More than 10,000 homes are still without power after engineers worked through the night to fix storm damage.
Scottish Hydro said huge efforts were made, particularly in Tayside and Central areas of Scotland, to bring the number down from about 29,000 on Friday night - and from about 105,000 at its peak.
The rural north and west of Scotland were worst hit, a spokesman for the company said.
About 6,400 homes were without power in Argyll and the west, while there were 1,250 still to reconnect in the Highlands and 424 in the Western Isles.
Around 830 homes were cut off in the north-east, mainly in Aberdeenshire, and work continues to connect 1,600 homes in Tayside.
A spokesman for Scottish Hydro said: "Access to many parts of the country continues to be an issue in some remote areas. Helicopters continue to be used today to identify damage.
"It is expected that customers will have their electricity supply restored by late this evening although a small number of customers in outlying areas could still be without electricity tomorrow."
Wind speeds up of up 165mph were recorded during the worst of the storm that hit parts of Scotland and northern England this week, bringing down trees and power lines, causing disruption to roads and closing schools.
Strong winds are predicted to return to the UK in the next few days, but not at the force experienced on Thursday.
Scotland will experience wintry showers, sleet and snow, particularly on high ground, according to MeteoGroup, the weather division of the Press Association.
