The coronavirus pandemic has played havoc with energy markets. Last month, the price of benchmark American crude oil fell below zero as the economy shut down and demand plunged.

And now a British utility this weekend will actually pay some of its residential consumers to use electricity — to plug in the appliances, and run them full blast.

So-called negative electricity prices usually show up in wholesale power markets, when a big electricity user like a factory or a water treatment plant is paid to consume more power. Having too much power on the line could lead to damaged equipment or even blackouts.

Negative prices were once relatively rare, but during the pandemic have suddenly become almost routine in Britain, Germany and other European countries.

In Britain, the price of power plunged into negative territory 66 times in April, more than twice as often as in any previous month in the last decade, according to Iain Staffell, senior lecturer in sustainable energy at Imperial College in London. The reason for these dips is similar to what caused the price of oil to plunge: oversupply meeting a collapse in demand.

With Britain in lockdown since March 23 and offices and factories closed, demand for electricity fell by around 15 percent in April, while at the same time wind farms, solar panels, nuclear plants and other generating sources continued to churn out power.

"Power systems all around the world are entering completely unprecedented territory," said Mr. Staffell. It used to be that energy use soared Monday through Friday, and then slumped on Sundays.

Now, Mr. Staffell said, "working days are now all Sundays."

These factors could be seen at work on Friday when British power prices reached as low as minus 70 pounds ($85) per megawatt-hour, which is enough electricity to light up several hundred homes for an hour. Demand was low on the eve of a three-day weekend during lockdown, while wind farms and nuclear plants were generating unusually high proportion of power, according to Drax Electric Insights, a website that tracks power statistics.

The below-zero price environment is allowing at least one innovative British power retailer called Octopus Energy to offer to pay some of its customers 2 pence to 5 pence per kilowatt-hour for electricity they consume in periods of slack demand, such as are expected on Sunday.

"This needs to become the normal," said Greg Jackson, the company’s founder and chief executive, who said that the pandemic in Britain was offering a preview of "what the future is going to look like" across the globe.

Analysts and industry executives share that view, assuming efforts to shift to a clean energy system continue.

But the trend away from gas- and coal-powered generators comes with risks. The power system may become less stable, and a tough place to make money.

In recent weeks, renewable energy sources like wind and solar have played an increasingly large role in the European power system both because of enormous investments in these installations and because of favorable weather conditions. At the same time, the burning of coal, the dirtiest fossil fuel, has slipped. Britain, for instance, has not consumed any coal for power generation for weeks.

Such a big drop is, of course, good news for tackling climate change, but the combination of low demand and high levels of wind- and solar-generated electricity is a big shift that power system operators are struggling to manage.

Renewables fluctuate in output — think of a windless, cloudy day — and are harder to turn off at times of low demand, leading to more negative prices and the potential for instability on the networks.

"The focus has been on generation and building more and more wind and solar onto the system," said Julian Leslie, head of networks at National Grid ESO, which operates the British power system operator.

Mr. Leslie said that in 10 or 15 years, it will likely be easier to match demand with supply through methods like charging electric vehicles when power supplies are high. "We will be able to have much more control over the demand," he said.

For now, though, the market takes over, causing prices to fall to a point where utilities decide it is better to shut down generators than pay to put power into the system.

"If you have too much production, you need to send a signal to the market to stop producing that much," said Philippe Vassilopoulos, director of product development at EPEX SPOT, an exchange where electric power is traded.

A negative price incentivizes large consumers of power to not hold back, Mr. Vassilopoulos said. For instance, a supermarket might profit from revving up its electricity-hungry refrigeration units during negative price periods. Households are less able to benefit from low prices because they often have inflexible contracts and lack the software and other tools to alert them to optimal times to consume power.

"The volatility in the system, the reduction in demand means that National Grid as a system operator is having to work really hard," said Ian Kinnaird, head of hydro at Drax, a British electricity generator.

Mr. Kinnaird runs a unit called the Cruachan Power Station that smooths the turbulence created by wind farms, 55 years after it was first opened by Queen Elizabeth. Consisting of a hollowed-out mountain in Scotland with reservoirs at the top and bottom, Cruachan releases water through a generating turbine when National Grid wants to add oomph to the system and then pumps it back up the hill when the call is to absorb excess electricity.

National Grid is also taking some extraordinary steps to reduce power supplies. It is paying EDF, the French utility that runs most of Britain’s nuclear fleet, to temporarily reduce by half the output from a reactor called Sizewell B. It has also worked out a deal with the owners of small renewable plants to compensate them if it asks them to shut down.

Still, analysts say that the unusual pressures in the market are unlikely to disappear overnight. Sunnier summer days, for instance, may increase the amount of solar power in the system, meaning negative prices are "only going to get to be more of an issue," Mr. Staffell said.