The power outage in Shetland has been declared a major incident.
SSEN Distribution is working to restore supplies to about 2,800 homes, but Keith Brown, Chief Minister for Resilience, said it was clear many properties would be without power for days.
Sumburgh Airport has now reopened and is working with carriers to maximize capacity.
Mr Brown urged residents to stay home and check on neighbours, family and friends.
He said he chaired a Scottish Government resilience chamber with partners from multiple agencies to ensure that every effort was made to restore power to households.
The power outages were caused by “line icing,” where snow and ice stick to overhead power lines, weighing them down and causing them to break.
SSEN Distribution said local teams described conditions as the worst they had seen in 20 years.
The company has mobilized additional support from the mainland, with around 70 staff traveling to Shetland.
While all efforts are focused on restoring customer supplies as quickly as possible, full recovery is likely to take until the end of this week.
Mae Jamieson told BBC Radio Scotland’s Drivetime that she lost power at 5pm on Monday.
“It’s white everywhere, it’s still snowing, the roads are like a few inches of snow and ice, it’s crazy,” she said.
She added that she was pretty well prepared with a gas stove, candles and head torches, but wouldn’t have anywhere to go.
More SSEN technicians are expected to arrive early Wednesday morning and will continue to supply Shetland with staff and equipment.
As of 5:30 p.m., the company had restored power to 1,000 properties in Unst, Gutcher and parts of Yell by repairing the main 33-kilovolt network.
About 2,800 customers are without power in Voe, Whalsay, Brae, Yell and the West Mainland.
Brown said: “Our top priority should be making sure people, especially the most vulnerable, are safe and warm.
“SSEN has contacted all priority customers and Shetland Islands Council has identified vulnerable people who may need additional support.
“It is also considering how buildings such as community centers could be used to provide respite centers when needed.”
He also urged people to stay home, find ways to stay warm and reach out to neighbors, family and friends, while listening to local radio or following social media for updates.
Mark Macdonald, head of the region at SSEN Distribution, said damage to the network was “considerable” and “particularly extensive” in the west of mainland Shetland.
He added: “We would like to thank NorthLink Ferries and Loganair for their continued support in getting our engineers to the islands as quickly as possible.
“I want to reassure customers that we are working to restore stocks as quickly as possible, working closely with our resilience partners to support joint wellness efforts.”
Customers in a vulnerable position can contact the power outage helpline. A further update is expected to be provided mid-morning on Wednesday.