Solar heating in homes is cheaper than conventional electric heating and may be less expensive then fuel oil in many parts of the country, an Energy Department study shows.

Solar heating still costs more than natural gas, however.

The study has broad implications for the expanded use of solar heating in virtually all regions of the country.

The study found that even without federal tax incentives, some solar water and space heating systems were economically competitive in 1977 and 1978 with electric heating systems for single-family homes in four "respresentative" cities - Boston, Washington, Los Angeles and Grand Junction, Colo.

Solar's economic advantages over electricity are "greatly ehanced" if the newly authorized solar tax credit of up to $2,200 for a residential system is taken into account, the study said. "The economics of solar versus electricity are improved to the point where many more systems may be installed when the all-electric home is the only alternative," it said.

For garden apartment buildings using a 10 percent solar tax credit, the combined solar water and space heating system was found to be substantially cheaper than electricity in Los Angeles and Grand Junction and economically competitive in Boston and Washington.

At present, nearly 15 percent of residential water heaters are electric. However, nearly half of new installations are electric, and the percentage is growing rapidly. For this reason, the main impact of solar water heating is likely to be on houses using electric water heating, the study said.

The study was performed by Roger Bezdek of the Energy Department's conservation and solar applications branch, and Alan Hirshberg and William Babcock, solar energy specialists with the consulting firm of Booz, Allen and Hamilton Inc. of Bethesda. The results were published in Science, journal of the American Association for the Advancement of Science.

The study underscored the potential significance of solar systems supplying hot water and space heating, which together account for 20 percent of annual U.S. energy consumption.