More than 100,000 households could be paid to use electricity over the Bank Holiday weekend.
Power usage is expected to be at a record low, partly because so few shops and other businesses are open.
Such a slump makes it harder for the National Grid to balance the supply of electricity with demand, and increases the risk of blackouts.
The Grid is looking at options to get rid of about 3.7 gigawatts of surplus power – enough for over three million homes for an hour.
The fall in demand also means energy from green sources, such as wind turbines, may go to waste.
Octopus Energy will pay customers in a bid for excess energy to be used. They will get money off for using electricity on Sunday from 5am to 7am and 2pm to 5pm.
It works out as around 20p an hour for an average household. The offer applies to the 100,000-plus Octopus customers with the right sort of smart meter.
Experts want the technology to be used so millions would pay higher prices at peak times and less when it is quieter.
Greg Jackson, the firm’s chief executive, said: “If the UK doesn’t urgently embrace the small changes needed to enable a smart energy grid, the country could end up missing net zero targets, and footing a £40billion bill for infrastructure it doesn’t need.”
A report has revealed more electricity was produced by green energy than fossil fuels for the first time ever in the UK.
Wind farms overtook gas as the biggest source, according to academics from Imperial College London for Drax Electric Insights.
Meanwhile, the UK is in a record run of more than 40 days without using coal to generate electricity.
The Fiddler’s Ferry coal-fired power station in Warrington, Cheshire, closed in March.