President Carter and West German Chancellor Helmut Schmidt have worked out an understanding in the past two days by which they will exchange general commitments to an American reduction in energy consumption and a West German effort to expand its economy.

Informed sources said last night that the Carter-Schmidt understanding enhances prospects for success of the summit meeting that gets under way here today at the Palais Schaumburg, the fourth in a series among heads of state on economic issues.

On both sides, efforts have been made to soften expectations of major or specific results. But beneath the soft sell designed to guard against the remote possibility of a complete failure, there is a degree of optimism that the seven leaders here will take political decisions designed to avert a new world recession.

"In the past two days." Treasury Secretary W. Michael Blumenthal said in an interview, "the president has come to believe that Schmidt is serious about (German) growth, and I think Schmidt believes that the president is serious about energy."

Blumentahl said he was optimistic that "they'll find the right words for the communique, and then we'll have 6 to 12 months to see what actually happens."

Since President Carter's arrival in Bonn Thursday night for a state visit, American and West German officials have agreed to language by which Carter will produce a generalized commitment to reduce U.S. energy consumption, and Schmidt will respond with an equally carefully phrased promise to expand West German economic growth.

These statements will focus on what each intends to achieve, rather than how to do it. Thus, Carter's energy statement might not promise a specific increase for oil, or important quotas, two of the possible ways in which carter could act to cut energy consumption.

Schmit's statement on West German economic growth - a sensitive political issue here - might not indicate whether the means of stimulus would be tax cuts, expenditure increases, or a blend of both. The details would be set a West German cabinet meeting at the end of the month.

By de-emphasizing specifics, the American side hopes to avoid the disappointing results of the three prior summits - at Rambouillet, France in November, 1975; in Puerto Rico in June, 1976, and at London, May, 1977.

World recovery and reduced employment, a major goal of each summit, have proved elusive. At the Downing Street session in London last year, the leaders made the mistake of being precise on numerical growth targets, which only the United States achieved and the others badly missed.

The aim of the London summit to enhance world trade and reduce protectionist barriers has remained more a rhetorical outburst than an accomplished fact. Thus, the summitteers this time settled on more modest goals, looking to longer-term objectives.

Beneath the presidential-prime ministerial level in almost all of the countries, there is a belief that bringing the leaders together to force them to contemplate economic realities if highly useful.

There is a shade less confidence on the West German side, which faces an internal political battle of some proportions. West German Economics Minister Otto Graf Lambsdorf favors a sizeable tax cut, and is opposed by Finance Minister Hans Matthoefer. There are other shades of division and opinion within the Cabinet.

In an interview Friday, Matthoefer said that "Schmidt will therefore have to be just as vague as Carter", when it comes to West German expansion plans.

This is a reference to the two key interrelated issues among the five summit agenda items. Faced with a huge trade deficit - $31 billion last year - the United States has been pressing West Germany to expand its economy so that it would be able to accept more imports, thus reducing the American red-ink totals, and taking the pressure off the American dollar.

Bonn's response has been that the American trade deficit is largely a function of excessive energy consumption that requires huge imports of oil from the Organization of Petroleum Exporting Countries.

In a way, the West German preoccupation with the U.S. oil imports of oil from the Organization of Petroleum Exporting Countries.

In a way, the West German preoccupation with U.S. oil imports - shared by other European countries and Japan - is a proxy for a real worry about the declining U.S. dollar. By previous put aside public craticism of the weak agreement, the West Germans have ness of the dollar.

Instead, they talk about oil imports, because if the United States manages to cut imports, then the trade deficit will be reduced, and the dollar, in theory, should rise in value. Failing that, Europeans believe not only that their products will be less competitive in export markets, but that investment in their own countries, already low, will be further worsened.

In an interview in Cologne, Dr. Otto Wolf, head of the West German equivalent of the U.S. Chamber of Commerce, said: "So long as the dollar remains weak, certain German companies will have to invest in the U.S. to maintain their sales."

What's needed, Wolf said, is "a signal" from Carter that the effort will be made to reduce energy consumption, even granting that significant changes will take a long time to put in effect.

In the pre-summit propagandizing, the West German response to the American suggestion that a higher growth rate is needed here is that they have done all that is possible without regenerating inflation. And besides, they add, the favorite American prescription of a tax cut won't work in West Germany because by habit - and tax incentives - people here tend to save an extraordinary part of their income. The current savings rate is 13.5 percent, double the U.S. savings rate.

On the American side, President Carter said last week that the United States in fact has reduced energy consumption. He added a new, and more sophisticated argument that had the Germans this week running to their computers.

That is the claim that most of the U.S. trade deficit now results from the purchase of manufactured goods, not oil. Statistics offered in rebuttal Friday by the West German Ministry of Finance show that of last year's $31.2 billion U.S. trade deficit, $22.8 billion is with OPEC, and only $900 million is with West Germany.

But what President Carter was emphasizing was that non-oil imports added more to the deficit last year than did oil. Imports of other goods and raw materials boosted the deficit by $14.9 billion - twice as much as the oil increase.

President Carter - who has said that a cut in oil imports is high on his list of priorities - is severly limited in what he can promise at the summit because Congress has failed to give him a free hand.

Similarly, there is a sharp division within Schmit's ruling coalition on whether the West German economy internally should risk - or even needs - further stimulation. The opposition party contrpls the upper chamber of the West German parliament, and will attemtp to frustrate whatever Schmidt might decide to do.

The growth issue, which also involves Japan, and the energy issue are surely the keys to this summit discussion, but they are intertwined with the three other agenda topics - trade, monetary questions, and North-South relations.

The monetary question in the minds of most people is the future course of the dollar. That depends on the differences in growth and inflation rates. And, obviously, that depends on what between the United States and the West Germans.