, totaling $181 million currently, would be shifted from the DOE budget into a proposed block grant program administered by the Department of Housing and Urban Development. Congressional supporters of the weatherization program doubt that it can compete with other demands on the block grant funds.

Under the Reagan plan, however, determining such needs becomes esentially a state and local responsibility, not the burden of the federal government.