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DTEK said that close to a million people don't have access to electricity.
Fears that Russia could target additional nuclear plants have been raised by the intensifying assaults.
Adam Stein, associate director for nuclear innovation at the Breakthrough Institute, says that attacking the energy system is a particularly effective war tactic, producing widespread damage through strikes on relatively small targets.
It can have deadly effects in the winter. Electricity is needed to run pumping stations and furnaces.
Let's not be mistaken: forcing Ukraine's power plants offline will kill civilians, says Jesse.
The subways, buses, and trains that citizens are using to flee can be shut down if electricity is cut off. It threatens to cut off communications, disrupt government planning, and impair military defenses.
According to the International Atomic Energy Agency, the Zaporizhzhia nuclear power plant in southeastern Ukraine had normal radiation levels as of Sunday. The normal team is still operating the plant, but they are doing so under orders from the commander of the Russian forces that took control of the site. They have also stopped using communications lines.
In the middle of a war, Ukraine has limited options for bolstering its electricity grid. The power lost from the nuclear plant caused DTEK to turn on nine additional coal turbines.
The country's coal and natural-gas reserves were lower than normal this winter. The usual supply lines from mines to ports are at risk of being attacked. The railway tracks that deliver coal to a separate power plant were blown up.
A senior fellow at the economic think tank Bruegel, who focuses on Ukrainian energy issues, says filling in for the output of a nuclear plant will drain reserves quickly.
In the event of a sudden or broader power failure, officials and energy executives in the nation want to quickly integrate the country's grid with the European Union's system.

PaVLO BALANENKO/ALAMY
The effort was already under way. Ukrenergo signed a connection agreement with ENTSO-E, Europe's association of more than 40 transmission operators. Installation of Frequency control capabilities and other technology would be required to ensure the grids can interoperate, as well as extensive system safety tests and a variety of complex regulatory and power market agreements.
A full integration would require turning on or building transmission lines through Hungary, Moldova, Poland, Romania, and Slovakia, according to an analysis last year. The EU and ENTSO-E require 10% of Ukraine's normal generation capacity for such cross-border integrations.
It was expected to cost at least $600 million and take years to complete.
The hope is that the parties can drop some of the usual requirements and agreements in order to have the systems synchronized in a matter of days or weeks. The lines already connecting Ukraine with Hungary and Slovakia might be tapped by the limited integration.
EU energy commissioner Kadri Simson said there was broad agreement on moving forward as quickly as possible.
There are still some technical and political challenges that could hold up the integration. Last month, ENTSO-E said its transmission operators would assess options and make the effort a priority.
In response to an MIT Technology Review inquiry, the press office said that its experts are assessing different options and must take into account technical considerations, system stability, regulatory issues, and cybersecurity concerns.