The Nuclear Regulatory Commission shut down a Michigan nuclear power plant yesterday and ordered studies at 12 others, including Virginia Electric and Power Co.'s Surry I and II plants, because of possible safety hazards in their electrical systems.

The closure the fourth for safety reasons in the past three years, resulted from an electrical systems review of all the nation's 65 operating nuclear power plants ordered last week by the NRC. The closing of the Donald C. Cook Unit I plant at Bridgman, Mich., on the southern part of Lake Michigan, affects the power supply to parts of seven states, including western Virginia.

The possible safety problem involves electrical connectors (special sockets or plugs) on safety system electric cables within the structure containing the nuclear reactor. Tests at Sandia Laboratories in New Mexico in July showed that certain kinds of connectors failed under the extreme heat pressure and chemical conditions that would occur if the reactor should somehow lose its cooling system.

That would mean that it would be more difficult to turn on safety devices to cool the reactor and that a highly dangerous situation could result.

The Michigan plant was found to have 70 connectors out of "several hundred" within its reactor container that were manufactured by one of the companies, ITT Cannon of Phoenix, whose similar connectors failed the Sandia tests.

Harold Johnson, spokesman for the American Electric Power Co., said AEP's subsidiary, Indiana and Michigan Power Co., which owns the cook units, plans to replace the questionable connectors as rapidly as possible and hopes to be back in operation within a week.

Twelve other U.S. power reactors use similar connectors, and the NRC has ordered additional tests and information on them to be supplied soon, according to Joe Reece, deputy director of the NRC's Operating Reactors Division.

He said that three reactors at the Tennessee Valley Authority's Brown's Ferry station in Alabama and Niagara Mohawk's Nine Mile Point plant near Syracuse, N.Y., have 10 days in which to document that their connectors have been satisfactorily tested or to show why they should be allowed to continue operating without that documentation.

The Surry I and II plants near Newport News, Va., and the Maine Yankee plant at Wiscasset, Maine, have 30 days to do the same thing. Five other plants appear to have satisfactory connectors but have been asked to confirm that: three at Duke Power Co.'s Oconee Station in South Carolina; Georgia Power Co.'s Hatch Unit I at Baxley, Ga., and Colorado Public Service Co.'s Fort St. Vrain plant near Platteville, Colo.

The overall review was ordered after the Union of Concerned Scientists, a group critical of nuclear power plant safety, called public attention to the Sandia tests and asked the NRC to close down affected reactors.

Robert Pollard of the scientists' group, a nuclear engineer, said the Michigan closure was "sad in some respects . . . if they're going to allow construction of plants with unresolved safety problems then you have to expect this kind of thing as you finally get around to doing tests."

Sen. Gary W. hart (D-Colo.), chairman of the Senate Nuclear Regulation Subcommittee, which has jurisdiction over the NRC said he found it "very disturbing" that the NRC knew of the Sandia tests in July but acted on them only after the Union of Concerned Scientists made its petition. He said he had asked the NRC for a full report on the scientists' charges that the tests had been ignored.

Previous safety-related shutdowns involved three other reactors and a further grouping of 23 plants. The Indian Point I plant at Peekskill, N.Y., was hsut in October, 1974, pending modernization of its reactor cooling system. The Humboldt Bay plant at Eureka, Calif., was closed in July, 1976, over questions of earthquake-resistant design, and a General Electirc test reactor was ordered closed at Pleasanton, Calif., Oct. 25 on receipt of new information on earthquakeprone geological faults in the area.