More than 10 million Ukrainians were left without power by mid-week last week, according to President Zelenskyy.
The situation in Ukraine's capital and other major cities has deteriorated drastically following the largest missile attack on the country's power grid on Tuesday.
Ukrainian state-owned grid operator Ukrenergo reported that 40% of Ukrainians were experiencing difficulties due to damage to at least 15 major energy hubs across the country.
Warning that electricity outages could last anywhere from several hours to several days, the network said that "resilience and courage are what we need this winter".
Kyiv Mayor Vitali Klitschko, too, stressed the need to be ready and resilient in the face of a potential blackout.
"Worst case scenario. Actually, I don't like to talk about that, but I have to be prepared if we (do not) have electricity, a blackout, no water, no heating, no services and no communication," Klitschko told the AP on Friday.
Ukrenergo said in a statement that "thousands of kilometres of key high-voltage lines are not working," affecting the entire country.
It published a picture of a transformer station that was destroyed by a Russian missile, leaving around 400,000 people without power. According to the report, "there are dozens of such transformers in the power system now. This equipment cannot be replaced quickly."
President Volodymyr Zelenskyy said after last week's strikes that more than 10 million Ukrainians were left without electricity; by Sunday, he said some areas had seen improvements.
"The restoration of networks and technical supply capabilities, the de-mining of power transmission lines, repairs — everything goes on round the clock," Zelenskyy said in his nightly address.
Blackouts were scheduled Sunday night in 15 regions and the city of Kyiv, he said. Ukrenergo said there would be scheduled outages in every region on Monday.
High-rises feel like deathtraps
A sharp cold snap and the first snow have significantly complicated the situation in Kyiv.
The cold forces people to turn on their heaters, which drastically increases the load on the grid and makes power outages longer.
In light of the dropping temperatures, the Kyiv authorities announced they were setting up communal heating points.
In the city of 3 million people, 528 emergency points have been identified. Here, residents will be able to keep warm, drink tea, recharge their phones and get any necessary help.
The heating points will be equipped with autonomous power sources, as well as special boiler rooms.
Mayor Klitschko, too, spoke of measures taken to prepare for energy outages with the onset of colder temperatures: "We prepared and we (asked for) electric generators (from) our partners, which they send to us. For this case, we have a reserve of diesel, (of) oil. We have a lot of warm stuff. We have medication."
Many residents in Kyiv have begun to leave boxes of food, flashlights and power banks in elevators in case anyone gets stuck in one for a long time.
Due to the lack of electricity, public transport is disrupted, and many small shops cannot operate.
Living in high-rise apartments overlooking Ukraine's war-torn capital feels like a deathtrap.
No lights, no water, and no way to cook food. And no elevator by which to escape from the 21st floor should a Russian missile strike. Even when the electricity comes back, it's never on for long.
"Russian strikes are plunging Ukraine into the Stone Age," says Anastasia Pyrozhenko. In a recent 24-hour spell, her 26-story high-rise only had power for half an hour.
She says the "military living conditions" have driven her and her husband from their apartment.
"Our building is the highest in the area and is a great target for Russian missiles, so we left our apartment for our parents' place and are preparing for the worst winter of our lives," said the 25-year-old.
Most hospitals in Kyiv have already received generators, and there are no power outages there yet.
'Live without light, but not with Russians'
The Oleksandrivska hospital, the largest and oldest one in the centre of Kyiv, reported that it had not cancelled elective surgeries because the hospital had received electric generators from France. Generators have also been supplied to educational institutions and social services.
"Such facilities are a priority for us, and most of them are equipped with autonomous energy sources," Ukrenergo head Volodymyr Kudrytskyi said on Friday.
However, many schools in Kyiv have endured significant disruption to the learning process, with a lack of electricity meaning internet outages that make remote learning near impossible.
Yaroslav, age 8, stopped attending his school in the Vynohradar district of Kyiv after a rocket attack blew out all the windows of the school and damaged a shelter there.
"Most of the children studied remotely, but now it is no longer possible to do this," said Yaroslav's mother, Olena, who asked for her last name to be withheld for safety reasons in a phone interview. "We are trying to protect children from the horrors of war, but the cold and the lack of power greatly hinder this."
Analysts say that Russian rocket attacks on the energy industry do not affect the successful advance of the Ukrainian army in the south and the situation on the battlefield in general.
"The Russians cannot win on the battlefield, and therefore they use cold and darkness as a weapon against the civilian population, trying to sow panic, depression and demoralize Ukrainians," Volodymyr Fesenko, an analyst at the Penta Centre think tank in Kyiv, told the AP.
"Putin is suffering military defeats and is in dire need of a military pause, which is why he is forcing Zelenskyy into negotiations in such a wild way."
The analyst believes the Kremlin is also trying to put pressure on Western support for Ukraine, as the EU and the US will be forced to expand aid packages to a freezing Kyiv amid growing domestic troubles.
"Putin is trying to make the price of supporting Ukraine too high — this applies both to money and to a possible new flow of refugees to Europe from a freezing country," Fesenko said.
Pyrozhenko, having left her high-rise, moved in with her mother in a small apartment in Kyiv, now home to five people. The family has a wooden house in a village near Kyiv and has already prepared firewood in case of a forced evacuation.
"We understand that winter can be long, cold and dark, but we are ready to endure," Pyrozhenko said. "We are ready to live without light, but not with the Russians."