Northern Powergrid say it is putting the lessons learnt from Storm Arwen "into practice" as it deals with the damage caused by Storm Malik.
Winds of up to 90mph were recorded in Northumberland during Saturday's storm, while thousands of households in Northumberland and County Durham have been left without power.
It comes just two months after Northern Powergrid were heavily criticised for their response to Storm Arwen in November, when it took almost two weeks to restore power to everyone affected.
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The company said 80,000 customers saw their electricity supplies affected by Storm Malik - but teams were out making progress in the field to restore supplies.
As of midday on Sunday, 16,000 people remained without power, but Northern Powergrid said most people would have their supply restored by the end of the day.
In a statement, Northern Powergrid said: "Two of the key lessons we learned from Storm Arwen were the need to make our website more resilient to keep the power cut logger up during periods of high demand and to do a better job in relation to how we provided estimated times of restoration when we still didn’t know the extent of the damage to our network.
"Accordingly, we implemented two changes that we have been able to use to provide a better service in this event. Firstly, we switched on the website queuing system before the storm hit.
"As a result, our website remained stable right through the peak of the event and our customers were able to log power cuts at all times.
"Secondly, we disabled the automatic text message updates early in the storm to avoid sending the automatically generated estimates that serve us well in business as usual but not during storms.
"We understand everybody wants to know when they are going to be reconnected, but the reality is there is a lot to do and the work involved is often not fully known until our teams get on site."
The company said it is also working with local resilience partners to support customers most affected, including in Kielder, Northumberland, where hot meals are being distributed to nearby residents.
It was confirmed that for any domestic customer still off supply at 8am on January 30 Northern Powergrid would pay reasonable costs for food up to £15 per person per meal.
Anybody not reconnected by 2pm would have the cost of alternative accommodation covered.
Northern Powergrid Director, Paul Glendinning, said: “We have successfully restored supplies to more than 60,000 customers but given the amount of work that there is to do and the fact that we are expecting more high winds during Sunday afternoon, we think that it is likely that a relatively small proportion of our customers will remain without power beyond Sunday night."
The level of damage is reportedly not as severe as seen during Storm Arwen, making repair work "less extensive."
Andy Bilclough, Director of Field Operations, said: “Our team put in another fantastic performance yesterday in extremely challenging circumstances.
"We still have a lot to do but we have a large team out there now in what are currently perfect conditions for the kind of work we do. Storm Corrie is a concern but we’re going to get as much done as we can today for as long as it is safe to do so."
While Storm Malik has now passed, Storm Corrie is now on the way, with a Met Office weather warning for wind in place from 3pm.
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