As they struggle to maintain a power grid badly damaged by Russian missiles, officials in the Ukrainian capital, Kyiv, say they have begun planning for a once-unthinkable possibility: a complete blackout that would require the evacuation of the city of three million residents.

The situation, as revealed by the New York Times, is already dire with 40% of Ukraine’s energy infrastructure damaged or destroyed. As winter approaches, the city is preparing 1,000 heated shelters that can also protect civilians from Russian missiles. Most are located within educational facilities. But the authorities asked that their exact locations not be disclosed so as not to make them easy targets.

To prevent a complete grid failure, Ukraine’s national energy company said Saturday it would continue to impose rolling blackouts in seven regions. The huge strain on Ukraine’s ability to provide power is the result of widespread shelling by Russian forces of critical energy infrastructure across the country, a tactic analysts say Russia’s President Vladimir Putin has resorted to as his troops have suffered repeated failures on the battlefield.

The damage caused by the Russian strikes has caused renewed suffering for Ukrainian citizens and forced officials to consider the possibility that further damage could render them unable to provide essential services.

“We understand that if Russia continues such attacks, we may lose our entire electrical system,” Roman Tkachuk, security director of Kyiv’s municipal government, said in an interview, speaking for the city. Officials in the capital have been told they are likely to have at least 12 hours’ notice that the network was on the verge of failure. If it gets to that point, Mr. Tkachuk said, “we will start informing people and asking them to leave.”