Work has been continuing through the night to try to reconnect thousands of storm-hit households left without power.
On Friday night, Scottish Hydro said 29,000 customers were cut off, down from 105,000 at its peak, but that it hoped to have the "vast majority" back on by Saturday morning.
However, the company said customers in outlying areas could still be without electricity.
Some of the areas that have been worst hit by power cuts are Argyll, Tayside, the Highlands, the North East, Orkney and Shetland, Ayrshire, Fife and Central Scotland.
ScottishPower said that it had 1,200 customers "off grid", but it was hopeful they would all have been reconnected late on Friday night.
It said any "small pockets" of people who did not have electricity last night would be offered alternative accommodation.
More than 1,000 engineers have been working across the country to get power back to both companies' customers.
Following a meeting of the Scottish Government Resilience Committee, Deputy First Minister Nicola Sturgeon said: "Contractors are working hard to resolve remaining issues with power supplies and on our transport network in difficult conditions.
"They report that they expect that the vast majority of homes will have power back over the course of today."
The Met Office issued warnings for snow, blizzards and ice across Orkney, Shetland, the Highlands and Grampian overnight and police warned motorists to take care on the roads.