Engineering teams have struggled to get electricity back to Shetland homes, with around 2,400 still without supplies.
Energy company Scottish and Southern Electricity Networks (SSEN) said its engineers had to rebuild the “critical backbone” of the network to allow more homes to be connected.
More than 60 schools have so far closed in Aberdeenshire due to snow.
And many of the area’s roads were affected by snowdrifts.
A yellow weather alert is in place in the north of Scotland with the central band expected to be affected by snow and ice on Friday morning.
Heavy snowstorms cut off the electricity supply in Shetland, with many left without electricity for days.
SSEN said electricity had been successfully restored to customers in the Out Skerries, parts of Voe, northern parts of Whalsay and clusters elsewhere in Shetland on Wednesday.
As of 10.45pm approximately 2,400 properties remained out of bid in Voe, Brae, Yell and Westeros.
SSEN has warned that some of them may be without power over the weekend.
The company said it replaced major infrastructure and damaged points at Voe and Yell and replaced miles of overhead line.
On Wednesday evening, Mark Macdonald, regional head of SSEN Distribution, said: “Today was a matter of rebuilding the central backbone of the network. After three days of significant travel constraints, severe access issues and continued adverse weather conditions, we are realizing for the lost time with the engineers working since the first light of today.”
He said a 125-strong team will continue to work on the rebuild, while simultaneously “reconnecting homes by rerouting the grid and connecting large-scale mobile generation to restore power.”
Several rest centers have been set up.
Dr Susan Bowie, who works out of the Hillswick practice in the northernmost part of Mainland Shetland, has no electricity at her home or surgery.
The surgery uses a diesel generator but does not provide heating.
He told BBC Radio’s Good Morning Scotland programme: ‘It’s really cold in the surgery. You can’t stay there too long because your hands get so cold, but there was a real community spirit about this situation.
“The roads are awful but the staff have come in, they’ve done their best. We’re wearing coats and sweaters and fleeces just to keep warm.”
The clinic had to move some of his medicines to a refrigerator in a nearby hotel to ensure they weren’t wasted.
Fifteen SSEN crews arrived in Lerwick by ferry on Wednesday to help with reconnection efforts, which were hampered by continuing bad weather.
The power outages were caused by “significant” damage to the grid from line icing, where snow and ice build up on overhead power lines and the extra weight causes them to break.
Customers are entitled to claim up to £30 per person for every 24 hours without power.
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