The Hamptons broke a power-use record on Sunday, as high heat and humidity drove up air-conditioner use in a region already identified by PSEG Long Island as needing new power resources to address looming energy-grid constraints.

As temperatures climbed to 93 degrees in Southampton, the South Fork’s usage hit 276 megawatts of power use at 3 p.m. on Sunday, topping a prior record set in July 2011 of 263 megawatts. A megawatt powers 800 to 1,000 homes.

The peak-power use highlighted an existing PSEG plan to boost power resources for the South Fork, which on the grid is considered from the Shinnecock Canal east to Montauk. LIPA is considering a wind farm in the waters off Rhode Island along with other measures to help alleviate that peak power gap as part of a request for proposals that LIPA trustees may vote on in the coming month.

At the same time, a plan to consider a range of green-energy solutions to address a similarly looming peak-power gap in two other LIPA regions, Glenwood Landing and Far Rockaway, will instead be addressed through high-voltage cable enhancements by PSEG, the utility confirmed Tuesday.

LIPA determined that enhancing the transmission system was a more economical solution, they said, despite receiving dozens of proposals from outside developers. The South Fork and Western Nassau bid requests were part of Gov. Andrew M. Cuomo’s Reforming the Energy Vision initiative, which specifically sought to use green-energy alternatives to address grid-infrastructure challenges.

“After a review of all of the proposals and a thorough analysis of the options to ensure the future reliability of the system . . . the most reliable and economical path forward is for two underground transmission lines to serve the area,” PSEG said.

For all of Long Island, meeting the summer peaks is the challenge. This summer it’s been particularly acute on the South Fork, which had its second all-time high energy use at 5:50 p.m. on Saturday of 274 megawatts, while Friday was the ninth highest at 255 megawatts, according to PSEG.

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For Long Island overall, this year’s peak was hit on Saturday, with 5,413 megawatts used. The system has capacity for more than 6,000 megawatts, and the record high was set on July 22, 2011, with a peak of 5,915 megawatts, according to PSEG, which manages the system under contract to LIPA.