Minnesota utility regulators on Thursday approved a rate increase for the state’s largest natural gas supplier, CenterPoint Energy, and ordered a change in how its customers are billed.

The permanent rate increase for the company’s 823,000 Minnesota customers is less than the 4.9 percent interim increase authorized last October. As a result, most customers will see a small refund on bills later this year.

The state Public Utilities Commission, in a 3-2 vote, also ordered a three-year billing experiment that aims to strengthen CenterPoint’s energy conservation efforts and smooth out the swings in customers’ bills — and the company’s revenue — when winters are bitterly cold or unseasonably mild. The program is to begin next year.

Overall, the Houston-based utility had sought a $44.3 million, or 5 percent, increase in revenue. But an administrative law judge recommended cutting the request to $31.6 million, or 3.6 percent. The final rate hike, after adjustments approved Thursday, is expected to be close to the lower number, but exact figures were not immediately available.

Regulators rejected CenterPoint’s request for a larger increase in its basic charge, agreeing to a $1.50 increase to $9.50 per month. The basic charge applies to customers no matter how much gas they use.

“It could be worse,” said Thomas Ambrose, a retired broadcaster who lives in Minneapolis and just finished paying off his winter heating bills. “We’ll just suck it up and go on.”

AARP Minnesota, which had launched a campaign against the rate increase and the proposed higher basic customer charge, also greeted the decision with relief. More than 700 AARP members weighed in against the higher rates.

“We are pleased that the overall increase and particularly the customer charge, was limited,” said state director Will Phillips in an interview Thursday.

Most of the extra revenue will fund CenterPoint’s plan to more than double its annual investment, to $150 million, in replacing aging pipeline infrastructure. Some pipes to be replaced include miles of cast-iron mains mostly installed before 1950 as well as 1960s-era polyvinyl chloride pipe that has turned brittle. The utility also is stepping up its replacement of tens of thousands of older meters inside customers’ homes.

Although CenterPoint won support for the investment program, regulators rejected its request for a 10.2 percent return on equity, instead approving a 9.6 percent rate. The Minnesota attorney general’s office pushed unsuccessfully for an even-lower rate.

The new billing method approved by regulators is known as “revenue decoupling” and is being used by at least 50 U.S. natural gas utilities. One goal is to eliminate market disincentives that discourage utilities from promoting energy conservation. Another is to stabilize utility revenue by giving customers a credit on their bills after a cold, profitable winter — and tacking on a surcharge after a mild, less-profitable one.

Just last week, CenterPoint reported a 17 percent increase in operating profit for its six-state gas distribution business after a winter in which customers watched their heating bills soar. If decoupled rates had been in place this winter, CenterPoint’s higher-then-expected revenue would be adjusted at year’s end, and customers would get credits on their bills next year.

Under the PUC order, the new system won’t be in place until the winter of 2015-2016, and customers wouldn’t see bill adjustments — up or down — until late in 2016.

Critics of the concept, including AARP, have worried about the effect when customers use less energy for other reasons, such as increased conservation measures or after a dip in the economy. In those cases, customers could see a bill surcharge.

Two commissioners, David Boyd and Betsy Wergin, voted against the new rate structure, and the state Commerce Department, which analyzes utility rates on behalf of the public, recommended only a limited version of it.

But Commissioner Dan Lipschultz, who took office in January, pushed for the rate structure, and was supported by Nancy Lange and Chairwoman Beverly Jones Heydinger. CenterPoint and three environmental groups also favored it.

It won’t be the first experiment at CenterPoint with rates tied to energy savings. In 2010, regulators imposed usage-based, tiered rates to promote conservation at CenterPoint. As gas usage went up, so did the customer’s rate, provoking such an outcry that the utility dropped the system 16 months later and issued 370,000 refunds.

Samantha Williams, a Natural Resources Defense Council attorney who supported the decoupled rate plan, said the monthly adjustments, which wouldn’t start until 2016, tend to be just a few dollars.

“I am not aware of there being customer revolts against decoupling because it is so minimal,” said Williams, a Chicago-based lawyer who has argued in favor of the concept in other states. “If there is an adjustment, one way or another, it is reflected on the bill over time. It doesn’t alter the fundamental structure of the rates.”