HARTFORD — Converting up to 300,000 households to natural gas by 2020 is the most ambitious piece of a sweeping energy plan that the governor will unveil Friday.

Aiming to provide residents with “cheaper, cleaner and more reliable electricity,” the Connecticut Comprehensive Energy Strategy outlines various methods to encourage individuals and businesses to move to cleaner sources of energy for heating, to buy more efficient appliances and to use additional insulation.

An executive summary of the energy strategy calls for millions of dollars for electric and natural gas fueling stations for cars and trucks and for alternative energy research to be based at the University of Connecticut. It also suggests that the existing requirement that utilities buy 20 percent renewable power by 2020 could be raised, and that an energy efficiency standard for new construction should be established.

The report notes that just 31 percent of Connecticut homes have natural gas heat — which is significantly less expensive than oil heat — compared with 47 percent in Massachusetts and 48 percent in Rhode Island. New Jersey has 70 percent of homes using natural gas.

For about 40,000 Connecticut homes, the switch from heating oil or propane would be easy because they already have gas lines in their houses for stoves or water heaters. There are another 187,000 houses within 150 feet of a gas line.

The typical oil-heat customer in Connecticut spends $2,650 a year on fuel, and the typical natural gas customer spends just $1,100 — which includes the whole year’s costs for gas cooking, water heaters and dryers.

Ron Araujo, manager of conservation for Connecticut Light & Power and Yankee Gas, has some experience with showing customers how spending some money now on insulation; a more efficient water heater, furnace or refrigerator; or other investments can save them money.

“Customers are very unwilling to take on debt,” Araujo said. “We have greater uptake on the zero percent for insulation. They look at it more as a repayment

The investment to buy and install a new furnace is substantial — about $7,500.

The state proposes that it link banks or other lenders with customers for loans, which would be paid back through utility bill payments over 10 years. If the interest rate was 5 percent — the highest interest rate now for loans for high-efficiency appliances subsidized through the utilities’ conservation programs — such a loan would cost $80 a month. Even after subtracting the cost of paying back the loan, a family would still save $600 a year by switching.

The state currently helps low-income families convert through its Connecticut Housing Investment Fund, but the scale of this proposed program is far larger. It would be available to families at all income levels, and would cost $6 billion over seven years, if demand materializes.

The utilities paid the full freight for 11,578 low-income households so far this year, with an average $1,500 in improvements.

So far this year, another 16,003 households that make too much money to qualify for free insulation or appliances have had energy audits, which include caulking and replacement light bulbs. Just 12 percent, or fewer than 2,000, ever go further, adding insulation or replacing appliances or windows. And that’s when the utilities are offering an interest-free loan for insulation projects of less than $2,500.

There have been 87 customers who accepted the interest-free loans for insulation, 57 customers who did more than one project and borrowed at 2.99 percent, and 32 customers who did a single project and borrowed at 4.99 percent.

Both of these programs are paid for with $123 million in the state’s energy efficiency fund. That fund also subsidizes businesses’ energy conservation investments, and pays for education promoting conversation and the financing of large-scale renewable energy installations to provide electricity to the utilities.

About $90 million of that fund comes from a surcharge on United Illuminating and CL&P bills. The draft plan would increase that surcharge by 0.37 cents a kilowatt hour, which would roughly double the money available.

Araujo said the residential and business audit and retrofitting programs — together close to $50 million a year — almost always have enough money to meet the demand.

“Demand isn’t as high as we would like it to see,” he said, although he expects to be able to spend it all by the end of the year. Last year, CL&P had $8 million left over, which rolled over to this year.

Araujo said that more people need to take out loans for thousands of dollars in improvements for the fund to be fully subscribed. He thinks that within three years, the spending could be doubled.

“There’s a commitment from the current administration making energy efficiency a key means of meeting its environmental and energy goals,” he said. Past administrations either diverted the surcharge or threatened to do so, he said, which dampened interest in the programs and led to energy auditor layoffs.

But if the current programs don’t have demand past $50 million, how is the state going to inspire almost $1 billion a year worth of spending on natural gas conversions?

A member of the administration of Gov. Dannel P. Malloy who asked to remain anonymous said there could be incentives to sign up, possibly a tax credit on the state income tax, or some kind of Groupon model that could persuade most households on a street to sign up, even where there is not a gas line now.

The cost to tap into a line at the street is small, Araujo said, but bringing a gas line to a street that doesn’t now have one is more expensive. There are about 80,000 homes in Connecticut near a gas main, but the street itself doesn’t have a gas line.

“We’re like uniquely missing the boat,” the source said, especially because Connecticut doesn’t have the excuse that New Hampshire and Maine do, that many people live in rural areas, where natural gas infrastructure isn’t as cost-effective.

If the marketing campaign can persuade people to borrow to realize immediate heating savings, the administration believes it will be easy to find private lenders for the billions needed. Defaults when loans are repaid through utility bills are exceedingly rare, so a 5 percent rate of return is considered good for such a low-risk loan.