More than 45,000 homes were without electricity following back-to-back storms which hit the UK over the weekend.
Storm Corrie brought winds of 92mph to Stornoway in the Western Isles of Scotland late on Sunday.
It followed Storm Malik, which blew down trees, damaged power lines and ripped roofs off homes in the north of England and Scotland on Saturday.
Network Rail said fallen trees were affecting train services.
On Monday, 45,500 customers remained without power, with about 40,000 of them in northern Scotland.
It was understood most of those lost power in the most recent storm, rather than being still affected by Storm Malik.
Energy industry spokesman Peter Kocen said: “Network operators restored power to 177,000 customers who have been affected by the storms over the weekend and last night.
“We are continuing to work as quickly and safely as possible to reconnect everyone, with 45,500 people without power just now.
“We are working closely with local authorities to co-ordinate a community response and provide support, including hot meals and respite, to those affected.”
Northern Powergrid said it was dealing with about 200 incidents in Tyne and Wear and Northumberland, with about 7,000 customers without power.
In a statement on its website it said: “There is the possibility that a small number will run into Tuesday, the weather has caused us some additional disruption overnight that we also need to handle during the course of today.”
The firm insisted it had learned lessons from November’s Storm Arwen, which led to widespread complaints about the way it communicated with customers who had lost power.
It said Storm Malik was worse than forecast and led to about 80,000 people losing power, mainly in County Durham and Northumberland, but it was not as devastating as Storm Arwen as there was no snow and ice this time.
Stewart Sexton, 58, from Alnwick, Northumberland, lost power for 35 hours over the weekend, having previously been badly affected by Storm Arwen.
Describing himself as “enraged”, he told the PA news agency: “It’s all about a lack of maintenance of the infrastructure and no resilience plan from Northern Powergrid.
“We have had power cuts for 298 hours since November 26, just over two months.
“By any reckoning that must be unacceptable and it indicates that there is certainly something wrong with the infrastructure around our communities, while neighbouring larger villagers didn’t lose power at all.”
Conservative MP for Berwick, Anne-Marie Trevelyan, said constituents were still complaining about poor communication regarding power cuts, adding: “I am getting reports that people are having similar issues with reporting the problem as they did with Storm Arwen.
“This is clearly not good enough and makes a difficult experience even more stressful.”
Work had been put in place to make sure Scotland was better prepared, Deputy First Minister John Swinney said.
He told the BBC’s Good Morning Scotland radio programme: “I think it was very clear that there was a much stronger join-up between the power companies and the local resilience partnerships over the course of the weekend.”
A nine-year-old boy in Staffordshire and a 60-year-old woman in Aberdeen died after trees were torn down on Saturday.
Several schools in Aberdeenshire and Northumberland said they will be shut or will delay opening on Monday.
Storm Corrie pushed into the North Sea in the early hours of Monday, leaving cold and blustery conditions behind.
A tidal surge caused by Storm Corrie led to the Thames Barrier being closed.
The Environment Agency said the barriers were closed more frequently during the winter.
Met Office spokesman Richard Miles said the next few days will be much calmer before a cold snap with wintry showers hits the UK on Thursday, followed by milder weather over the weekend.
