President Carter announced last night the formation of an "independent" commission to investigate the causes of last week's nuclear power plant accident at Three Mile Island near Harrisburg, Pa.

The president, promising a "full accounting" said in his television message on energy policy that his commission also will make recommendations on steps to improve safety at other nuclear power plants.

Carter's reassertion of earlier pledges came as Hazel Rollins, as official of the Department of Energy, told a congressional committee that one result of the accident is that consumers in the Harrisburg area soon may be paying as much as $7.50 a month more for their electricity.

She said that customers of Metropolitan Edison Co., operator of the crippled Three Mile Island Unit No. 2 (TMI 2), could expect such new expenses if the utility is forced to switch to oil or coal for power generation.

Metropolitan Edison has been spending more than $500,000 a day for electricity from other sources to supply customers who relied on power from TMI 2. Rollin's estimate of an average rate increase of $7.50 would be on top of a 19 percent rate increase approved last week.

The question of the company's finances was raised again by Public Citizen, Ralph Nader's lobbying group, which charged that Metropolitan Edison had reaped huge tax benefits by pushing TMI 2 into service before the end of 1978.

Nader associates said that the firm gained at least $40 million in tax advantages by putting the plant into service on Dec. 30 at 11 p.m.-25 hours before the new year-despite a long and troubled history of mechanical malfunctions at the island.

The company declined moment on those computations, but Public Citizen said the firm got about $20 million as a depreciation deduction and between $17 million and $28 million in investment tax credits -direct tax writeoffs.

In other developments:

In Middletown, about three miles from the plant in the Susquehanna River, Harold C. Denton of the Nuclear Regulatory Commission said conditions at the plant remained stable, with very little change in temperature or pressure inside the damaged reactor. He described it as "a very routine day" with conditions "essentially unchanged."

The five members of the NRC, meeting with nine scientists who form NRC's advisory committee on reactor safeguards, agreed that the most serious element that led to the accident was the company's removal of three coolant pumps from service-a violation of an NRC rule. The auxillary pumps had been closed for at least two weeks. NRC also dispatched inspectors to seven other "sister plants" made by Babeock & Wilcox Co., woth instructions to keep all pumps in operation.

In Harrisburg, the state Public Utility Commission said it would conduct an investigation, but a question remained open about Metropolitan Edison collecting a $49 million rate increase that took effect a day after the accident.

A central question continued to be that of the cost of cleanup operations, the expense of additional electricity being brought into the system and who ultimately will pay for it all. Company officials were declining comment on such questions yesterday.

It was learned that the company's insurance will pay up to $300 million to repair damage at the plant, regardless of responsibility. The insurance is provided by two syndicates of underwriters, whose most expensive claim to date has been $13 million. The TMI 2 damage bill is expected to be much higher, which led Richard Pye, vice president of American Nuclear Insurors, to say yesterday, "This has been a very profitable business until now."

In a letter to President Carter, Nader and other associates from Public Citizen urged that the federal investigation of the accident also touch on the relationship of tax incentives to nuclear safety regulation.

A Public Citizen study released here said that of the eight nuclear plants with reactors built by Babcock & Wilcox, the fabricator of TMI-2, four of them went into commercial service in December and one in late November.

The report quoted Richard Muranaka, chief of NRC's operating data section, as saying that timing depends on a company's tax structure but that there is "some advantage for a plant to go into operation before the end of the year."

The advantage was cited in the 1978 annual report of General Public Utilities, the holding company of which Met-Ed is a part. The report said that depreciation "principally resulting from the placing in service of the TMI 2 nuclear generating unit in December" had enchanced corporate earnings.

Public Citizen suggested in its study, and in a news conference, that the decision to put the unit into commercial operation was an economic decision that disregarded a troubling record of mechanical malfunctions.

Between March 28, 1978, when the plant went "critical"-that is, when the chain reaction began inside the reactor-and Dec. 30, when it was put into commercial service, the unit was shut down for repairs for 195 of the 274 days.

Met Ed president Walter Creitz acknowledged last week that his company had achieved some tax savingss by putting the unit into service in December. But he and John Herbein, a company vice president, denied that they had "rushed" into opeeration or that safety had been ignored.

And in a telephone interview from Reno, Nev., the president of the union local that represents 325 workers at the plant said he was unaware of any pressure of get TMI 2 into quick operation.

"I can't say that they pushed that plant unusually hard to get it on line or neglected any safety problems," said James Kimmey, president of Local 563 of the International Brotherhood of Electrical Workers. He was in Reno yesterday attending a union conference.

Denton, the NRC's operations chief, said in Middletwon that he could not respond to Public Citizen's charge of speed-ups at the plant. But, he added, "We don't issue a license to operate until our inspection and enforcement people tell us a plant is ready go." It was licensed in February 1978.

At the meeting here, NRC Chairman Joseph M. Hendrie said inspectors have been sent to other Babcock & Wilcox plants to notify each operator of the seriousness of the rule that no pumps be taken out of service while the reactor is operating. If a pump needs to be repaired or tested, the reactor must first be shut down.

"It was a grievous mistake," said the University of Illinois' Dr. Chester P. Siess of Metropolitan Edison's decision to "lock out" three auxiliary pumps at the plant.

At TMI 2, there were still three "hot spots" in the reactor core, where temperatures are at least 328 degrees Fahrenheit. One hot spot is as high as 460 degrees, suggesting that fuel rods at these hot spots were so badly damaged by the accident that they were bent and clumped together in a way that the cooling water can't reach them.